Clinical Mastitis in Dairy Cows: Studies of Bacterial Ecology and Somatic Cell Count Patterns by Martin Jeremy Green BVSc DCHP MRCVS A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Veterinary Epidemiology University of Warwick, Department of Biological Sciences, October 2003 2 Table of Contents List of Tables ......................................................................................................................6 List of Figures.....................................................................................................................9 Acknowledgements...........................................................................................................14 Declaration .......................................................................................................................14 Dedication........................................................................................................................15 Thesis Summary…...........................................................................................................16 Abbreviations ...................................................................................................................17 Chapter 1: General Introduction.....................................................................................18 1.1. MASTITIS IN DAIRY COWS ........................................................................................................18 1.1.1. Aetiology and historical perspective of mastitis................................................................18 1.1.2. The importance of mastitis...............................................................................................20 1.2. THE DRY PERIOD AND CLINICAL MASTITIS ..............................................................................20 1.2.1. Dry Period: Aims of the thesis .........................................................................................21 1.3. SOMATIC CELLS IN MILK ..........................................................................................................21 1.3.1. Somatic cell counts and clinical mastitis: Aims of the thesis. ............................................22 1.3.2. Patterns of somatic cells during lactation.........................................................................23 1.3.3. Lactation patterns of somatic cell counts and clinical mastitis: Aims of the thesis. ............24 1.4. STATISTICAL BACKGROUND ....................................................................................................24 1.4.1. Generalised linear mixed models .....................................................................................24 1.4.2. Estimating model parameters...........................................................................................24 1.4.2.1. Maximum likelihood (ML)......................................................................................................24 1.4.2.2. Alternatives to maximum likelihood for generalised linear mixed models .................................25 1.4.2.3. Markov Chain Monte Carlo for parameter estimation...............................................................26 1.4.3. Statistical methods implemented throughout the thesis .....................................................27 1.4.3.1. Generalised linear mixed models.............................................................................................27 1.4.3.2. Modelling strategies for generalised linear mixed models.........................................................28 1.4.3.3. GLMM assessment of fit.........................................................................................................31 1.4.3.4. Other statistical methods used .................................................................................................33 Chapter 2: Influence of Dry Period Bacterial Intramammary Isolates on Clinical Mastitis ..............................................................................................36 3 2.1. CHAPTER SUMMARY ................................................................................................................36 2.2. AIM .......................................................................................................................................37 2.3. MATERIALS AND METHODS ......................................................................................................37 2.3.1. Definition of terms for analysis........................................................................................38 2.3.2. Data recording and analysis............................................................................................39 2.4. RESULTS ................................................................................................................................42 2.4.1. Univariable analysis of potential confounders for the risk of clinical mastitis ...................44 2.4.2. Univariable analysis of clinical mastitis and bacteria isolated in screening samples.........45 2.4.3. Modelling bacterial isolations and clinical mastitis..........................................................46 2.4.4. Model fit..........................................................................................................................49 2.4.5. Survival curves of clinical mastitis...................................................................................53 2.5. DISCUSSION ............................................................................................................................55 Chapter 3: Bacterial isolates in the dry bovine mammary gland: Prevalence and Associations..............................................................................................59 3.1. CHAPTER SUMMARY ................................................................................................................59 3.2. INTRODUCTION.......................................................................................................................60 3.3. MATERIALS AND METHODS .....................................................................................................60 3.3.1. Definition of Terms for Analysis.......................................................................................60 3.3.2. Data recording and analysis............................................................................................60 3.3.3. Patterns of bacterial isolates ...........................................................................................61 3.3.4. Generalised linear mixed models of intramammary bacterial isolates...............................62 3.4. RESULTS ................................................................................................................................64 3.4.1. Numbers of cows and quarters.........................................................................................64 3.4.2. Influence of sample collection..........................................................................................64 3.4.3. Description of bacterial isolates ......................................................................................64 3.4.4. Patterns of bacterial isolates in the LDC period...............................................................70 3.4.5. Associations between bacterial species ............................................................................73 3.5. DISCUSSION ............................................................................................................................80 Chapter 4: Somatic Cell Concentrations in Milk Protect and Predict Clinical Mastitis............................................................................................................83 4.1. CHAPTER SUMMARY ................................................................................................................83 4.2. AIMS......................................................................................................................................84 4.3. MATERIALS AND METHODS ......................................................................................................84 4.3.1. Herd selection .................................................................................................................84 4.3.2. Milk samples and clinical mastitis....................................................................................84 4.3.3. Data analysis ..................................................................................................................85 4.3.4. Model 4.1 – Conditional logistic regression analysis........................................................85 4.3.5. Model 4.2 - Analysis of quarters in all cows .....................................................................87 4.4. RESULTS ................................................................................................................................88 4.4.1. Model 4.1: Conditional logistic analysis ..........................................................................92 4 4.4.2. Model 4.2: Analysis of quarters in all cows......................................................................94 4.5. DISCUSSION ............................................................................................................................98 Chapter 5: Variance components of quarter somatic cell counts in three commercial dairy herds ................................................................................101 5.1. CHAPTER SUMMARY ..............................................................................................................101 5.2. INTRODUCTION.....................................................................................................................101 5.3. THE DATA .............................................................................................................................102 5.4. VARIANCE COMPONENTS OF QSCC: DESCRIPTIVE AND UNIVARIABLE ANALYSIS......................102 5.4.1. Denominators................................................................................................................102 5.4.2. Raw data.......................................................................................................................103 5.4.3. Univariable analysis QSCC...........................................................................................105 5.5. VARIANCE COMPONENTS OF QSCC: MULTIVARIATE ANALYSIS...............................................110 5.5.1. Model 5.1 - Log QSCC as a normally distributed response variable ...............................110 5.5.2. Model 5.1 - Results........................................................................................................112 5.5.3. Model 5.1. - Graphic representations.............................................................................114 5.5.4. Model 5.1 - Goodness of fit............................................................................................116 5.5.5. Model 5.2 - Generalised linear mixed model of log QSCC in quarters that did not exceeded 100,000 cells / ml....................................................................................................................118 5.5.6. Model 5.2 goodness of fit...............................................................................................121 5.6. ANALYSIS OF MONTHLY CHANGES IN QUARTER SOMATIC CELL COUNT BETWEEN CATEGORIES..122 5.6.1. QSCC transition matrix .................................................................................................122 5.6.2. Categories of QSCC in different lactation months. ........................................................125 5.6.3. Model 5.3 – Generalised linear mixed model of QSCC transitions between categories....127 5.7. DISCUSSION ..........................................................................................................................130 5.7.1. Month of Lactation........................................................................................................131 5.7.2. Parity...........................................................................................................................131 5.7.3. Time of year ..................................................................................................................132 5.7.4. Quarter position............................................................................................................132 5.7.5. Clinical mastitis affecting QSCC....................................................................................133 5.7.6. Variation in hierarchical levels......................................................................................133 5.7.7. QSCC in categories.......................................................................................................134 Chapter 6: Somatic Cell Count Distributions during Lactation Predict Clinical Mastitis. .........................................................................................................136 6.1. CHAPTER SUMMARY ..............................................................................................................136 6.2. AIMS....................................................................................................................................137 6.3. MATERIALS AND METHODS ....................................................................................................137 6.3.1. Data-Set One.................................................................................................................137 6.3.2. Data-Set Two. ...............................................................................................................137 6.3.3. Data-Set Three ..............................................................................................................137 6.3.4. Analysis........................................................................................................................138 5 6.3.5. Modelling strategy.........................................................................................................138 6.4. RESULTS ...............................................................................................................................139 6.4.1. Description of SCC distributions in lactations with and without clinical mastitis ............140 6.4.2. Models of all Clinical Mastitis.......................................................................................143 6.4.3. Models of Pathogen-Specific Clinical Mastitis ...............................................................147 6.5. DISCUSSION ..........................................................................................................................153 Chapter 7 General Discussion and Conclusions...........................................................156 7.1. DISCUSSION ..........................................................................................................................156 7.1.1. Clinical mastitis ............................................................................................................156 7.1.2. Statistical methods.........................................................................................................158 7.2. CONCLUSIONS .......................................................................................................................165 7.2.1. Chapter Two .................................................................................................................165 7.2.2. Chapter Three ...............................................................................................................165 7.2.3. Chapter Four ................................................................................................................165 7.2.4. Chapter Five .................................................................................................................166 7.2.5. Chapter Six ...................................................................................................................166 7.2.6. Statistical approaches....................................................................................................167 References and Bibliography .........................................................................................168 Appendices: WinBUGS model codes and kernal densities. ..........................................179 APPENDIX 1: EXAMPLE OF THE WINBUGS CODE AND KERNAL DENSITY PLOTS FOR SURVIVAL MODELS IN CHAPTER THREE, BASED ON THE E. COLI MODEL 3.1. ..................................................179 APPENDIX 2: EXAMPLE OF THE WINBUGS CODE AND KERNAL DENSITY PLOTS FOR GENERALISED LINEAR MIXED MODELS IN CHAPTER 3 (BASED ON THE STREPTOCOCCUS UBERIS MODEL 3.5)..........182 APPENDIX 3: GRAPHS OF DELTA-BETAS FOR THE SEVEN EXPLANATORY COVARIATES IN CONDITIONAL LOGISTIC REGRESSION MODEL 4.1, CHAPTER 4..............................................................................185 APPENDIX 4: WINBUGS CODE AND PARAMETER KERNAL DENSITIES FOR GLMM MODEL 4.2, CHAPTER 4. ................................................................................................................................186 APPENDIX 5: WINBUGS CODE AND PARAMETER KERNAL DENSITIES FOR MODEL 5.1, CHAPTER FIVE.189 APPENDIX 6: WINBUGS CODE AND PARAMETER KERNAL DENSITIES FOR MODEL 5.3, CHAPTER FIVE.193 APPENDIX 7: AN EXAMPLE OF THE WINBUGS CODE AND PARAMETER KERNAL DENSITIES FOR THE GLMMS CONSTRUCTED IN CHAPTER SIX, BASED ON THE MODEL 6.3 .............................................196 6 List of Tables Table 2.1. Herd distribution of quarters, cows and clinical mastitis used for modelling clinical mastitis.................................................................................42 Table 2.2. Bacterial species isolated from cases of clinical mastitis.....................................43 Table 2.3. Prevalence of major bacterial isolates during the dry period in the 954 quarters used for statistical models of clinical mastitis. ......................................44 Table 2.4. Logistic binomial regression model with random effects for distinguishable data - Model 2.1........................................................................47 Table 2.5. Logistic binomial regression model with random effects for distinguishable data - Model 2.2........................................................................48 Table 2.6. The proportion of quarters from which coagulase positive staphylococci, Strep. uberis and Strep. dysgalactiae were isolated at least twice in the LDC period that subsequently got clinical mastitis caused by the respective pathogen...........................................................................................49 Table 3.1. Prevalence and culture concentrations (x 102 / ml) of gram-positive major pathogens isolated at each sample time..............................................................66 Table 3.2. Prevalence and culture concentrations (x 102 / ml) of gram-negative major pathogens isolated at each sample time....................................................67 Table 3.3. Prevalence and culture concentrations (x 102 / ml) of minor pathogens isolated at each sample time. .............................................................................68 Table 3.4. Quarters (n = 954) from which a bacterial species was isolated in the late dry –calving (LDC) period, but not at drying off. ..............................................68 Table 3.5. Quarters sampled at each point in the LDC period (n = 957) from which a bacterial species was isolated on one, two or three occasions. .........................69 Table 3.6. Models 3.1, 3.2 and 3.3: Cox Proportional Hazards models, using Markov Chain Monte Carlo, for survival of quarters (n = 957) to the first 7 isolation of E. coli, Strep. uberis and coagulase positive staphylococci in the LDC period. ................................................................................................72 Table 3.7. Model 3.4: Generalised linear mixed model with Bernoulli response variable being the presence of E. coli at any sample time (n = 236). ..................74 Table 3.8. Model 3.5: Generalised linear mixed model with Bernoulli response variable being the presence of Strep. uberis at any sample time (n =84).............75 Table 3.9. Model 3.6: Generalised linear mixed model with Bernoulli response variable being the presence of coagulase positive staphylococcus at any sample time (n = 83). ........................................................................................76 Table 4.1. Model 4.1: Conditional logistic regression model for clinical mastitis. All cows selected had clinical mastitis, and unaffected quarters were matched with mastitic quarters within cow, at the time of a clinical case............93 Table 4.2. Model 4.2: Bernoulli GLMM of clinical mastitis using MCMC with Gibbs sampling. ................................................................................................95 Table 5.1. The number of cows, quarters and QSCC readings grouped by farm.................102 Table 5.2. The number of QSCC readings obtained from each farm grouped by month of lactation. ..........................................................................................103 Table 5.3. The number of QSCC readings grouped by month of sampling. .......................103 Table 5.4. The number of QSCC readings grouped by parity of cow. ................................103 Table 5.5. Descriptive statistics of QSCC readings grouped by farm. ................................105 Table 5.6. Model 5.1: Generalised linear mixed model incorporating variance components of log QSCC; all readings included. .............................................113 Table 5.7. Model 5.2: Generalised linear mixed model incorporating variance components of log QSCC; readings only included from quarters in which the QSCC did not exceed 100,000 cells / ml..........................................120 Table 5.8. Transition matrices of quarter somatic cell count movements between categories during lactation...............................................................................123 8 Table 5.9. Model 5.3: Generalised linear mixed model of movements of quarters into the lowest risk QSCC category for clinical mastitis in the next month (41-100,000 cells / ml). ........................................................................129 Table 6.1. Numbers in the table describe the antilog of the mean log transformed SCC parameters. .............................................................................................141 Table 6.2. Log SCC distributions between lactations with and without clinical mastitis. ..........................................................................................................141 Table 6.3. Log SCC distributions in lactations with and without clinical mastitis caused by specific pathogens (data-set three)...................................................142 Table 6.4. Generalised linear mixed models for all clinical mastitis in data-sets one, two and three. .................................................................................................143 Table 6.5. Generalised linear mixed models of SCC distributional characteristics for Staph. aureus , Strep. dysgalactiae and Strep. uberis clinical mastitis in data-set three...................................................................................................148 Table 6.6 Generalised linear mixed models of SCC distributional characteristics for Escherichia coli, and no growth clinical mastitis in data-set three....................149 9 List of Figures Figure 1.1. An example of poor mixing of Markov Chains taken from the random effect variance in Model 3.3, Chapter Three. .....................................................31 Figure 1.2. An example of Pearson residuals plotted against fitted values from a Bernoulli generalised linear mixed model..........................................................32 Figure 1.3. Mean of aggregated Pearson residuals plotted in five groups in order of ascending fitted values, from a Bernoulli generalised linear mixed model................................................................................................................33 Figure 2.1. Pearson residuals for Model 2.1. .......................................................................50 Figure 2.2. Pearson residuals for Model 2.2. .......................................................................51 Figure 2.3. Graphs of fitted values from Model 2.1.............................................................52 Figure 2.4. Survival curves of the proportion of quarters without clinical mastitis over lactation: A comparison of quarters in which the same pathogen was isolated in the screening period and at the time of clinical mastitis, (A) and those in which the same pathogen was not isolated in the screening period, (B).........................................................................................53 Figure 2.5. Survival curves of the proportion of quarters without clinical mastitis over lactation: A comparison of quarters in which a Corynebacterium spp. was isolated in the LDC period without previous isolation of a major pathogen in that period, (A), quarters in which a Corynebacterium spp. was isolated at drying off, (B) and quarters in which a Corynebacterium spp. was not isolated at any time, (C).....................................54 Figure 3.1. Kaplan Meier survival plot, indicating the probability of remaining free from isolation of Strep. uberis (a), E coli (b) and coagulase positive staphylococci (c) during the late dry - calving period.........................................70 Figure 3.2. Diagramatic representation of the interactions between different bacterial species, identified from Generalised linear Mixed Models 3.4, 3.5 and 3.6. .......................................................................................................77 10 Figure 3.3. Pearson residual plots for generalised linear Models 3.4, 3.5 and 3.6.................78 Figure 4.1. A graph of the occurrence of clinical mastitis during lactation in quarters used for models of QSCC (n =122). ..................................................................89 Figure 4.2. Histograms a, b, c and d illustrate univariable analysis of the proportion of quarters with clinical mastitis in different categories of QSCC: .....................90 Figure 4.3. Graphs of Pearson Residulas for Model 4.1: a. Pearson residuals plotted against fitted values, and b. Aggregates of Pearson residuals in ascending quintiles plotted against fitted values.................................................93 Figure 4.4. Summary of the relationship between quarter somatic cell count and the risk of clinical mastitis, over a three month period, calculated from Model 4.2.. .......................................................................................................96 Figure 4.5. Graphs of Pearson Residulas for Model 4.2: a. Pearson residuals plotted against fitted values, and b. Aggregates of Pearson residuals in ascending quintiles plotted against fitted values.................................................97 Figure 4.6. Schematic representation of the hypothesis: Reduced quarter somatic cell count (QSCC) is causally related to increased risk of acquiring an infection. Increased QSCC is indicative of a current infection. The combination of these two processes results in the risk of clinical infection being lowest for intermediate levels of QSCC...................................100 Figure 5.1. Scatter plot of log10 QSCC (cells / ml) against days in milk illustrating the raw data (n = 12637). ................................................................................104 Figure 5.2. Histogram illustrating the distribution of the log QSCC data (n = 12696) around the mean (set at zero)..........................................................................104 Figure 5.3. Mean, and one standard deviation (depicted with a continuous line) of log10 QSCC (cells / ml) for each farm (n = 12696)...........................................106 Figure 5.4. Mean, and one standard deviation (depicted with a continuous line) of log10 QSCC (cells / ml) for each month of lactation (n = 12637)......................106 Figure 5.5. Mean, and standard deviation (depicted with a continuous line), log10 QSCC (cells / ml) for cows of different calving months (n = 12696)................107 11 Figure 5.6. Mean, and standard deviation (depicted with a continuous line), log10 QSCC (cells / ml) for cows of different parity (n = 12696). .............................107 Figure 5.7. Mean, and standard deviation (depicted with a continuous line), log10 QSCC (cells / ml) during the different months of sampling (n = 12696)...........108 Figure 5.8. Mean and standard deviation (depicted with a continuous line), log10 QSCC (cells / ml) for different quarter positions: (Left fore n = 3168, Right fore n =3178, Left hind n = 3173, Right hind n = 3177). ........................108 Figure 5.9. Mean and standard deviation (depicted with a continuous line), log10 QSCC (cells / ml) in milk samples taken within 30 days before clinical mastitis (n = 122), within 30 days after clinical mastitis (n = 145) and in other milk samples. .........................................................................................109 Figure 5.10. Mean and standard deviation (depicted with a continuous line), log10 QSCC (cells / ml) in all milk samples from 166 quarters with clinical mastitis during the sampling period (n QSCC = 1210), and samples from unaffected quarters (n = 11486)…...................................................................109 Figure 5.11. Geometric mean log QSCC during lactation in quarters from cows of different parities, (Model 5.1)..........................................................................114 Figure 5.12. Geometric mean log QSCC in quarters from cows of different parities, with and without clinical mastitis during the study period, (Model 5.1)............115 Figure 5.13. Geometric mean log QSCC in quarters up to 30 days before or up to 30 days after clinical mastitis, compared with other QSCC readings, (Model 5.1). ................................................................................................................115 Figure 5.14. Bar chart of level one standardised residuals from Model 5.1 in descending (positive residuals) or ascending (negative residuals) order of magnitude...................................................................................................116 Figure 5.15. Bar chart of level two (between quarter) standardised Bayesian residuals from Model 5.1 in descending (positive residuals) or ascending (negative residuals) order of magnitude. ..........................................................117 12 Figure 5.16. Bar chart of level three (between cow) standardised Bayesian residuals from Model 5.1 in descending (positive residuals) or ascending (negative residuals) order of magnitude. ..........................................................117 Figure 5.17. Geometric mean log QSCC during lactation in quarters from cows of different parities, calculated from Model 5.2. ..................................................119 Figure 5.18. Bar chart of level one standardised residuals from Model 5.2 in descending (positive residuals) or ascending (negative residuals) order of magnitude...................................................................................................121 Figure 5.19. Bar chart of level two (quarter) standardised Bayesian residuals from Model 5.2 in descending (positive residuals) or ascending (negative residuals) order of magnitude. .........................................................................121 Figure 5.20. Bar chart of level three (cow) standardised Bayesian residuals from Model 5.2 in descending (positive residuals) or ascending (negative residuals) order of magnitude. .........................................................................122 Figure 5.21. Illustration of movements of quarters between somatic cell count categories at consecutive monthly recordings. .................................................124 Figure 5.22. Illustration of movements of quarters between QSCC categories at different risk of clinical mastitis in the next month. .........................................125 Figure 5.23 Proportion of QSCC in nine categories (000’s cells/ml) during the first ten months of lactation (n = 11381).................................................................126 Figure 5.24 Proportion of QSCC in four categories (000’s cells/ml) during the first ten months of lactation....................................................................................126 Figure 5.25. Graphs of Pearson Residuals for Model 5.3: a. Pearson residuals plotted against fitted values, and b. Aggregates of Pearson residuals in ten equal groups in order of ascending fitted value. .........................................130 Figure 6.1. Histogram illustrating the proportional differences in lactation log SCC characteristics (data-set three), between lactations with pathogenspecific causes of clinical mastitis and lactations without clinical mastitis .......143 13 Figure 6.2. Graphs of Pearson residuals for Models 6.1, 6.2 and 6.3: The graphs illustrate Pearson residuals plotted against fitted values, and aggregates of Pearson residuals in ascending groups plotted against fitted values, for each model......................................................................................................145 Figure 6.3. Graphs of Pearson Residuals for Models 6.4 to 6.8: ........................................150 Figure 7.1 Pearson residuals from Model 4.2, Chapter 4: ..................................................160 Figure 7.2. Pearson residuals from Model 4.2, Chapter 4: a. Mean and 95% confidence intervals of the aggregated groups of Pearson residuals, and b. 95% confidence intervals for rolling groups of 3000 Pearson residuals in ascending order of fitted value.....................................................................162 Figure 7.3. Model 4.2, Chapter 4: Observed and expected number of cases in each of ten aggregates of Pearson residuals. ............................................................162 Figure 7.4. Higher level Bayesian residuals from Model 4.2. ............................................164 14 Acknowledgements I would like to thank many people who have contributed in various ways to the completion of this thesis. Dr Graham Medley and Dr Laura Green, thank you for your patience, depth of thought and encouragement in providing my main supervision. Dr Andrew Bradley, I am grateful for sharing collection of the data for Chapters One and Two and for your constant enthusiasm to take a fresh look at bovine mastitis. Professor Paul Burton, sincere thanks for your time and effort in helping with WinBUGS and a variety of statistical issues. Dr Ynte Schukken, thank you for your insight and encouragement at all stages. Dr Edmund Peeler, many thanks for collecting all the quarter somatic cell count data. Drs Yvette de Haas, Herman Barkema and Gerben de Jong, thank you for the use of the large Dutch data set in Chapter Six, and also for your co-operation for the resulting publication. Dr Ginny Hedges and Dr Carsten Poetzch, thank you for collecting and collating data-set two in Chapter Six. Janet and Jim Green, thank you for your interest in my thesis, as well as the proof reading! I am indebted to BBSRC, Leo Animal Health UK, Milk Development Council, Roche Vitamins UK and CR delta (The Netherlands) for financial support and provision of data. I would also like to express my gratitude to all the farmers and herdspersons who have allowed access to their cows and farm information. Declaration All the work in this thesis is my own, is original in nature and has not been presented previously for another degree. The contents of Chapter Two have been published (Green et al., 2002). The contents of Chapter Six are in press (Green et al., 2003a), the contents of Chapter Four have been accepted for publication subject to minor revisions (Green et al., 2003b) and the contents of Chapter Three have been accepted for publication subject to minor revisions (Green et al., 2003c). 15 Dedication I dedicate this work to Laura, Olivia, Nat and Charlotte. Your love and patience for the last three years has made it possible. “To arrive at the simplest truth, as Newton knew and practiced, requires years of contemplation.” Brown, George Spencer “Perhaps the greatest paradox of all is that there are paradoxes in mathematics” Kasner, E. and Newman, J. 16 Summary Patterns of bacterial intramammary isolates and somatic cell counts were studied in dairy cows. A quantitative assessment was made of the relationship between intramammary bacterial isolates during the dry period and clinical mastitis. The probability of a quarter succumbing to clinical mastitis during lactation increased when a number of different bacterial species were cultured during the dry and post-calving period. There was evidence of synergistic and inhibitory associations between different species of bacteria and evidence of differences in the force of infection between farms and in different months of the year. Patterns of quarter and cow somatic cell counts were investigated in relation to clinical mastitis. Quarters with a somatic cell count in the range 41 – 100,000 cells/ml had the lowest risk of clinical mastitis in the following month. Quarters with a somatic cell count greater than 200,000 cells/ml were at the greatest risk of clinical mastitis in the following month. There was a reduced risk of clinical mastitis between one and three months later in quarters with intermediate somatic cell counts (61,000 – 150,000 cells/ml) compared with quarters above or below this level. Quarters with intermediate somatic cell counts were most likely to remain in this range over time, and this may partially explain why quarters were at a reduced risk of clinical mastitis for up to three consecutive months. Investigations of patterns of cow somatic cell count over lactation, identified that increased maximum and standard deviation log SCC, rather than increased geometric mean, were the best indicators of clinical mastitis. Increased maximum log SCC was associated with clinical mastitis caused by all pathogen types. Increased standard deviation log SCC was associated with Staph. aureus, and Strep. uberis clinical mastitis and increased coefficient of variation log SCC was associated with E. coli clinical mastitis. Increased geometric mean lactation SCC was associated with an increased risk of Staphylococcus aureus clinical mastitis but a reduced risk of E. coli clinical mastitis. The use of Markov Chain Monte Carlo analyses provided a useful platform for estimating parameters in hierarchical Bernoulli models. The main advantage was the flexibility allowed in the approach to modelling. The main disadvantage was that the technique was computer intensive and model exploration was extremely slow. A variety of methods were used to explore goodness of fit of multilevel Bernoulli models and these are discussed. 17 Abbreviations List of abbreviations in alphabetical order: CFU Colony forming unit CLR Conditional logistic regression CM Clinical mastitis CSCC Cow Somatic Cell Count E. coli Escherichia coli GLMM Generalised linear mixed model LDC period Late dry to calving period - the period of time from 14 days before calving to 7 days after calving LLS Log likelihood statistic LR Logistic regression MCMC Markov Chain Monte Carlo ML Maximum likelihood MQL Marginal quasi-likelihood PQL Penalised quasi-likelihood PR Pearson residual QSCC Quarter Somatic Cell Count SCC Somatic Cell Count spp. Species Staph. Staphylococcus Strep. Streptococcus 18 Chapter 1: General Introduction 1.1. Mastitis in dairy cows 1.1.1. Aetiology and historical perspective of mastitis Mastitis is defined as an inflammation of the mammary gland. In dairy cattle, mastitis can have an infectious or non-infectious aetiology, although the vast majority of bovine mastitis is of bacterial origin. In the UK, five species of bacteria, Escherichia coli, Streptococcus uberis, Staphylococcus aureus, Streptococcus dysgalactiae and Streptococcus agalactiae, account for around 80% of clinical and sub-clinical cases in which a pathogen is identified (Anon., 2001). Historically, mastitis pathogens have been classified as either ‘contagious’ or ‘environmental’ (Blowey & Edmondson, 1995). The contagious pathogens are considered as organisms adapted to survive within the host, in particular within the mammary gland, and are typically spread from cow to cow at or around the time of milking (Radostits et al., 1994, Blowey and Edmonson, 1995). In contrast, the environmental pathogens are best described as opportunistic invaders of the mammary gland, not especially adapted to survival within the host; typically they enter, multiply, illicit a host immune response and are eliminated. The major contagious pathogens are Staph. aureus , Strep. dysgalactiae and Strep. agalactiae and the major environmental pathogens are the Enterobacteriacae and Strep. uberis. The line between classic contagious and environmental behaviour of mastitis pathogens has become blurred. Persistent infection with both Strep. uberis (Todhunter et al., 1995; Zadoks, 2003) and E. coli (Hill et al.,, 1979; Lam et al., 1996; Dopfer et al., 1999; Bradley & Green, 2001b) has been reported. Studies in the Netherlands have stated that 9.1% (Lam et al., 1996) and 4.8% (Dopfer et al., 1999) of clinical E. coli mastitis recurred in a quarter. A more recent study of clinical mastitis in the UK identified E. coli as being the most common cause of recurrent clinical mastitis, with 20.5% of all cases being recurrent, as confirmed by DNA fingerprinting (Bradley & Green, 2001b). If these ‘environmental’ pathogens can exist in the mammary environment for prolonged periods, it is likely that contagious spread will occur between cows and this has been suggested for Strep. uberis infections (Zadoks, 2003). 19 During the 1960’s rapid progress was made in the control of mastitis when the Five-Point Plan was devised through research at the National Institute for Research in Dairying (NIRD), (Neave et al., 1966; Smith et al., 1967b; Kingwill et al., 1970). Uptake of this plan resulted in progress in control of both clinical and sub-clinical mastitis in the UK. Implementation of EC Milk Hygiene Directive (92/46, 1991) that imposed a European upper limit of 400,000 somatic cells / ml in bulk milk for human consumption, added further impetus to the reduction of sub-clinical mastitis. The initial impact of implementation of the Five-Point Plan, was very successful in controlling the contagious pathogens and led to a large reduction in the incidences of clinical and sub-clinical mastitis and herd bulk milk somatic cell counts (BMSCC). In 1960 the estimated incidence rate of clinical mastitis (IRCM) in Great Britain was 120 cases / 100 cows / year (Wilson & Kingwill, 1975), and in 1983 it was 41 cases / 100 cows / year (Wilesmith et al., 1986). The prevalence of sub-clinical mastitis in the UK has also declined: Herd bulk milk somatic cell counts have reduced from 573,000 cells/ml in 1971 to a current level of approximately 180,000 cells/ml (Booth, 1997; www.mdcdatum.org.uk). Although since 1982 quantitative information on the incidence and aetiology of mastitis in the UK is sparse, recent studies suggest the incidence rate of clinical mastitis remains between 35 and 45 quarter cases / 100 cows / year (Berry, 1998; Kossaibati et al., 1998; Peeler et al., 2002). It therefore appears that in the last 20 years there has been a reduction in somatic cell counts and in contagious pathogens in the UK but little change in the incidence rate of clinical mastitis (Booth, 1997; Green and Bradley, 1998). There has been a shift towards environmental pathogens as the major causes of clinical mastitis (Anon, 2001; Green and Bradley, 1998). One of the mysteries of mastitis is that while many herds have been able to make managemental changes to reduce the amount of contagious mastitis and therefore BMSCC, there has been no parallel reduction of environmental infections. Research suggests that apparently well managed herds that maintain low somatic cell counts (SCC), find it difficult to control environmental mastitis (Hogan et al., 1988), and may even experience a higher incidence of disease, than high BMSCC herds (Erskine et al., 1988; Miltenburg et al., 1996). It is unclear why herds that are capable of controlling contagious mastitis are less able to reliably prevent environmental mastitis and therefore environmental mastitis continues to be the subject of much scientific investigation. 20 1.1.2. The importance of mastitis Controlling mastitis is important for the UK dairy industry because the condition has significant ramifications. These include financial losses to dairy farmers, adverse effects on cow welfare and potential influences on public health. Financial loss from clinical mastitis arises from the costs of treatment, culling, death, decreased milk production and decreased milk value. A single case of clinical mastitis is associated with average losses of around Ł175 (Kossaibati, 2000), and clinical mastitis on an average dairy unit accounts for approximately 38% of the total direct costs of the common production diseases (Kossaibati & Esslemont, 1997). Clinical mastitis alone has been estimated to cost the UK dairy industry in excess of Ł168 million per annum (Bradley, 2002). It is more difficult to quantify the losses associated with sub-clinical mastitis, because these are more variable, but losses arise from treatment costs, reduced milk yield, decreased constituent quality, loss of payment bonuses and an increase in the risk of culling. Mastitis is a painful condition, and therefore adversely affects cow welfare. The welfare implications of mastitis have been detailed in the UK Farm Animal Welfare Council Report, titled ‘Welfare of Dairy Cattle’ (FAWC, 1997), and since there are approximately 40 cases / 100 cows / year in the UK, this is a major concern. Similarly, the potential significance of bovine mastitis in relation to public health should not be disregarded. The broad use of antibiotics in the treatment and control of mastitis has possible implications for human health through an increased risk of antibiotic resistant strains of bacteria emerging that may enter the food chain (White and McDermott, 2001). The potential spread of zoonotic organisms via milk could also occur through the marketing of unpasteurised dairy products, through pasteurisation failure, or by organisms resistant to current pasteurisation processes. Clinical mastitis on UK dairy farms therefore remains a major problem and provides the theme for this thesis. The research has concentrated on two particular areas related to clinical mastitis; the dry period and patterns of somatic cell counts. 1.2. The Dry Period and Clinical Mastitis The importance of the dry (non-lactating) period in the dynamics of intramammary infections in dairy cattle has been studied over many decades (Neave et al., 1950; Oliver et al., 1962; Oliver and Michell, 1983; Smith et al., 1985; Oliver, 1988; Todhunter et al., 1991). In one Ohio dairy herd, approximately 60% of all new intramammary infections during the production cycle were reported to occur during the dry period (Todhunter et al., 1991). Mammary glands that are infected during the dry period produce less milk (Smith et al., 1968) and produce milk of poor composition (Oliver, 1988, Oliver and Sordillo, 1988). 21 From previous dry period field studies, however, it is difficult to quantitatively assess the impact of dry period bacterial infections on clinical mastitis. Whilst not all new dry period isolates persist through to lactation (Oliver, 1988), there is evidence that some infections present in the dry period will result in clinical disease in lactation (Neave et al., 1950; Bramley, 1976; McDonald and Anderson; 1981). This has been confirmed in the UK with DNA fingerprinting of some Enterobacterial strains (Bradley and Green, 2000). A greater understanding of the associations between dry period bacterial infections and clinical mastitis in the next lactation may assist with the prevention of clinical mastitis. Such associations can only be estimated accurately if correlations within the data are accounted for: Quarters being clustered within cows and cows within herds (Goldstein, 1995). Without allowing for correlations, erroneous conclusions may be drawn (McDermott and Schukken, 1994, Schukken et al., 2003), and this has been omitted from earlier analysis of dry period research data. Research into dry period bacterial infections in the UK is sparse; surveys that include bacterial isolates from samples taken during the dry period have not been carried out on commercial UK farms for several decades. 1.2.1. Dry Period: Aims of this thesis The aim of Chapter Two of this thesis was to quantitatively investigate relationships between dry period bacterial isolates and subsequent clinical mastitis. In Chapter Three, further investigations were made of patterns and associations of different bacterial species during the dry period. 1.3. Somatic cells in milk The presence of cells in bovine milk has been recognised and studied for many years and they are commonly known as ‘somatic cells’. More than 95% of somatic cells in milk are leukocytes including neutrophils, macrophages and lymphocytes (Lee et al., 1980; Sordillo et al., 1997). The somatic cell count is therefore a useful proxy for the concentration of leukocytes in milk. Whilst macrophages are considered to be the dominant cell type in the healthy gland, neutrophils are the predominant cell type found in milk and mammary tissue following bacterial invasion (Sordillo et al., 1997). Changes in milk lymphocyte populations have been reported following bacterial infection (Park et al., 1993; Taylor et al., 1997; Soltys and Quinn, 1999), although the exact roles of different lymphocyte subsets have yet to be fully defined. Somatic cell concentrations in milk are commonly used as indicators of mammary health on the basis that they reflect an immune response and therefore the presence of infection. An SCC < 100,000 cells/ml is reported to be ‘normal’ in a healthy mammary 22 gland (quarter) (Sordillo et al., 1997) whereas an SCC > 200,000 cells/ml is suggestive of bacterial infection (Brolund, 1985; Schepers et al., 1997). Although raised SCC is an accepted indicator of bacterial infection, there is controversy over whether a low somatic cell count can result in increased susceptibility to mastitis. This has been of particular interest in the UK since associations were reported between low herd bulk milk somatic cell counts and an increased risk of toxic mastitis (Green et al., 1996; Tadich et al., 1998). Numerous studies have been carried out into the relationship between cow level SCC (measured in milk pooled from all four quarters), and naturally occurring bovine mastitis (Coffey et al., 1986; Deluyker et al., 1993; Beaudeau et al., 1998, Rupp and Boichard, 2000; Suriyasathaporn et al., 2000; Beaudeau et al., 2002). Results are variable, and difficult to interpret because these associations are between clinical mastitis in a single quarter and the average SCC in milk pooled from all four quarters, most of which will be unaffected. Studies on individual quarters are more useful to assess the precise relationship between somatic cell concentration and clinical mastitis. Experimental bacterial challenge studies have been carried out with individual quarters (Shuster et al., 1996; Schukken et al., 1999; van Werven, 1999). These all report that a low quarter SCC (QSCC) is associated with increased risk or severity of mastitis. Such findings need to be tested with naturally occurring infections. Two investigations have been carried out examining individual quarters under field conditions. An investigation of three UK dairy herds identified that QSCC in the range 1,000 - 5,000 cells/ml were at approximately twice the risk of clinical E coli mastitis in the next month, compared with quarters 6,000 - 200,000 cells/ml (Peeler et al., 2003). However, another field study in three Dutch dairy herds, reported that low QSCC were not a risk for clinical mastitis in the next month, caused by Strep. uberis or Staph. aureus (Zadoks et al., 2001). To date, no research has examined QSCC for more than one month before clinical mastitis. This may be important to capture the true pre-infection conditions within the mammary gland. Similarly, no studies have compared the SCC between affected and unaffected quarters of cows with clinical mastitis. This could be of particular value because it would inherently control for differences between cows (such as parity and stage of lactation) whilst comparing quarter SCC. 1.3.1. Somatic cell counts and clinical mastitis: Aims of this thesis. The aim of Chapter Four of this thesis was to investigate whether the level of QSCC influenced the risk of naturally occurring clinical mastitis over a subsequent four month 23 period. Investigations were also carried out into patterns and variance components of quarter somatic cell counts and these are presented in Chapter Five. 1.3.2. Patterns of somatic cells during lactation. Genetic evaluation programs for mastitis are used throughout the world with the intention that bulls with resistance to mastitis can be identified for breeding purposes. The traits used to calculate genetic indices for mastitis differ slightly between countries (Mark et al., 2002). Denmark, Sweden and Finland use cow clinical mastitis records and SCC data, whereas other countries, including France, The Netherlands, The United Kingdom and The United States use cow SCC (CSCC) information alone. Genetic evaluations using CSCC are based on logged test-day CSCC records or the mean of logged test-day records during lactation. Somatic cell counts are therefore used widely in genetic programs as an indicator of clinical and sub-clinical intramammary infection. The correlation between lactation mean CSCC and clinical mastitis has been reported to be positive and linear (Philipsson et al., 1995). Estimates of this correlation vary and have been estimated at 0.3 (Weller et al., 1992), 0.6 (Emanuelson et al., 1988) and 0.79 (Philipsson et al., 1995). The correlation between somatic cell production deviance (a measure of the mean difference in somatic cell production from an expected uninfected cow, corrected for stage of lactation) and clinical mastitis has been reported to be 0.80 (Lund et al., 1999). One of the potential shortcomings of breeding for clinical mastitis resistance using SCC was pointed out by Shook (1993). Since most cell counting programs observe SCC at approximately monthly intervals, acute, short lasting infections may be difficult to identify from increased mean SCC during lactation. It is also apparent that different mastitis pathogens elicit different SCC responses (de Haas et al., 2002) and in particular that clinical mastitis associated with ‘environmental’ organisms, such as E. coli may result in a high SCC for a short period of time (van Werven, 1999; de Haas et al., 2002). It may be possible to improve the prediction of clinical mastitis from SCC by using characteristics of SCC distributions, other than the lactation mean. For example, a method was recently described which assessed the effect of pathogen-specific clinical mastitis on the lactation curve for SCC (de Haas et al., 2002). Improving the prediction of clinical mastitis from SCC patterns would therefore be useful because it could be incorporated into genetic evaluation programs to refine the selection of resistant bulls. 24 1.3.3. Lactation patterns of somatic cell counts and clinical mastitis: Aims of this thesis. In Chapter Six, characteristics of SCC distributions during lactation were investigated in three different data-sets, with the purpose of identifying features most closely associated with clinical mastitis. This was carried out for clinical mastitis as a whole and also for pathogen-specific causes of clinical mastitis. 1.4. Statistical Background 1.4.1. Generalised linear mixed models An important problem that commonly arises in field-based veterinary research data is that the base units being considered (in this case, measurements made sequentially from quarter milk samples) are often not independent of each other (i.e. measurements from one quarter are more likely to be similar than measurements from two different quarters). Many simple statistical techniques rely on the assumption that these base units are independent, but when this is not the case, it is necessary to use methods that account for the lack of independence. Many statistical methods applied throughout this thesis have been based on generalised linear mixed models (GLMM). Variation that arises from correlations within the data is modelled, and the lack of independence of data points is accounted for (Snijders and Bosker, 1999). Throughout this research, the clustering of data was hierarchical in nature; that is level one units were nested within level two, level two within level three, and so on. Statistical models used in this case are often termed “hierarchical” or “multilevel” GLMM. 1.4.2. Estimating model parameters The parameters in GLMM can be estimated using a variety of methods. Different approaches have been described (Snijders and Bosker, 1999) and these are summarised below. 1.4.2.1. Maximum likelihood (ML) The likelihood (L) is the “probability” of the observed data as a function of the unknown parameters in the model. The maximum likelihood (ML) provides the values of model parameters that maximises the value of L. In logistic regression, for each pair of points (x, y), where y is the binary outcome, the contribution to L is (µi)yi * (1 - µ i )1-yi (1.0) 25 where µ i is the model fitted value of y, given x. Thus, for an outcome y = 1, the contribution to L is µ i and so the nearer the fitted value is to 1, the greater value L. Conversely, for an outcome of y = 0, the contribution to L is (1 - µ i) and so the nearer the fitted value is to 0, the greater value of L. Therefore, for n pairs of (xi, yi); n L = . [(µi)yi (1 - µi)1-yi] (1.1) i =1 L is commonly transformed to –2 * loge[L] and the result is termed the deviance. The ratio in likelihoods (which corresponds to the difference in deviance) can be used to make statistical comparisons between models. 1.4.2.2. Alternatives to maximum likelihood for generalised linear mixed models Most of the GLMM in this research incorporated a binary response and parameter estimation in multilevel Bernoulli models is more complicated than in multilevel Normal models. This is because exact or closed solutions cannot be calculated to give the best estimates for all model parameters. Various approximations to ML are used and these include marginal quasi-likelihood (MQL) (approximation based on the fixed parameters in the model), penalised quasi-likelihood (PQL) (approximation based on the random parameters in the model) and the Laplace approximation. These algorithms are not always stable, leading to problems with convergence (particularly in complex models) and are not always considered to give accurate parameter estimates (Snijders and Bosker, 1999; Rasbash et al., 1999), particularly for three level logistic GLMM (Browne and Draper, 2003). Furthermore, MQL and PQL do not provide an easy method for hypothesis testing since they do not produce a suitable ML or deviance statistic. One alternative to iterative algorithms to make parameter estimates is bootstrapping. This technique uses replicate sets of data to make estimates of the parameters of interest and by including hundreds or thousands of replicates, estimates can be made of the shape and properties of the sample distribution of each parameter. Parametric bootstrapping assumes the distributional characteristics are known and then uses samples generated from that 26 distribution. Non-parametric bootstrapping either generates samples by replacement from the original data or by re-sampling the estimated residuals (Rasbash et al., 1999). 1.4.2.3. Markov Chain Monte Carlo for parameter estimation An alternative approach for estimating parameters in multidimensional models can be achieved by constructing Markov Chains using Monte Carlo Integration (MCMC). An important element of this thesis was constructing and exploring hierarchical GLMM using this technique. A Bayesian context is normally chosen and the joint probability distribution of all model parameters (the ‘joint posterior distribution’) is estimated in this case using MCMC. The posterior distribution is dependent on previous beliefs of the parameter distributions (‘priors’) and the data. Priors can be selected to reflect the previous knowledge or beliefs of parameters, or to be less influential (‘vague’) if there is no appropriate information. A Markov Chain is formed by continually updating parameter estimates until a stable state is reached. If, at iteration t, the parameter . has an estimate .t, then in the next state of the chain, the parameter will be .t+1, and this value is only depends on the previous state (.t), so the chain gradually becomes independent of past values, including initial conditions. A Markov Chain can be updated (that is transferred from .t to .t+1) using a variety of probabilistic processes (Gilks et al 1995). That is the new state, .t+1, can be accepted or rejected according to a probability function. In this thesis, a particular sampling procedure was used for constructing the Markov Chains, namely Gibbs sampling. With this procedure each chain is updated using conditional probability distributions. If the current parameter value of the chain is .t, then a probability distribution is calculated, conditional upon the prior distribution, the current point estimates of all parameters in the model, and the data. A new value is sampled from this conditional distribution and this becomes the next value in the Markov chain, .t+1. With Gibbs sampling, the next parameter value is always accepted. A Markov Chain should converge to a stationary or non-variant state, a process considered in more detail below. The sampling process up to convergence is usually termed ‘burn in’. Models should be specified such that the stationary state of the Markov Chain coincides with the posterior distribution of model parameters that are being estimated. Continued sampling from the joint posterior distribution will allow that distribution to be described, for instance, in terms of the mean, median, mode, standard error and 95% credibility interval (the range within which there is a 95% probability that the true mean value lies). 27 1.4.3. Statistical methods implemented throughout the thesis 1.4.3.1. Generalised linear mixed models Although my original objectives were to address biological hypotheses, an important element of my learning during this thesis has surrounded the use of statistical techniques required to investigate the biological processes. During the course of the research, a variety of techniques were used and these changed as the complexity of mixed models increased. In Chapter Two, a hierarchical Bernoulli model with two levels (i.e. quarters (i) within cows (j)), was used to investigate the risk of clinical mastitis following bacterial infections. A technique for this was applied using ‘Egret’ (Version 2.0.3, Anon, 1999). This application used a scalar adjustment and an overdispersion parameter for the jth cluster, and implemented ML to obtain parameter estimates. Although the technique was useful to control for the correlation structure within the data, it was relatively inflexible and made interpretation of random variation difficult. This application only allowed a two level structure and was therefore not suitable for more complex GLMM. In Chapters Three to Six, more complicated GLMM were constructed and these took the general form: Yijk = a response variable, denoting the observed value in the ith lowest level unit within the jth middle level unit within the kth highest level unit. µijk = a + ß’1ijkX1ijk + ß’2jkX2jk + ß’3kX3k + vk + ujk+ eijk (1.3) where the subscripts i, j and k denote the ith lowest level unit within the jth middle level unit within the kth highest level unit; µijk = the fitted probability of Y for the lowest level units i, within unit j of unit k. a = regression intercept X1ijk = vector of covariates associated with lowest level units i. ß’1ijk = vector of coefficients for X1ijk. X2jk = vector of covariates for units j. ß’2jk = vector of coefficients for X2jk. X3k = vector of covariates for units k. ß’3k = vector of coefficients for X3k. vk = random effect reflecting residual variation between units k. 28 ujk = random effect reflecting residual variation between units j, within units k. eijk = random effect reflecting residual variation between units i within unit j of unit k. For most of the GLMM in this thesis, the response variable had a Bernoulli distribution (Y=1 or Y=0). For example, response variables were: the presence or absence of clinical mastitis in a quarter or the presence or absence of a bacterial isolate. GLMM that fit a Bernoulli response require a transformation (function) of the fitted mean response. The function used throughout this thesis, was the logistic function (Hosmer and Lemeshow, 1989): p(x) = {e (a +ßX) } / {1 + e (a +ßX)} (1.4) where p(x) is the conditional mean of the outcome given the vector of explanatory covariates X, a is a constant and ß the vector of coefficients of X. A transformation of this function, the logit transformation, was carried out to give the conventional logit link function (Hosmer and Lemeshow, 1989) and this was applied in all Bernoulli models during the thesis: Ln { p(x) / ( 1- p(x)) } = a + ßX (1.5) Since much of the data investigated in this thesis had a discrete response variable and a reasonably complex structure with three hierarchical levels, it was decided to use MCMC for parameter estimation (Browne and Draper, 2003). An additional reason for this choice was that previous reports of analysis of the type of data used in this thesis, indicated difficulties with model convergence when likelihood-based methods were employed (Zadoks et al.,, 2001; Peeler et al.,, 2003)). The software used for MCMC was WinBUGS, Version 1.3 (Spiegelhalter et al., 2000). 1.4.3.2. Modelling strategies for generalised linear mixed models Many texts have been written on strategies for statistical modelling and there is no one correct method to suit all circumstances. Most importantly, it is necessary to gain an indepth understanding of the data; the relationships between the response and explanatory / confounding covariates, the correlation structure and the affects of outlying data points. As this research progressed, it was felt that an exploratory approach to model construction best met these requirements. Covariates were screened using univariable statistical tests, such as .2 and Kruskal Wallis tests (Petrie and Watson, 1999), and those with 29 a trend towards an association (p < 0.25), were initially considered for inclusion in subsequent models. Covariates remained in the final model when the 95% credibility interval for a coefficient did not include zero. Each time significant covariates (or interactions) were identified, all other covariates were again offered for inclusion in the model, to examine whether they significantly influenced the outcome, or confounded the relationships between the outcome and explanatory covariates. Biologically plausible interactions were tested between significant covariates to identify correlations between these variables. Although time consuming, this approach to modelling meant that associations within the data were likely to be identified, and final model parameters likely to be robust. Since estimating parameters using MCMC is computer intensive and therefore slow (some models took over 12 hours to complete), much of the initial model exploration was carried out using PQL, with the second order Taylor expansion, in MLwiN. General principles of MCMC and Gibbs sampling were described above (Section 1.4.2.3.). For models in this research, vague prior distributions were specified for the fixed effect parameters (a Normal distribution with mean = 0, and variance = 106)) and for the random effect precisions (a Gamma distribution (shape parameter = 0.001, mean = 0.001)). This meant that the conditional distribution at each step in the Markov Chain was influenced overwhelmingly by the data and the current chain parameter values. It was felt that there was insufficient useful information available to include informative priors, and because data was plentiful, it was deemed preferable to let the data ‘drive’ the Gibbs sampling. This could have been unwise if data were sparse, but this was not the case throughout the research. Starting values for parameters in the Markov Chains were selected to be both close to and more distant from values obtained when models were run using PQL. When different starting values were used, however, final parameter estimates were unchanged in all models, although convergence was sometimes prolonged. Assessing convergence of models using MCMC (i.e. ensuring the chains have reached the joint posterior distribution) can be problematic (Gilks et al., 1995). For this research, visual assessment of chain stability (Gilks et al., 1995) and the Gelman Rubin convergence diagnostic (Brooks and Gelman, 1998) were used. The latter diagnostic is based on a comparison of within-chain and between chain variances, when more than one chain is run for each parameter and in this research, three parallel chains were run for all model parameters. Convergence was accepted when the Gelman Rubin diagnostic approximated to one, (when the chains had forgotten their starting value and their output was indistinguishable). The diagnostic was used for parameters with a Normal posterior distribution. These approaches to convergence do not necessarily prevent the problem of chains becoming ‘stuck’ in a parameter space outside the true posterior distribution. However, 30 the use of three parallel chains, the variation of initial values and the running chains for prolonged periods, will have reduced the likelihood of this problem. Poor mixing of chains (Gilks et al., 1995) is described below. After convergence, Markov Chains were run for between 15,000 and 210,000 iterations to estimate parameters. Chains were run until the Monte Carlo Standard Error (standard deviation of chain values divided by square root of number of values in chain) was < 0.05 for all model parameters. Model parameter distributions were assessed using kernel density plots and models were run until these plots were reasonably smooth. In a few instances, the mixing of Markov Chains (Gilks et al., 1995) was poor for the random effect variances (i.e. chains moved unevenly through the parameter space, see Figure 1.1 below). Four techniques were used to overcome this problem: 1. Markov Chains were run for prolonged periods (106 total iterations) to ensure that parameter estimates did not change. This technique was used in Model 3.3, Chapter Three and Model 4.2, Chapter 4. 2. When random terms were not themselves the focus of interest, the terms were set at either a high value (97.5 % ile of initial model value) or removed from the model altogether, to assess whether the fixed effect parameters were robust to the changes. This technique was used in Model 4.2, Chapter 4. 3. Data augmentation was used to improve mixing: A number (n) replicates of the data were made and incorporated in the model. Final parameter standard deviations of normally distributed parameters were increased by a factor of [n]1/2 to calculate the credibility interval. This technique was used in Model 3.3, Chapter Three and Model 4.2, Chapter Four. 4. Uniform priors were investigated for random effect variances/standard deviations. However, this appeared to have no effect on chain mixing or on model parameter estimates. 31 Figure 1.1. An example of poor mixing of Markov Chains taken from the random effect variance in Model 3.3, Chapter Three. 1.4.3.3. GLMM assessment of fit Generalised linear mixed models that incorporate a continuous, normally distributed response variable, allow us to compare the effects of certain explanatory variables on an outcome. Goodness of fit of these models can be measured from the difference between observed and fitted values (residuals) and there are several aspects to assessing the fit of the GLMM: Evidence of failure of systematic (fixed) part of model (e.g. are linear relationships truly linear?). Inadequacy of standard assumptions on error structure. Influence and leverage of individual or clusters of observations – do some data points greatly affect the biological interpretation of model parameters? Residuals calculated from a GLMM with a normally distributed response variable can be evaluated at each hierarchical level (Snijders and Bosker, 1999). A model of good fit may have normally distributed residuals with a mean of zero at each level (Snijders and Bosker, 1999, Rasbash et al., 1999). Bayesian residuals from a three level hierarchical GLMM with a normally distributed response variable, were examined in Chapter Five, and the presence of outlying units at each level investigated. One area in which binary response GLMM are quite different to GLMM with a Normal response variable is the residual error structure. Residuals in the Bernoulli model are constrained because the outcome is always 1 or 0. Therefore, for a fitted value µ, the residual will be either (1 - µ) and be a positive value, or (0 - µ) and be negative. Methods of assessing fit of multilevel Bernoulli models are not fully resolved. During this thesis, investigations of model fit have been based on distributions of Pearson residuals (PR); binomial residuals main[13] chains 3:1 iteration 900 850 800 750 0.0 5.0 10.0 15.0 20.0 32 standardised by dividing each residual by its standard deviation (McCullagh and Nelder, 1989): Pearson residual = (Y - µ) / {(µ * (1 - µ)}1/2 (1.6) Where Y is the response variable (Y= 1 or Y=0) and µ is the model fitted value. Pearson residuals are therefore a function of fitted values, and the graphical plot of PR against fitted value (µ), has a characteristic shape, as shown below, in Figure 1.2: Figure 1.2. An example of Pearson residuals plotted against fitted values from a Bernoulli generalised linear mixed model. In a Bernoulli model with good fit, outcomes, Y = 1, should generally have higher fitted values than outcomes Y = 0, and therefore be positioned further to the right along the X- axis. For example, a data point with a fitted value of 0.1 indicates that there is a 1 in 10 probability of having a positive outcome (Y = 1). Therefore, a model of good fit should fit approximately ten Y = 0 for each Y = 1. Similarly, a fitted value of 0.5 should have approximately equal numbers of outcomes Y = 1 as Y = 0. Therefore, the ratio of positive to negative PR at different fitted values can be evaluated. In this research, this was done by aggregating the residuals into five or ten equally sized groups (in order of ascending fitted value) and calculating the means of these aggregates -4 -2 0 2 4 6 8 10 12 14 16 0 0.2 0.4 0.6 0.8 1 Fitted value Pearson residual 33 (see Figure 1.3, below). If the ratio of Y = 1: Y = 0 was approximately correct across all fitted values, the mean of these aggregates should approximate to zero (Hosmer and Lemeshow, 1989). When this was not the case, data points within these aggregates were investigated for their influence / leverage in the model and to examine whether they were associated with any particular covariates, covariate patterns or higher level units. Methods of assessing PR and model fit are discussed further in Chapter Seven. Figure 1.3. Mean of aggregated Pearson residuals plotted in five groups in order of ascending fitted values, from a Bernoulli generalised linear mixed model. 1.4.3.4. Other statistical methods used a. Conditional logistic regression (CLR) Conventional conditional logistic regression (Hosmer and Lemeshow, 1989) was used during this research to analyse matched data. CLR used conditional ML estimation as the basis for parameter estimation. This method included the matched group as a ‘level’ (stratum) and each group was given a dummy variable, = 1, for members of that group, otherwise = 0. Therefore, for n number matched sets, there were n-1 dummy variables (the first group used as the reference group). The models then took the form (Hosmer and Lemeshow, 1989): Logit (p(µi)) = a0 + ß’x Xi + ß’DDi + ß’CCi + ß’IIi (1.7) where -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4 5 Five aggregated groups in order of ascending fitted value Mean Pearson residual 34 p(µ) = probability of an outcome p given variable value x a 0 = constant X = vector of explanatory covariates D = vector of dummy variables relating to the matched groups C = vector of confounding covariates I = vector of interaction terms ß’ = coefficients of covariates X, D, C, I respectively CLR is used when the number of parameters in a model is large relative to the number of measurements per subject. The likelihood used in unconditional LR describes the joint probability of the data as the product of the joint probability of the cases (y = 1) and the joint probability of the controls. The conditional likelihood reflects the probability of the observed data relative to all possible combinations of the data (Hosmer and Lemeshow, 1989) and is calculated from the likelihood divided by the sum of the joint probability, for all combinations of explanatory variables. Model fit was assessed using delta-betas (Hosmer and Lemeshow, 1989). b. Survival analysis Kaplan-Meier survival curves (Collett, 1994; Parmer and Machin, 1995) were constructed during the thesis to examine infection patterns over time. The conventional survival function was calculated; S(t) = (1- {d1 / n1}) (1- {d2 / n2})…. (1- {dt / nt}) (1.8) where nt = the number of units at risk at the start of time interval t. dt = the number of units that ‘failed’ during time interval t. S(t) = the probability of a unit not ‘failing’ by time t. Units entered an analysis when first at risk of failure and were censored when no longer at risk. To examine factors that influenced the instantaneous risk (hazard) of ‘failure’, a conventional Cox Proportional Hazards model was specified. The standard model was extended when necessary, to account for random variation by including a frailty term: .ij = .0 * exp(ßx’ + uj) (1.9) where 35 .ij = Hazard function (instantaneous risk of failure in unit i of cluster j) .0 = Baseline Hazard ßx’ = Linear predictor containing a vector of covariates x, with regression coefficients ß. uj = a random variable to account for the correlation between level i units. 36 Chapter 2: Influence of Dry Period Bacterial Intramammary Isolates on Clinical Mastitis 2.1. Chapter summary Milk samples were taken from 1920 quarters (480 cows, six herds) on four occasions to examine the relationship between quarter level intramammary infection during the dry period and clinical mastitis in the next lactation. All quarters were sampled at drying off and within one week of calving and two quarters from each cow were sampled both 0-7 and 8-14 days before calving. Milk samples were collected from all cases of clinical mastitis during the following lactation. Logistic regression models were developed to investigate the associations between intramammary infections present during the sampling period and clinical mastitis. The probability of a quarter succumbing to clinical mastitis increased when Strep. dysgalactiae, Enterococcus faecalis, E. coli, or Enterobacter spp. were cultured at drying off and when E. coli, coagulase positive staphylococcus, Serratia spp. or Enterococcus faecalis were cultured in two out of three late dry and post-calving samples. Quarters from which Corynebacterium spp. were isolated at drying off were at an increased risk of clinical mastitis, whereas the presence of Corynebacterium spp. in the late dry and post-calving samples was associated with a reduction in the risk of clinical mastitis. The risk of mastitis for specific pathogens increased if the same species of bacteria that had caused mastitis was isolated at least twice in the late dry and post-calving samples. Kaplan Meier survival plots indicated that clinical mastitis associated with dry period infections were more likely to occur earlier in lactation than clinical mastitis not associated with dry period infections. There was evidence of quarter susceptibility to intramammary infection or the possibility that infection with one organism led to clinical mastitis with another. The contents of this chapter have been published (Green et al., 2002). 37 2.2. Aim The purpose of this chapter was to examine the relationship of quarter bacterial isolates at drying off and during the late dry - calving period, with clinical mastitis in the same quarter, in the next lactation. 2.3. Materials and methods Six dairy herds were selected on the basis of location (Somerset), and likelihood of owner compliance. The herds were generally well managed with an average milk yield between 6000 and 8000 litres and a three monthly geometric mean bulk milk somatic cell count under 250,000 cells/ml. The calving pattern in all herds was non-seasonal. Dry cows were managed at grass during the summer months and in cubicle or straw yard systems during the housing period. Peri-parturient cows were managed at grass or in loose boxes and lactating cows at grass or in cubicle house systems. All cows that were dried off over a one year period on each farm were recruited to the study. No cows were accepted into the study for a second time (i.e. for a second dry period). Two lacteal secretion samples were collected at each sample time either by the author, or by Dr Andrew Bradley. Samples were taken from all four quarters at ‘drying off’ and 0-7 days after calving. During the dry period, samples were taken from the ipsilateral quarters (left fore and left hind, odd numbered cows or right fore and right hind, even numbered cows), once 0-7 days and once 8-14 days before the anticipated calving date. Two quarters were left unsampled throughout the dry period as ‘controls’, to assess the influence of the sampling procedure on clinical mastitis. Any cow not calving by her ‘expected’ date was sampled every week until parturition. During the subsequent lactation, milk samples were collected from all quarters with clinical mastitis identified by the herdspersons who had been previously trained in identification and sample collection. These samples were frozen and submitted once each week to the laboratory for bacteriological analysis. Teats were thoroughly disinfected, dried and cleaned twice with surgical spirit before being sampled and then disinfected after sampling. Milk samples were stored in a cool box immediately after collection and maintained at or below 4oC. Samples were submitted to an accredited laboratory (Veterinary Laboratories Agency, Langford, Bristol, UK) for bacteriological analysis. Ten microlitres of secretion were inoculated onto sheep blood agar and Edward’s agar and 100 microlitres of secretion were inoculated onto MacConkey agar to enhance the detection of Enterobacteriaceae (Smith et al., 1985). Plates were incubated at 37oC and read 24 and 48 hours later. Bacterial species were identified and quantified using recommended techniques for mastitis pathogens (National Mastitis Council, 1999). Bacteria 38 were tentatively identified by gross colony morphology and gram stain, and further confirmatory tests used as necessary. Each colony that was visually different on a plate was carried forward for further tests. A sample was recorded as ‘contaminated’ when greater than three colony types (three species of bacteria) were cultured. Two milk samples were collected at each sample time and the second sample, having been frozen, was cultured if the first was contaminated. If both milk samples were contaminated, the results were excluded, this occurred in less than 0.5% samples. The number of colony forming units of each bacterial species on the blood agar plate after 48 hours was recorded. E. coli was identified by oxidase and indole tests, and other less common Enterobacteriaceae were identified to genus level, using a microtube identification system (RapiD 20 E, bioMérieux, UK). Staphylococci were differentiated from Streptococci using a catalase test (National Mastitis Council, 1999) and categorised as coagulase positive or negative using a 24 hour tube coagulase test (National Mastitis Council, 1999; Boerlin et al., 2003). Strep. uberis, Strep. dysgalactiae (subsp dysgalactiae), and Strep. agalactiae were identified according to their ability to split aesculin and Lancefield Group (National Mastitis Council, 1999). Corynebacteria were not differentiated into species. Dry cow therapy was administered to all cows, immediately after collection of the ‘drying off’ samples. Dry cow products containing cloxacillin (Orbenin Extra, Pfizer, Sandwich, UK), cephalonium (Cepravin, Schering-Plough, Harefield, UK) or procaine penicillin G (Mylipen, Schering-Plough, Harefield, UK) were used. Only one of these products was used per farm. 2.3.1. Definition of terms for analysis Days at risk. Quarters were considered at risk from the date of drying off, until 300 days into the following lactation, unless the cow was censored earlier because the data collection ended (15 months after sampling commenced) or because the cow was dried off or culled. Seasonality. Months were either categorised individually (January to December) or aggregated into seasons. Seasons were defined as: Winter (Dec, Jan, Feb); Spring (Mar, Apr, May); Summer (Jun, Jul, Aug) and Autumn (Sep, Oct, Nov) Dry period. The time between the intramammary infusion of dry cow antibiotic and calving. LDC period. Late dry–calving period: The time period from 14 days before calving to 7 days after calving, during which three samples were taken. Intramammary infection: Screening Samples. Isolation of at least one colony of one to three species of bacteria was considered to be an intramammary infection, as recommended for mastitis research of this nature (International Dairy Federation, 1987). The presence of more than three bacterial species was ‘contaminated’ and re-culture of the second sample was 39 performed. Infection status was then based on isolation of organisms in the second sample. If the second sample was contaminated, the results were not used in data analysis. Causes of clinical mastitis. Major pathogens - defined as the mastitis causing organisms; Strep. agalactiae, Strep. uberis, Strep. dysgalactiae, coagulase positive staphylococci, E. coli, Klebsiella spp., Enterobacter spp., Citrobacter spp., Serratia spp., and Arcanobacter pyogenes. Minor pathogens - defined as Corynebacterium spp. and coagulase negative staphylococci. Causes of clinical mastitis were defined as follows; i. A bacterial species in pure growth - causal. ii. Major pathogen + minor pathogen(s) – major pathogen causal. iii. More than one major pathogen – mixed aetiology, specified by organisms present, both causal. iv. Greater than three bacteria – contaminated sample. A quarter with clinical mastitis. Analysis was performed at the quarter level. A quarter with one or more cases of clinical mastitis during the study period was a positive (mastitic) quarter. A cow could have up to four quarters affected. The bacterial species causing clinical mastitis in a quarter was defined as that associated with the first case during lactation. A non-mastitic quarter. A quarter with no clinical mastitis throughout the study period. 2.3.2. Data recording and analysis Herd, cow and quarter identity, dates and culture results were entered into a database (Microsoft Access, Microsoft Corp. US). Univariable analysis was performed using Microsoft Excel (Microsoft Corp. US), Minitab 10.51 (Minitab inc. US) and Egret 2.0.3 (Cytel Software Corp. US). The association between the incidence of clinical mastitis and bacterial species isolated in screening samples was assessed at quarter level. This was done initially using .2 tests (Petrie and Watson, 1999) and then using binomial logistic regression with a random effect, (see below). Single time-point and multiple isolations of the same bacteria through the sample period in each quarter were examined to investigate associations with clinical mastitis. The following patterns of infection were considered independently and together, in relation to clinical mastitis: i. Each bacterial species at each sample-point. ii. Presence of a bacterial species in at least one of the three LDC samples iii. Presence of a bacterial species in at least two of the three LDC samples iv. Presence of a bacterial species in at least one of the three LDC samples without the same species being present at drying off (‘New’ bacterial infection). 40 v. Presence of a bacterial species in at least two out of the three LDC samples when the same species was not present at drying off (‘New’ double bacterial infection). vi. Presence of a bacterial species both at drying off and in at least one of the LDC samples (‘persistent’ infection). vii. Presence of Corynebacterium spp. and coagulase negative staphylococci in the LDC period without a previous LDC infection with a major pathogen. The effect of farm, month of calving, parity, days at risk, length of dry period and the number of dry period screening samples, on the incidence of clinical mastitis, were investigated using .2 tests for categorical data and Kruskal Wallis tests for non-parametric continuous data (Petrie and Watson, 1999). These were also included as covariates in the statistical models to check for any confounding influence on the relationship between clinical mastitis and bacterial isolations. Logistic binomial regression with random effects for distinguishable data (Egret 2.0.3, Cytel Software Corp. USA) was used to model the occurrence of clinical mastitis and patterns of bacterial isolates as defined above. Bernoulli models were fitted with the response variables being: i. Model 2.1: All pathogen types of clinical mastitis considered together (‘all clinical mastitis’). ii. Model 2.2: Clinical E. coli mastitis. Since there were insufficient cases of mastitis caused by coagulase positive staphylococci, Strep. dysgalactiae and Strep. uberis to allow pathogen-specific modelling, .2 analysis was used to estimate the influence of bacterial isolates in the sampling period on clinical mastitis. A random term for cow was included in the models to account for the effect of clustering of quarters within cow. Farm level variation was accounted for by including ‘herd’ as a fixed effect where this improved the model (see below). Therefore, the model for the response probability p ij for the jth quarter within the ith cow was: Logit (pij) = a + ß1X 1ij +……+ ßp X pij + suj (2.1) Where a = regression intercept. ß1 = coefficient of covariate X 1 and there are p covariates. 41 suj = a random term in which s is a positive scalar coefficient (overdispersion parameter). A value of s = 0 meant no overdispersion and s > 0 indicated overdispersion. uj was a standardised binomial random variable (Anon, 1999). Explanatory variables were selected from the univariable analysis if there was a trend to increase or decrease the risk of clinical mastitis (p < 0.25) and modelled using a forward stepwise procedure (Hosmer and Lemeshow, 1989, Kleinbaum, 1994). Covariates were left in the model when there was a significant reduction in deviance computed from the likelihood ratio statistic. Potential confounders and a random term for cow were included in the model when there was a biological improvement in the model; a change in the odds ratios or confidence intervals for the covariate coefficients (Hosmer and Lemeshow, 1989; Kleinbaum, 1994). The significance probability was set at 0.05 for a two-tailed test. Interactions between significant covariates remained in the model if there was a significant improvement as judged by the likelihood ratio statistic. When the prevalence of infection for an outcome was zero, which precluded calculation of an odds ratio using normal logistic regression, combinations of time points were used, rather than exact analytical methods, or the variable was removed if it was judged to be of no biological importance. Assessment of model fit involved plotting Pearson residuals against fitted values as described in Chapter One (McCullagh and Nelder, 1989). Fitted values were plotted in order of magnitude to illustrate the differentiation of quarters with and without clinical mastitis. Kaplan-Meier curves were constructed of survival time to clinical mastitis (Parmer and Machin, 1995) in quarters with and without bacterial isolates during the dry period. The survival function was: S(t) = (1- {d1 / n1}) (1- {d2 / n2})…. (1- {dt / nt}) (2.2) where nt = the number of quarters at risk (not yet having mastitis) at the start of time interval t. dt = the number of quarters which got clinical mastitis during time interval t. S(t) = the probability of a quarter not getting clinical mastitis by time t. Curves were evaluated for statistical differences using the hazard ratio calculated from a Cox Proportional Hazards Model (Parmer and Machin, 1995). As before, the significance probability was set at 0.05 for the likelihood ratio statistic. To check that the 42 assumption of proportionality of hazards between groups was correct, a visual assessment was performed of the log-transformed cumulative hazard (Parmer and Machin, 1995). 2.4. Results A total 1920 quarters from 480 cows entered the study. Twenty-two quarters were omitted from the analysis because they had one or more missing data points. Nine hundred and fifty four quarters that were sampled on all four occasions were used for the main analysis, and 944 quarters that were not sampled during the dry period were used as the controls to assess the dry period sampling process. The distribution between herds, of quarters, cows and clinical mastitis available for modelling is shown below (Table 2.1). Table 2.1. Herd distribution of quarters, cows and clinical mastitis used for modelling clinical mastitis. Herd Number Approximate rolling herd size (number of cows in milking herd) Number of quarters (cows) sampled at drying off, during the dry period and at calving Number of quarters (cows) with clinical mastitis 1 110 148 (74) 19 (18) 2 120 131 (66) 20 (18) 3 100 116 (58) 14 (12) 4 190 208 (105) 11 (11) 5 140 179 (90) 4 (4) 6 150 172 (87) 16 (12) TOTAL 954 (480) 84 (75) Of the 149 cases of clinical mastitis that occurred, 84 were in sampled quarters and 65 in controls. The bacteria isolated from the 84 cases are listed below in Table 2.2. In 32 (38.1%) of the 84 mastitis cases in sampled quarters, the species of bacteria isolated at the time of clinical mastitis was isolated in one or more of the screening samples. The prevalence of bacterial isolates in the 954 quarters sampled at each time point during the dry period, is presented below in Table 2.3. 43 Table 2.2. Bacterial species isolated from cases of clinical mastitis. Bacterial species Number of Cases E. coli 37 No Growth 9 Streptococcus dysgalactiae 5 Streptococcus uberis 5 Coagulase positive staphylococci 5 Mixed growth 3 Serratia spp. 3 Enterococcus faecalis 2 Pseudomonas spp. 2 Bacillus spp. 2 Yeast 2 Contaminated 2 Coagulase negative staphylococci 2 Klebsiella spp. 2 Corynebacterium spp. 1 Enterobacter spp. 1 Citerobacter spp. 1 Total 84 44 Table 2.3. Prevalence of major bacterial isolates (in alphabetical order) during the dry period in the 954 quarters used for statistical models of clinical mastitis. Bacterial species isolated Dry 8-14 0-7 Calving Citerobacter spp. n 0 4 5 2 % 0.0 0.4 0.5 0.2 Coagulase negative staphylococci n 64 136 124 41 % 6.7 14.3 13.0 4.3 Coagulase positive staphylococci n 15 12 13 13 % 1.6 1.3 1.4 1.4 Corynebacterium spp. n 341 25 27 16 % 35.7 2.6 2.8 1.7 Escherichia coli n 15 38 55 58 % 1.6 4.0 5.8 6.1 Enterobacter spp. n 4 7 12 3 % 0.4 0.7 1.3 0.3 Klebsiella spp. n 0 3 1 5 % 0.0 0.3 0.1 0.5 Serratia spp. n 2 6 2 1 % 0.2 0.6 0.2 0.1 Streptococcus agalactiae n 0 0 0 0 % 0.0 0.0 0.0 0.0 Streptococcus dysgalactiae n 5 1 2 5 % 0.5 0.1 0.2 0.5 Enterococcus faecalis n 22 31 36 36 % 2.3 3.2 3.8 3.8 Streptococcus uberis n 9 12 25 15 % 0.9 1.3 2.6 1.6 Key to Table 2.3: Dry - Drying off sample. 8-14 - Sample 8-14 days prior to calving. 0-7 - Sample 0-7 days prior to calving. Calving - Sample 0-7 days post calving. n – number of isolates. % – percentage of quarters with an infection. 2.4.1. Univariable analysis of potential confounders for the risk of clinical mastitis As a result of the sampling protocol, individual quarters were sampled on 2, 3, 4 or 5 occasions during the dry period. Repeated sampling occurred when a cow calved later than the expected date. There was an increased risk of clinical mastitis in quarters sampled 4 times compared to quarters not sampled (p < 0.05) but no difference between those sampled on 2, 3 or 5 occasions and quarters not sampled. 45 Considering all herds together, quarters from cows of greater than 3rd parity were at increased risk of clinical mastitis compared with those of parity 3 or less, (p < 0.01). There was a trend for quarters from cows calving in the summer to have more clinical mastitis than those calving in spring (p = 0.17). Quarters from cows in Herds 4 and 5 were at a significantly reduced risk of clinical mastitis compared with Herd 1, (p < 0.01). Quarters with clinical mastitis had significantly fewer days at risk during the study period (mean = 210.9, median = 229.0 days, interquartile range = 144.3 - 300.0 days) than non-mastitis quarters (mean = 232.8 median = 261.0, interquartile range = 169.0 - 300.0 days), (p = 0.044) because clinical mastitis occasionally resulted in premature culling. Since quarters with a case of clinical mastitis had fewer days at risk than other quarters, an increased days at risk was not a cause of an increased probability of clinical mastitis. No effect of the length of the dry period was found on clinical mastitis incidence. 2.4.2. Univariable analysis of clinical mastitis and bacteria isolated in screening samples Bacteria present at drying off. When the following bacteria were isolated at drying off, there was a trend for an increased risk of clinical mastitis (p < 0.25), Strep. dysgalactiae, Strep uberis, Enterococcus faecalis, coagulase positive staphylococci, E. coli, Enterobacter spp., Serratia spp. and Corynebacterium spp. Bacteria present from 2 weeks before calving to 1 week after calving. A trend for increased risk of clinical mastitis (p < 0.25) was associated with isolation of Strep. uberis, Enterococcus faecalis, coagulase positive staphylococci, Serratia spp., and Klebsiella spp., 8-14 days before calving and Strep dysgalactiae, Strep. uberis, Enterococcus faecalis, coagulase positive staphylococci, E. coli, Serratia spp., and coagulase negative staphylococci, 0-7 days before calving. Isolation of the following organisms in at least two out of three samples during the LDC period was also associated with a trend for an increased risk of clinical mastitis (p < 0.25); Strep. dysgalactiae, Strep. uberis, Enterococcus faecalis, coagulase positive staphylococci, E. coli, Serratia spp., Klebsiella spp., coagulase negative staphylococci. The presence of Corynebacterium spp. 0-14 days before calving were associated with a decreased likelihood of clinical mastitis (p < 0.25). When the following bacteria were isolated in the post calving sample, there was a trend for an increased likelihood of clinical mastitis; Strep. uberis, coagulase positive staphylococci, E. coli, and Klebsiella spp. (p < 0.25). When Corynebacterium spp. were isolated in the post calving sample there was a trend for less clinical mastitis (p < 0.25). 46 2.4.3. Modelling bacterial isolations and clinical mastitis Clinical mastitis Models 2.1 and 2.2 are presented in Tables 2.4 and 2.5, below. When the outcome variable was all cases of clinical mastitis, the probability of a quarter succumbing to clinical mastitis was increased significantly (p < 0.05) with the presence of bacterial isolates caused by Strep. dysgalactiae, Corynebacterium spp., E. coli, Enterococcus faecalis and Enterobacter spp. at drying off. The probability also increased with isolation of E. coli, Serratia spp., coagulase positive staphylococci, and Enterococcus faecalis in at least 2 of the LDC screening samples in quarters not infected with the same bacteria at drying off. The presence of Corynebacterium spp. in any one of the LDC samples, in quarters not already infected with a major pathogen in the LDC period, was associated with a significant reduction in the likelihood of subsequent clinical mastitis. Quarters in cows from Herds 4 and 5 were at significantly reduced risk of clinical mastitis compared to Herd 1. Quarters in cows of parity greater than three were at significantly greater risk of clinical mastitis compared with those of parity two and three. Calving season and the number of dry period samples taken did not influence the risk of clinical mastitis. The E. coli model indicated that the risk of clinical E. coli mastitis was increased with isolation of E. coli and coagulase positive staphylococci at drying off and isolation of Enterococcus faecalis and E. coli at least twice in the LDC period in quarters not infected with them at drying off (Table 2.5). Quarters of cows from Herds 4 and 5 were at significantly reduced risk of clinical E. coli mastitis compared to Herd 1 but there was no significant effect of parity, calving season or the number of dry period samples taken. Inclusion of the random effect of ‘cow’ influenced parameter estimate confidence intervals in both models and was therefore included in the models. 47 Table 2.4. Logistic binomial regression model with random effects for distinguishable data - Model 2.1: Response variable - all causes of clinical mastitis at quarter level (yes/no); 84 quarters got clinical mastitis out of 954 sampled during the dry period. Random effect for cow. Exposures Coefficient S.E. Odds Ratio 95% C.I. Lower Upper pvalue Intercept a -3.18 0.50 Confounders Herd 1 reference Herd 2 0.39 1.47 0.61 3.59 0.39 Herd 3 0.06 1.06 0.43 2.58 0.90 Herd 4 -1.10 0.33 0.13 0.86 0.02 Herd 5 -2.01 0.13 0.03 0.56 0.01 Herd 6 -0.25 0. 78 0.34 1.82 0.57 Parity 2 and 3 reference Parity 4 and 5 0.59 1.81 0.94 3.48 0.08 Parity > 5 0.85 2.33 1.10 4.95 0.03 Bacterial isolates E. coli D 2.99 19.82 4.02 97.65 < 0.01 Enterobacter spp. D 2.53 12.60 1.17 135.9 0.04 Corynebacterium spp. D 0.60 1.83 0.98 3.41 0.05 Strep. dysgalactiae D 2.45 11.56 1.18 113.2 0.05 Enterococcus faecalis D 1.10 3.01 0.88 10.28 0.05 NEW coagulase positive staphylococcus Twice 3.26 25.92 3.11 216.0 < 0.01 NEW E. coli Twice 1.86 6.41 1.79 22.94 < 0.01 NEW Enterococcus faecalis Twice 1.77 5.86 1.37 25.02 0.03 NEW Serratia spp. Twice 3.29 26.84 0.95 760.4 0.05 Corynebacterium spp. and No Major Pathogen LDC -1.82 0.16 0.02 1.43 0.03 s ( positive scalar coefficient of random term) 0.72 0.49 Key to Table 2.4: D – isolate present at drying off, regardless of other isolations. Twice – isolate present in 2 out of 3 samples in LDC period. NEW – an isolate present in the LDC period but not at drying off. Corynebacterium spp. and No Major Pathogen LDC - Corynebacteria spp. isolated at least once in LDC period without prior infection with a major pathogen in LDC period. S. E. – standard error. 48 Table 2.5. Logistic binomial regression model with random effects for distinguishable data - Model 2.2: Response variable is clinical E. coli mastitis at quarter level (yes/no); 37 cases occurred in 954 quarters sampled during the dry period. Random effect for cow. Exposures Coefficient S.E. Odds Ratio 95% CI Lower Upper p-value Intercept a -3.26 0.64 Confounders Herd 1 reference Herd 2 -0.38 0.68 0.19 0.56 Herd 3 -0.92 0.40 0.09 0.22 Herd 4 -1.70 0.18 0.04 0.02 Herd 5 -2.66 0.07 0.01 0.01 Herd 6 -1.27 0.28 0.07 0.07 Bacterial isolates E. coli D 3.43 30.97 3.38 283.34 < 0.01 Coagulase positive Staphylococcus D 2.32 10.14 1.29 79.76 0.03 NEW E. coli Twice 3.68 39.69 6.60 238.51 < 0.01 NEW Enterococcus faecalis Twice 2.50 12.15 1.56 94.52 0.02 s ( positive scalar coefficient of random term) 1.48 0.65 Key to Table 2.5: D – isolate present at drying off, regardless of other isolations. Twice – isolate present in 2 out of 3 samples in LDC period. NEW – an isolate present in the LDC period but not at drying off. S. E. – standard error. The risk of clinical mastitis caused by Strep. uberis, Strep. dysgalactiae or coagulase positive staphylococci was significantly increased if the organism causing mastitis was isolated in at least 2 of the LDC samples (Table 2.6): 49 Table 2.6. The proportion of quarters from which coagulase positive staphylococci, Strep. uberis and Strep. dysgalactiae were isolated at least twice in the LDC period that subsequently got clinical mastitis caused by the respective pathogen. Bacteria cultured in at least 2 of the LDC samples Number of quarters with clinical mastitis caused by that species of bacteria Odds Ratio 95% Confidence intervals .2 p value No Yes Lower Upper Coagulase +ve No 943 2 staphylococci Yes 6 3 235.7 25.2 2612 < 0.001 Streptococcus No 941 2 uberis Yes 8 3 176.4 19.9 1821 < 0.001 Streptococcus No 948 4 dysgalactiae Yes 1 1 237.0 5. 3 11176 < 0.001 2.4.4. Model fit Pearson residuals for Models 2.1 and 2.2 are shown below in Figures 2.1 and 2.2, respectively. Assessment of residuals suggested the models were of generally good fit with aggregated residuals approximating to zero. A discussion of the approaches to residual analysis for Bernoulli GLMM is provided in Chapter Seven. 50 Figure 2.1. Pearson residuals for Model 2.1: a. Pearson residuals plotted against fitted values, b. Aggregates of residuals in ascending quintiles plotted against fitted values and c. Cumulative mean Pearson residual plotted against ascending fitted value. a b c -4 -2 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 Fitted Value Pearson Residual -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 Residuals aggregated in ascending quintiles Mean Pearson Residual -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.03 0.03 0.04 0.04 0.04 0.05 0.05 0.05 0.05 0.07 0.07 0.07 0.07 0.08 0.09 0.09 0.1 0.12 0.12 0.12 0.14 0.14 0.15 0.15 0.15 0.22 0.44 0.83 Ascending Fitted Value Cumulative Mean Pearson residual 51 Figure 2.2. Pearson residuals for Model 2.2: a. Pearson residuals plotted against fitted values, b. Aggregates of residuals in ascending quintiles plotted against fitted values and c. Cumulative mean Pearson residual plotted against ascending fitted value. a. b. c. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 Residuals in ascending quintiles of fitted value Mean Pearson Residual -2 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 Fitted Value Pearson Residual -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.04 0.04 0.04 0.04 0.04 0.06 0.06 0.06 0.06 0.06 0.13 0.84 Ascending Fitted Value Cumulative Frequency of Pearson Residuals 52 Figure 2.3. Graphs of fitted values from model 2.1 (all causes of clinical mastitis) for quarters that a. got mastitis (n = 84) and those b. that did not (n = 870). Quarters are placed in descending order of fitted value to allow comparison between graphs. a. b. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Quarters that got mastitis (descending order of fitted value) Model fitted value 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Non-mastitis quarters (descending order of fitted value) Model fitted value 53 2.4.5. Survival curves of clinical mastitis There was a different pattern of clinical mastitis in quarters that had the same species of bacteria isolated during the screening period and at the time of clinical mastitis (n = 32, group A), from quarters that did not (n = 52, group B) as illustrated in Figure 2.4, below: Figure 2.4. Proportion of quarters without clinical mastitis (St = survival time) over lactation: A comparison of quarters in which the same pathogen was isolated in the screening period and at the time of clinical mastitis, (A) and those in which the same pathogen was not isolated in the screening period, (B). Sixty percent of quarters in group A got clinical mastitis within 14 days of calving compared with 20% in group B. Over 80% of mastitis in group A had occurred by day 120 of lactation whereas only 50% had occurred by this time in group B. The probability of a case of clinical mastitis was fairly constant throughout lactation for group B quarters. The two curves were significantly different with group A being at an increased hazard of mastitis (Hazard Ratio = 1.86, 95% confidence interval = 1.17 - 2.95, p = 0.01). Survival times to mastitis for quarters with Corynebacterium spp. isolates is illustrated in Figure 2.5, below. Quarters infected at drying off (n = 341) were more likely to get clinical mastitis at any time during the next lactation compared with uninfected quarters (Hazard Ratio = 1.85, 95% confidence intervals =1.20 - 2.84, p < 0.01). Quarters in which Corynebacterium spp. isolates were found during the LDC period, with no previous major A B 54 pathogen isolated during the LDC period (n = 42), were less likely to get clinical mastitis during the next lactation compared with quarters not infected with Corynebacterium spp. (Hazard Ratio = 0.21, 95% confidence interval = 0.03 - 1.49, p = 0.03). Figure 2.5. Proportion of quarters without clinical mastitis (St = survival time) over lactation: A comparison of quarters in which a Corynebacterium spp. was isolated in the LDC period without previous isolation of a major pathogen in that period, (A), quarters in which a Corynebacterium spp. was isolated at drying off, (B) and quarters in which a Corynebacterium spp. was not isolated at any time, (C). A B C 55 2.5. Discussion Bacterial isolates present both at drying off and during the LDC period increased the risk of clinical mastitis in this study. LDC infections with major pathogens increased the risk of clinical mastitis with the same organism although it was not possible to determine whether all these bacteria persisted in the mammary gland from the time of dry period isolation to the time of mastitis, or whether a new infection occurred. Previous work with DNA fingerprinting of the Enterobacterial strains in this dataset, indicated that persistence of these particular organisms from the dry period to clinical mastitis was likely (Bradley and Green, 2000). Over 60% of clinical mastitis in quarters in which the same pathogen was identified during the dry period, occurred within two weeks of calving and 90% within 150 days of calving. This is in contrast to the approximately constant rate of clinical mastitis during lactation that occurred in quarters from which the same pathogens were not cultured during the dry period. The pattern and rate of clinical mastitis over lactation on a dairy farm may therefore give an indication of the impact of dry period infections on clinical mastitis and moreover, the areas to target preventive measures. Herds with a high incidence of clinical mastitis in the first two weeks after calving would be wise to consider dry period infections as a potential risk factor. The presence of Strep. dysgalactiae, Enterococcus faecalis, E. coli, Enterobacter spp., and Corynebacterium spp. at drying off, increased the probability of subsequent lactational clinical mastitis. The influence of bacterial isolates in the LDC period on subsequent clinical mastitis was statistically separate to the influence of those at drying off since both sample times remained in the models. The data do not support the hypothesis that bacteria present at drying off influenced the risk of clinical mastitis by persisting through to the LDC period; this was tested in the models and not found to be significant. Similarly, these findings are unlikely to be because of contamination of milk samples since the sampling technique was fastidious, sampling during the dry period was always performed by the author or Dr Andrew Bradley. There was also no reason that contamination should occur more often at drying off in quarters that got clinical mastitis the next lactation, compared with unaffected quarters. One plausible explanation for the increased risk of clinical mastitis in quarters with infections at drying off, is that certain quarters are simply susceptible to infection. An alternative explanation is that the previous bacterial infection increases the risk of subsequent infection. Quarter susceptibility may occur because of anatomical features such as short wide teat canals (Grega and Szarek, 1985; Grindal et al., 1991) or immunological characteristics, such as poor white cell function (Hill, 1981) or low white cell number (see Chapter Four). 56 Alternatively, previous infection may cause damage or alteration to the mammary environment in some way and reduce innate defence mechanisms. An interesting finding of this research, was that the timing of isolation of Corynebacterium spp. was important in determining its association with clinical mastitis. If infection was present at drying off, then the quarter was at greater risk of clinical mastitis and the Kaplan-Meier curves show that these cases occurred evenly throughout lactation. It is possible though unlikely that infection with Corynebacterium spp. occurred because of poor teat hygiene procedures and this continued into the next lactation and predisposed the quarters to clinical mastitis. Alternatively, it is possible that Corynebacterium spp. infection at drying off was an indicator of quarters that had poor defence mechanisms such as poor teat closure. This would mean these quarters were generally prone to infection and would be more likely to get clinical mastitis in the next lactation. A previous field study has also found that quarters with Corynebacterium bovis infections were at an increased risk of subsequent bacterial infection (Hogan et al, 1988). In this study, however, if Corynebacterium spp. were isolated in the LDC period, in a quarter not already infected with a major pathogen, then the quarter was at a reduced risk of clinical mastitis. The data therefore suggest that the timing of Corynebacterium spp. infection may be important in determining whether a quarter is at greater or reduced risk of clinical mastitis and this may explain why some authors have found protective effects (Lam et al, 1997; Rainard and Poutrel, 1988) whilst others found an increase in susceptibility (Hogan et al, 1988). It would be useful to understand the exact conditions that dictate whether infection with Corynebacterium spp. indicates either a more susceptible quarter or a quarter at reduced risk of clinical mastitis. These conditions may include the species and strains of the Corynebacteria involved, the timing of infection and whether the Corynebacterium spp. is present at the actual time of challenge by a major pathogen. The clinical value of protection afforded by Corynebacterium spp. in this study was limited. Only 42 out of 954 (4.4 %) quarters were infected with Corynebacterium spp. in the LDC period without previous major pathogen infection, and this indicates that the vast majority of quarters did not benefit from protection. Since the prevalence of Corynebacterium spp. has been found to decrease during the dry period, even when no antibiotic dry cow therapy is used (Harmon et al., 1986; Oliver and Juneja, 1990), any protective effect is only likely to be of value in the field if methods to safely increase its prevalence are found. The current study could not determine whether there was a varying level of protection from Corynebacterium spp. infection to different major pathogens. There were insufficient Corynebacterium spp. infections in the LDC period to perform this analysis. It remains possible therefore, that protection may occur for some major pathogens and not 57 others, as has been reported experimentally (Linde et al 1980; Brooks and Barnum, 1984a; Pankey et al, 1985; Doane et al., 1987). Enterococcus faecalis isolation in the LDC period was also a risk factor for clinical mastitis (Model 2.1). Again, this may be an indicator of increased quarter susceptibility to infection or be a result of synergistic action between Enterococcus faecalis and other organisms, particularly E. coli, for which it increased the risk of clinical mastitis (Model 2.2). Previous reports have suggested that there is more likely to be competition and exclusion, however, rather than synergy between Enterococcus faecalis and E. coli (Dalhoff, 1982). Further research into the interactions between Enterococcus faecalis and other pathogenic bacteria in the mammary gland may be fruitful but these data suggest that Enterococcus faecalis may not necessarily be indicative of a contaminated milk sample, as would commonly be reported from UK laboratories. Data from this study highlight the difficulties of defining intramammary infections. Previous longitudinal studies have defined an infection as present when a pathogen is cultured on 2 out of 3 occasions from consecutive samples 1-30 days apart (Smith et al 1985; Hogan et al., 1988; Lam et al., 1997). This definition is likely to represent long-term infections and will miss those that are transient. Various combinations of isolates were considered in this study; single isolates, at least one infection in 3 consecutive LDC period samples, and at least 2 infections in 3 consecutive LDC period samples. Whilst 2 infections out of 3 samples was the best indicator of clinical mastitis in the models, it was found that this definition of an infection gave a greater specificity and predictive value for clinical mastitis but a poorer sensitivity than including single infections. This is likely to be because whilst some single bacterial isolates can lead to clinical mastitis many will be removed by the cow’s defences without the appearance of clinical signs. The use of a single milk sample at drying off to identify an infection, rather than two or three, will have reduced the sensitivity of diagnosis. It is considered that false negative samples are most likely to occur with coliforms and coagulase positive staphylococci (National Mastitis Council, 1999) although it has been estimated that a single quarter milk sample from a lactating gland has 75-90% sensitivity and > 97% specificity for diagnosis of coagulase positive staphylococci infection (Sears et al., 1990; Buelow et al., 1996). Under diagnosis of true infections at drying off in this study will have caused an underestimate of the importance of infections at this time and an overestimate of those considered to be ‘new’ in the LDC period. False negative coliform cultures were reduced by using 0.1ml secretion instead of 0.01ml (National Mastitis Council, 1999). Whilst recognising the constraints of bacteriological culture, all isolates in the LDC period as well as apparent new infections were modelled and it was found that only the new infections remained in the models. Although not 58 all of these may be truly new infections, this supports the view that new infection in the dry period are important (Eberhart, 1986, Smith et al., 1985, Todhunter et al., 1991). The graphs of fitted values (prediction by the model for each quarter to get mastitis or not) showed a reasonably good differentiation between mastitic and normal quarters (Figure 2.3). The relatively high fitted values (> 0.2) for mastitic quarters related to quarters with dry period infections and the lower values to quarters with mastitis not associated with dry period infections. The model could not predict all quarters that got mastitis and this was expected because not all clinical mastitis was associated with dry period infection. The number of quarters (32 out of 84), however, in which clinical mastitis was associated with infection by the same organism during the sampling period, was surprisingly high. The model could differentiate quarters that did not get mastitis as shown by low fitted values, and this indicated that few of these non-mastitis quarters had dry period infections. A further discussion of hierarchical Bernoulli model fit is made in Chapter Seven. Confounders, such as parity and herd, were included in the statistical models to control for variation that may affect the relationship between dry period infections and clinical mastitis. This meant that estimates of the coefficients of the explanatory variables were adjusted for these influences (Hosmer and Lemeshow, 1989, Kleinbaum, 1994). Herd and parity were the only confounders identified in the final models and it is noteworthy that quarters from cows of parity greater than 3 were at approximately twice the risk of clinical mastitis compared to those of parity 2 and 3. Cows of parity 1 did not participate in the study because they did not have a dry period. There was a small increase in the proportion of quarters that got clinical mastitis when sampled during the dry period compared to those not sampled. This was mainly because of an increased risk in quarters sampled four times during the dry period. The number of dry period samples taken was therefore used as a covariate for modelling clinical mastitis but it did not remain in any model and this indicated that sampling did not significantly influence the risk of clinical mastitis. Alteration of parameter coefficients / confidence intervals in the models with the inclusion of a random term for cow, indicated that quarters within a cow were not behaving independently. That is, 2 quarters of the same cow were more likely to show similar patterns of infections and clinical mastitis than 2 quarters of different cows. Correcting for this potential bias in the data was important and shows that this is a necessary consideration when handling quarter level mastitis data from dairy cows. 59 Chapter 3: Bacterial isolates in the dry bovine mammary gland: Prevalence and Associations 3.1. Chapter summary Bacterial culture was used to assess the prevalence and patterns of bacterial isolates during the dry period of dairy cows in six commercial UK dairy herds. Milk samples were taken from 1920 quarters of 480 cows at drying off and at weekly intervals 14 days before, to 7 days after calving. Two quarters of each cow were not sampled during the dry period to allow a comparison between sampled and non-sampled quarters. Of the 480 cows in the study, 220 (45.8%) had a major mastitis pathogen isolated from at least one quarter and 90 (18.8%) had a major pathogen isolated from more than one quarter. During the late dry–calving period, a major mastitis pathogen was cultured at least once from 24.7 % quarters (38.8% cows) and the same bacterial species was isolated from at least two out of three samples from 5.2% quarters (9.8% cows). The most commonly isolated major pathogen was E. coli, followed by Strep. uberis and coagulase positive staphylococci. Survival analysis was used to investigate patterns of bacterial isolates. Significant differences occurred between farms and in different calving months, suggesting the force of infection was dependent on external conditions. Bayesian generalised linear mixed models were used to assess associations between different bacterial species throughout the sampling period. The probability of isolating E. coli or Strep. uberis significantly increased when the other organism was cultured in a milk sample; this was also true of coagulase positive staphylococci and Strep. uberis. When Corynebacteria spp. were isolated in a milk sample, the probability of isolating coagulase positive staphylococci or Strep. uberis significantly decreased and when coagulase negative staphylococci were isolated there was a reduced probability of coagulase positive staphylococci being cultured. The role of interactions between infections of the bovine udder in determining the epidemiology of mastitis is discussed. 60 3.2. Introduction Following results from Chapter Two, the purpose of this chapter was to explore in greater detail the prevalence and patterns of bacterial intramammary isolates in the six dairy herds. Interactions between different bacterial species, such as those described during lactation (Rainard and Poutrel, 1988; Lam et al, 1997; White et al, 2001) have not previously been investigated during the dry period. Therefore, particular focus was placed on associations between different bacterial species. 3.3. Materials and Methods Study design, milk sample collection and bacterial identification has been described in Chapter Two. Throughout this chapter, however, all 1920 quarters sampled from the 480 cows were considered in analysis, rather than solely the 954 quarters sampled at each time point, during the dry period. Therefore, culture results of milk samples from all four quarters at drying off and after calving were included. Additionally, the number of colony forming units (cfu) of each bacterial species on the blood agar plate after 48 hours was used in analysis. These were recorded for each culture result and categorised as follows; • No bacteria identified. • One to five cfu (concentration of 100 – 500 cfu per ml of milk). • Six to ten cfu (concentration of 600 – 1000 cfu per ml of milk). • Eleven to 20 cfu (concentration of 1100 – 2000 cfu per ml of milk). • Twenty one or more cfu (concentration = 2,000 cfu per ml of milk). 3.3.1. Definition of Terms for Analysis These were described in, and are consistent with Chapter Two. 3.3.2. Data recording and analysis Cow and quarter identity, dates and bacterial culture results were entered into a database (Microsoft Access, Microsoft Corp. US). Analysis was performed using Microsoft Excel (Microsoft Corp. US), Egret 2.0.3 (Cytel Software Corp. US) and WinBUGS (Version 1.3, Spiegelhalter et al, 2000). Conditional logistic regression (Hosmer and Lemeshow, 1989) was used, with quarters matched within cow, to investigate the effect of taking milk samples during the dry period. A comparison of bacterial isolations at calving was made between quarters sampled and not sampled during the dry period. 61 3.3.3. Patterns of bacterial isolates The prevalence of each bacterial species, categorised by concentration, was calculated for each sample time. The proportion of quarters from which a bacterial species was isolated at least once in the LDC period, but not at drying off, was calculated, as were the proportions of quarters with one, two and three isolates of the same bacterial species during the LDC period. Conventional Kaplan-Meier survival curves (Collett, 1994) were constructed to examine patterns of E. coli, Strep. uberis and Staph. aureus isolates with respect to time of calving. The survival function was: S(t) = (1- {d1 / n1}) (1- {d2 / n2})…. (1- {dt / nt}) (3.1) where nt = the number of quarters at risk (not yet having the bacterial species isolated) at the start of time interval t. dt = the number of quarters from which the bacterial species was isolated during time interval t. S(t) = the probability of a quarter not having the bacterial species isolated by time t. Quarters entered this analysis at the time of milk sampling, between 8 and 14 days before calving and ‘failed’ when the bacterial species was first isolated. Quarters were censored when no longer at risk of infection, after their final milk sample was taken, 0-7 days after calving. To examine factors that influenced the risk of culturing E. coli, Strep. uberis and coagulase positive staphylococci during the LDC period, a Cox Proportional Hazards model was specified. The standard model was extended by including a frailty term reflecting a latent effect associated with each cow. .i = .0 * exp(ßx’ + uc) (3.2) uc (cow effect) ~ Normal distribution(Mean = 0, variance = s2 cow) where 62 .i = Hazard function (instantaneous risk of bacterial isolation in quarter i at time t, where t is the time from 14 days before calving to 7 days after calving) .0 = Baseline Hazard ßx’ = Linear predictor containing a vector of covariates x, with regression coefficients ß. uc = a random variable to account for the clustering of quarters within cows. The covariates herd, parity, month of calving (coded 1 to 12, January to December respectively) and quarter position (left hind, right hind, left fore or right fore) were included as explanatory covariates, to estimate their effect on the hazard of culturing each major pathogen. To check that the assumption of proportionality of hazards was correct (Collett, 1994), a visual assessment was performed of the log-transformed cumulative hazard for the explanatory variables. When cumulative hazard curves were approximately parallel between groups, it was accepted that there was proportionality of hazards during the study period. Parameter estimation was carried out using MCMC with Gibbs sampling in WinBUGS (Vs 1.3, Spiegelhalter et al, 2000) and followed the methods described in Chapter One. An example of the WinBUGS codes for these models is provided in Appendix 1. Markov Chains were run for a minimum of 15,000 iterations each after burn in, from which model parameter distributions were assessed and the posterior means and credibility intervals derived. 3.3.4. Generalised linear mixed models of intramammary bacterial isolates To investigate whether the probability of isolating the major mastitis pathogens E. coli, Strep. uberis and coagulase positive staphylococci was influenced by the presence of other bacteria, GLMM were constructed. Milk samples from drying off to seven days after calving, were included in this analysis. Initial statistical exploration was conducted using different concentrations of each bacterial species. However, because the associations between bacterial species was similar at each concentration and also there was a lack of numbers at some concentrations, models were simplified to include presence or absence of a bacterial species. Therefore, the presence of E. coli (Model 3.1), Strep. uberis (Model 3.2) and coagulase positive staphylococci (Model 3.3) were coded in three separate models as a Bernoulli outcome, presence = 1, absence = 0. Isolations of other bacterial species were incorporated in the models as explanatory covariates as follows; • Concurrent isolation of a different bacterial species. • Presence of a bacterial species in the previous milk sample taken from that quarter (coded as missing for a drying off sample). 63 • Presence of a bacterial species in the milk sample taken at drying off from that quarter (coded as missing for a drying off sample). Univariable analysis using .2 tests (Petrie and Watson, 1999) were initially used to assess relationships between the response and explanatory covariates. Bacterial species were carried forward as candidate covariates for modelling when the a .2 p value was < 0.25. The generalised linear mixed models were specified as follows (Zeger and Karim, 1991; Burton et al, 1999): BIijk = Bernoulli response variable (mean = µijk) [1 = bacteria isolated, 0 = bacteria not isolated] denoting one or more bacteria isolated from the ith milk sample in the jth quarter of the kth cow. logit(µijk) = a + ß’1ijkX1ijk + ß’2jkX2jk + ß’3kX3k + vk + ujk (3.3) where the subscripts i, j and k denote the ith milk sample, the jth quarter and the kth cow respectively; µijk = the fitted probability of BI from the ith milk sample in the jth quarter of the kth cow. a = regression intercept X1ijk = vector of covariates associated with milk sample i from quarter j of cow k. ß’1ijk = vector of coefficients for X1ijk. X2jk = vector of quarter-level exposures for quarter j of cow k. ß’2jk = vector of coefficients for X2jk. X3k = vector of cow-level exposures for cow k. ß’3k = vector of coefficients for X3k. vk = random effect reflecting residual variation between cows. ujk = random effect reflecting residual variation between quarters, within cows. Scientific interest focused on estimating the change in risk (measured as an odds ratio) of isolating a major pathogen, dependent upon current or previous isolations of other bacteria. The following covariates were tested in the models and were included when they confounded the relationship between the explanatory and response covariates (Hosmer and Lemeshow, 1989); herd, calving month, time of sampling (categorised as drying off, 8-14 days pre-calving, 0-7 days pre calving or 0-7 days post-calving), parity, quarter position (left hind, left fore, right hind or right fore), number of quarter samples taken during the dry period and length of dry period. Interactions between significant covariates were tested in the model. 64 Explanatory covariates and interaction terms remained in the final models when the 95% credibility interval for the odds ratio did not include one. MCMC with Gibbs sampling was used to obtain parameter estimates according to methods described in Chapter One. An example of the WinBUGS code used for these GLMM is provided in Appendix 2. Markov Chains were run for a minimum of 10,000 iterations each after ‘burn in’, and the posterior means and credibility intervals of parameters were derived from these iterations. Model parameter distributions were assessed using kernel density plots. Model fit was assessed graphically by plotting Pearson residuals against fitted values (McCullagh and Nelder, 1989) and by investigating aggregations of these residuals (see Chapter Seven). 3.4. Results 3.4.1. Numbers of cows and quarters As described in Chapter Two, 1920 quarters from 480 cows entered the study. Nine hundred and sixty quarters were sampled during the dry period and 960 remained unsampled. Twenty-two out of 5760 (0.38%) samples were omitted from analysis because the sample was either contaminated, or mis-recorded, therefore 5738 samples were used for analysis. 3.4.2. Influence of sample collection Conditional logistic regression indicated that there was no significant increased risk of major pathogen infection (104/960 = 10.8%) or minor pathogen infection (59/960 = 6.1%) at calving in quarters sampled before calving, compared with those not sampled (85/956 = 8.9%, and 67/956 = 7.0%, respectively), p > 0.30. 3.4.3. Description of bacterial isolates Of the 480 cows, 220 (45.8%) had a major mastitis pathogen isolated from at least one quarter during the study and of these, 90 (18.8%) cows had a major pathogen isolated from more than one quarter. The quarter prevalence and concentrations of major and minor mastitis pathogens at each time-point is presented below in Tables 3.1, 3.2 and 3.3. Out of 957 quarters with all three culture results during the LDC period, 236 (24.7%) quarters in 186 (38.8%) cows had a major mastitis pathogen cultured from at least one milk sample. Fifty (5.2%) quarters, in 47 (9.8%) cows, had the same major pathogen isolated in at least two of the three LDC samples. At every sample time, the major pathogens most commonly isolated were E. coli, Strep. uberis and coagulase positive staphylococci. The total quarter prevalence of all major 65 pathogen isolates increased from 5.7% at drying off, to 8.6% at 8-14 days before calving, to 12.0% quarters at 0-7 days before calving and reduced to 9.8% at 0-7 days after calving. Bacterial species were most commonly isolated at a concentration = 2,000 cfu / ml of milk. The total quarter prevalence of minor pathogens (Corynebacterium spp. and coagulase negative staphylococci) was 41.4% at drying off; this decreased to 16.4% at 8-14 days before calving, to 5.8% at 0-7 days before calving and was 6.6% at 0-7 days after calving. The prevalence of Corynebacterium spp. decreased markedly between drying off and the LDC period whereas the prevalence of coagulase negative staphylococci was higher during the dry period than at drying off or after calving. Over 90% of the bacterial species identified during the LDC period were not isolated from the same quarter in the milk sample at drying off (Table 3.4, below). The exception to this was Corynebacterium spp. Approximately two thirds of quarters from which Corynebacterium spp. were isolated in the LDC period had the bacteria also cultured from the drying off milk sample. 66 Table 3.1. Prevalence and culture concentrations (x 102 / ml) of gram-positive major pathogens isolated at each sample time. Prevalence of isolates at different sample times (% of quarters) Dry 2 wk 1 wk Calving n = 1905 n = 959 n = 958 n = 1916 STREPTOCOCCI Strep. agalactiae 1 - 5 cfu 0.00 0.00 0.00 0.00 Strep. agalactiae 6 - 10 cfu 0.00 0.00 0.00 0.00 Strep. agalactiae 11-20 cfu 0.00 0.00 0.00 0.00 Strep. agalactiae > 20 cfu 0.00 0.00 0.00 0.00 Total Strep. agalactiae 0.00 0.00 0.00 0.00 Strep. dysgalactiae 1 - 5 cfu 0.00 0.00 0.00 0.05 Strep. dysgalactiae 6 - 10 cfu 0.00 0.10 0.00 0.10 Strep. dysgalactiae 11-20 cfu 0.05 0.00 0.00 0.00 Strep. dysgalactiae > 20 cfu 0.52 0.00 0.21 0.16 Total Strep. dysgalactiae 0.57 0.10 0.21 0.31 Strep. uberis 1 - 5 cfu 0.21 0.10 0.31 0.16 Strep. uberis 6 - 10 cfu 0.10 0.00 0.10 0.16 Strep. uberis 11-20 cfu 0.00 0.10 0.21 0.10 Strep. uberis > 20 cfu 0.78 1.03 1.98 0.94 Total Strep. uberis 1.09 1.23 2.60 1.36 STAPHYLOCOCCI Coagulase positive staphylococci 1 - 5 cfu 0.21 0.21 0.21 0.47 Coagulase positive staphylococci 6 - 10 cfu 0.05 0.00 0.21 0.05 Coagulase positive staphylococci 11-20 cfu 0.16 0.00 0.10 0.00 Coagulase positive staphylococci >20 cfu 1.10 1.03 0.83 0.99 Total coagulase positive staphylococci 1.52 1.24 1.35 1.51 ARCANOBACTERIUM SPP. Arcanobacterium pyogenes 1 - 5 cfu 0.00 0.00 0.00 0.00 Arcanobacterium pyogenes 6 - 10 cfu 0.00 0.00 0.00 0.00 Arcanobacterium pyogenes 11-20 cfu 0.00 0.00 0.00 0.00 Arcanobacterium pyogenes >20 cfu 0.05 0.00 0.00 0.21 Total Arcanobacterium pyogenes 0.05 0.00 0.00 0.21 Key to Table 3.1: Dry - Drying off sample. 2 wk - Sample 8-14 days prior to calving. 1 wk - Sample 0-7 days prior to calving. Calving - Sample 0-7 days post calving. cfu – colony forming unit. 67 Table 3.2. Prevalence and culture concentrations (x 102 / ml) of gram-negative major pathogens isolated at each sample time. Prevalence of isolates at different sample times (% of quarters) Dry 2 wk 1 wk Calving n = 1905 n = 959 n = 958 n = 1916 GRAM NEGATIVE BACTERIA E. coli 1 - 5 cfu 0.68 1.04 1.67 2.19 E. coli 6 - 10 cfu 0.16 0.84 0.83 0.31 E. coli 1-20 cfu 0.10 0.42 0.21 0.52 E. coli >20 cfu 1.00 1.67 3.02 2.51 Total E. coli 1.94 3.96 5.73 5.53 Enterobacter spp. 1 - 5 cfu 0.05 0.10 0.10 0.10 Enterobacter spp. 6 - 10 cfu 0.00 0.21 0.00 0.05 Enterobacter spp. 11-20 cfu 0.16 0.00 0.00 0.00 Enterobacter spp. >20 cfu 0.10 0.41 1.15 0.16 Total Enterobacter spp. 0.31 0.72 1.25 0.31 Klebsiella spp. 1 - 5 cfu 0.00 0.10 0.10 0.10 Klebsiella spp. 6 - 10 cfu 0.00 0.00 0.00 0.05 Klebsiella spp. 11-20 cfu 0.00 0.00 0.00 0.05 Klebsiella spp. >20 cfu 0.00 0.10 0.00 0.10 Total Klebsiella spp. 0.00 0.20 0.10 0.30 Citrobacter spp. 1 - 5 cfu 0.00 0.00 0.00 0.00 Citrobacter spp. 6 - 10 cfu 0.05 0.00 0.00 0.00 Citrobacter spp. 11-20 cfu 0.00 0.00 0.00 0.00 Citrobacter spp. >20 cfu 0.05 0.41 0.52 0.21 Total Citrobacter spp. 0.10 0.41 0.52 0.21 Serratia spp. 1 - 5 cfu 0.05 0.00 0.00 0.00 Serratia spp. 6 - 10 cfu 0.00 0.21 0.00 0.00 Serratia spp. 11-20 cfu 0.05 0.21 0.00 0.00 Serratia spp. >20 cfu 0.00 0.21 0.21 0.10 Total Serratia spp. 0.10 0.63 0.21 0.10 Key to Table 3.2: Dry - Drying off sample. 2 wk - Sample 8-14 days prior to calving. 1 wk - Sample 0-7 days prior to calving. Calving - Sample 0-7 days post calving, cfu – colony forming unit. 68 Table 3.3 Prevalence and culture concentrations (x 102 / ml) of minor pathogens isolated at each sample time. Prevalence of isolates at different sample times (% of quarters) Dry 2 wk 1 wk Calving n = 1905 n = 959 n = 958 n = 1916 Coagulase negative staphylococci 1 - 5 cfu 2.89 5.11 6.47 2.19 Coagulase negative staphylococci 6 - 10 cfu 0.79 0.42 1.57 0.31 Coagulase negative staphylococci 11-20 cfu 0.47 0.63 0.73 0.10 Coagulase negative staphylococci >20 cfu 2.10 6.78 5.11 2.19 Total coagulase negative staphylococci 6.25 12.93 13.88 4.80 Corynebacterium spp. 1 - 5 cfu 3.83 0.73 0.21 0.68 Corynebacterium spp. 6 - 10 cfu 3.62 0.63 0.31 0.26 Corynebacterium spp. 11-20 cfu 3.57 0.31 0.21 0.26 Corynebacterium spp. >20 cfu 24.09 1.15 1.77 0.57 Total Corynebacterium spp. 35.12 2.82 2.51 1.77 Key to Table 3.3: Dry - Drying off sample. 2 wk - Sample 8-14 days prior to calving. 1 wk - Sample 0-7 days prior to calving. Calving - Sample 0-7 days post calving, cfu – colony forming unit. Table 3.4. Quarters (n = 954) from which a bacterial species was isolated in the late dry –calving (LDC) period, but not at drying off. Quarters with bacteria isolated in the LDC period, but not at drying off Number of quarters % of LDC isolates STREPTOCCOCI Streptococcus dysgalactiae 5 100.0 Streptococcus uberis 37 97.4 STAPHYLOCOCCI Coagulase positive staphylococci 21 91.3 Coagulase negative staphylococci 203 91.0 GRAM NEGATIVE BACTERIA E. Coli 129 98.5 Enterobacter spp. 17 100.0 Klebsiella spp. 7 100.0 Citrobacter spp. 8 100.0 Serratia spp. 7 100.0 Corynebacterium spp. 20 36.4 69 The majority of bacterial species identified in the LDC period were cultured in only one of the three milk samples taken (Table 3.5, below). Coagulase positive and negative staphylococci were the bacteria most likely to be isolated in more than one milk sample during the LDC period and this occurred in 29.7% (73 / 246) quarters. Table 3.5. Quarters sampled at each point in the LDC period (n = 957) from which a bacterial species was isolated on one, two or three occasions. Bacterial species isolated once in LDC period Bacterial species isolated twice in LDC period Bacterial species isolated three times in LDC period STREPTOCCOCI Streptococcus dysgalactiae Number of quarters 3 1 1 % of quarters 0.31 0.10 0.10 Streptococcus uberis Number of quarters 27 8 3 % of quarters 2.83 0.84 0.31 STAPHYLOCOCCI Coagulase positive staphylococci Number of quarters 14 3 6 % of quarters 1.47 0.31 0.63 Coagulase negative staphylococci Number of quarters 159 53 11 % of quarters 16.67 5.56 1.15 GRAM NEGATIVE BACTERIA E. coli Number of quarters 113 16 2 % of quarters 11.84 1.68 0.21 Enterobacter spp. Number of quarters 12 4 1 % of quarters 1.26 0.42 0.10 Klebsiella spp. Number of quarters 6 1 0 % of quarters 0.63 0.10 0.00 Citrobacter spp. Number of quarters 6 1 1 % of quarters 0.63 0.10 0.10 Serratia spp. Number of quarters 5 2 0 % of quarters 0.52 0.21 0.00 CORYNEBACTERIUM SPP. Corynebacterium spp. Number of quarters 44 8 3 % of quarters 4.61 0.84 0.31 70 3.4.4. Patterns of bacterial isolates in the LDC period Kaplan Meier plots for isolates of E. coli, Strep. uberis and coagulase positive staphylococci are shown in Figure 3.1, below. The probability of isolating E. coli during the LDC period was greater than the probability of isolating Strep. uberis or coagulase positive staphylococci. Figure 3.1. Kaplan Meier survival plot, indicating the probability of remaining free from isolation of Strep. uberis (a), E coli (b) and coagulase positive staphylococci (c) during the late dry - calving period. . Results of the survival models are shown in Table 3.6, below. The hazard of isolating each bacterial species during the LDC period was significantly different between herds. Quarters of cows from Herds Three, Five and Six were at an increased hazard of isolation of E. coli, compared with Herd One. For Strep. uberis isolates, quarters of cows from Herds Four and Five were at a reduced hazard, compared with Herd One. For coagulase positive staphylococci isolates, quarters of cows from Herds Three, Four and Five (aggregated because of small numbers) were at a significantly reduced hazard, compared to Herd One. 0.7 0.75 0.8 0.85 0.9 0.95 1 -15 -13 -11 -9 -7 -5 -3 -1 1 3 5 7 Time with respect to calving (days) Survival function c a b 71 Month of calving had an impact on the hazard of isolating E. coli and coagulase positive staphylococci. Quarters from cows calving from June to February were at over twice the hazard of E. coli isolation compared with those calving from March to May. Quarters from cows calving from June to August were at increased hazard of coagulase positive staphylococcus isolation compared with those calving from March to May. There was greater between cow variance in the coagulase positive staphylococcus model than E. coli or Strep. uberis models (Table 3.6). This indicated that cows were more likely to have two or more quarters affected with coagulase positive staphylococci than the other bacteria. Log cumulative hazard lines for the survival model covariates were approximately parallel, suggesting the assumptions of proportionality of hazards was correct. Examples of posterior parameter kernal density plots from WinBUGS, are provided in Appendix 1. 72 Table 3.6. Models 3.1, 3.2 and 3.3: Cox Proportional Hazards models, using Markov Chain Monte Carlo, for survival of quarters (n = 957) to the first isolation of E. coli, Strep. uberis and coagulase positive staphylococci in the LDC period. Coefficient Hazard Ratio 95% C.I. for Hazard Ratio 2.5% 97.5% Model 3.1: Outcome is first E. coli isolate during the LDC period (n = 131) Herd 1 Reference Herd 2 0.95 0.35 2.56 Herd 3 2.71 1.15 6.64 Herd 4 1.24 0.54 3.02 Herd 5 3.00 1.37 7.07 Herd 6 3.29 1.54 7.56 Calving months March to May Reference Calving months June to August 2.60 1.33 5.31 Calving months September to November 3.00 1.55 6.03 Calving months December to February 2.39 1.18 4.98 Between cow variance 0.78 0.03 1.75 Model 3.2: Outcome is first Strep. uberis isolate during the LDC period (n = 38) Herd 1 Reference Herd 2 0.72 0.20 2.19 Herd 3 0.28 0.04 1.41 Herd 4 0.14 0.02 0.66 Herd 5 0.22 0.06 0.98 Herd 6 2.05 0.82 5.65 Parity > 3 Reference Parity 2 and 3 0.32 0.13 0.70 Between cow variance 0.83 0.00 3.35 Model 3.3: Outcome is first coagulase positive staphylococcus isolate during the LDC period (n = 23) Herd 1 Reference Herd 2 1.06 0.10 13.75 Herds 3, 4, and 5 0.01 0.00 0.14 Herd 6 0.14 0.01 1.10 Calving months March to May Reference Calving months June to August 15.55 1.15 198.66 Calving months September to November 2.22 0.18 28.42 Calving months December to February 8.94 0.48 293.27 Between cow variance 3.10 0.00 6.28 73 3.4.5. Associations between bacterial species The models of bacterial associations are shown in Tables 3.7 – 3.9, below. Having accounted for confounding variables, the probability of isolating E. coli in a milk sample significantly increased when Strep. uberis was cultured in a sample. No other bacteria were associated with isolation of E. coli. The presence of three bacterial species influenced the probability of isolating Strep. uberis. The risk significantly increased when E. coli and coagulase positive staphylococci were cultured in a milk sample but significantly decreased when Corynebacterium spp. were cultured. The likelihood of isolating Strep. uberis in a milk sample also significantly increased when Strep. uberis had been cultured in the previous sample. Similarly, the presence of three bacterial species affected the risk of isolating coagulase positive staphylococci. The probability significantly increased when Strep. uberis was cultured in a sample but significantly reduced when coagulase negative staphylococci or Corynebacterium spp. were cultured. The probability of isolating coagulase positive staphylococci in a milk sample also significantly increased when coagulase positive staphylococci was cultured in the previous sample. A diagrammatic representation of the associations identified between bacterial species in the GLMM is presented in Figure 3.2, below. Analysis of Pearson residuals suggested that these models were of adequate fit with the data, as shown in Figure 3.3 below. The fit of the E coli model (Model 3..4) was not as good as the other two models (mean of PR aggregates were further from zero), but no particular data points or groups of points were found to have a large influence on the model parameters. An example of a posterior parameter kernal density plot from WinBUGS is provided in Appendix 2. 74 Table 3.7. Model 3.4: Generalised linear mixed model with Bernoulli response variable being the presence of E. coli at any sample time (n = 236). Coefficient Odds Ratio 95% Credibility Interval 2.5% 97.5% Intercept -5.12 Farm 1 Reference Farm 2 0.59 0.26 1.29 Farm 3 1.49 0.74 3.01 Farm 4 0.96 0.50 1.86 Farm 5 2.47 1.34 4.59 Farm 6 2.52 1.37 4.74 Milk Sample at Drying Off Reference Milk Sample 8-14 days before calving 3.15 2.12 4.73 Milk Sample 0-7 days before calving 2.16 1.34 3.51 Milk Sample 0-7 days after calving 3.16 2.02 4.97 Calved March, April, May Reference Calved June, July, August 1.46 0.86 2.49 Calved September, October, November 1.95 1.17 3.29 Calved December, January, February 1.41 0.81 2.44 Parity > 3 Reference Parity 2 and 3 0.66 0.46 0.95 Strep. uberis not isolated in current milk sample Reference Strep. uberis isolated in current milk sample 4.98 2.46 9.96 Between cow variance 1.04 0.54 1.64 Between quarter variance 0.13 0.002 0.47 75 Table 3.8. Model 3.5: Generalised linear mixed model with Bernoulli response variable being the presence of Strep. uberis at any sample time (n =84). Coefficient Odds Ratio 95% Credibility Interval 2.5% 97.5% Intercept -4.64 Farm 1 Farm 2 0.29 0.08 1.02 Farm 3 1.15 0.37 3.44 Farm 4 0.45 0.15 1.34 Farm 5 0.26 0.07 0.88 Farm 6 1.67 0.66 4.45 Milk Sample at Drying Off Reference Milk Sample 8-14 days before calving 0.59 0.25 1.35 Milk Sample 0-7 days before calving 1.34 0.66 2.77 Milk Sample 0-7 days after calving 0.54 0.26 1.11 Parity > 3 Reference Parity 2 and 3 0.25 0.11 0.51 Strep. uberis not isolated in previous milk sample Reference Strep. uberis isolated in previous milk sample 5.33 1.87 14.37 E. coli not isolated in current milk sample Reference E. coli isolated in current milk sample 6.30 3.08 12.72 Corynebacterium spp. not isolated in current milk sample Reference Corynebacterium spp. isolated in current milk sample 0.28 0.09 0.73 CPS not isolated in current milk sample Reference CPS isolated in current milk sample 4.78 1.39 15.33 Between cow variance 2.20 0.94 4.21 Between quarter variance 0.22 0.001 1.03 76 Table 3.9. Model 3.6: Generalised linear mixed model with Bernoulli response variable being the presence of coagulase positive staphylococcus at any sample time (n = 83). Coefficient Odds Ratio 95% Credibility Interval 2.5% 97.5% Intercept -5.55 Farm 1 Reference Farm 2 0.74 0.17 2.94 Farm 3 0.63 0.13 2.81 Farm 4 0.03 0.00 0.24 Farm 5 0.18 0.03 0.84 Farm 6 0.22 0.04 0.97 Parity > 3 Reference Parity 2 or 3 0.35 0.12 0.93 Strep. uberis not isolated in current milk sample Reference Strep. uberis isolated in current milk sample 7.32 1.74 32.14 CNS not isolated in current milk sample Reference CNS isolated in current milk sample 0.03 0.001 0.29 Corynebacterium spp. not isolated in current milk sample Reference Corynebacterium spp. isolated in current milk sample 0.31 0.08 0.95 CPS not isolated in previous milk sample Reference CPS isolated in previous milk sample 5.41 1.37 17.73 Between cow variance 5.56 2.27 12.03 Between quarter variance 1.35 0.01 4.76 77 Figure 3.2. Diagramatic representation of the interactions between different bacterial species, identified from Generalised linear Mixed Models 3.4, 3.5 and 3.6. Complete arrows represent positive associations and dotted arrows represent negative associations. The numbers attached to each arrow indicate the change in probability (as the mean odds ratio) linked to each relationship. E coli Coagulase positive staphylococcus S uberis 6.30 4.98 7.32 4.78 Corynebacterium species 0.31 0.28 Coagulase negative staphylococcus 0.03 78 Figure 3.3. Pearson residual plots for generalised linear Models 3.4, 3.5 and 3.6. Model 3.4: Outcome is an E. coli isolate : Model 3.5: Outcome is an Strep. uberis isolate: -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 Residuals aggregated in ascending quintiles Mean Pearson Residual -2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Fitted value Pearson Residual -2 0 2 4 6 8 10 12 14 0 0.2 0.4 0.6 0.8 1 Fitted Value Pearson Residual 79 Model 3.6: Outcome is an coagulase positive staphylococcus isolate: -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 Residuals aggregated in quintiles in order of ascending fitted value Mean Pearson Residual -2 -1 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 Fitted Value Pearson Residual -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 Residuals aggregated in quintiles in order of ascending fitted value Mean Pearson Residual 80 3.5. Discussion There are three significant aspects to the findings in this chapter; the high prevalence of bacteria isolated, variations in isolation patterns and associations between different bacterial species. Nearly 25% of quarters and 40% of cows had a major mastitis pathogen isolated at least once, between 14 days before and 7 days after calving and a major mastitis pathogen was cultured from approximately 10% quarters at each sample time. This high prevalence occurred despite the use of antibiotic dry cow therapy in all cows and is significant because it has been shown that bacteria present in the dry period have deleterious effects on the subsequent health and production of the cows (Smith et al., 1968; Oliver and Sordillo, 1988; Green et al., 2002). The prevalence of major pathogens approximately doubled between drying off and the end of the dry period, this was largely caused by an increase in E. coli and Strep. uberis. This increase in prevalence, and the fact that most isolates identified during the LDC period were not found at drying off (Table 4), suggest many LDC isolations were new intramammary infections and not carried over from the previous lactation. This concurs with other studies that reported that new infections during the dry period were common (Oliver and Mitchell, 1983; Smith et al., 1985). This research identified large differences in patterns of bacterial isolates between farms and between cows calving in different months. This implies that environmental conditions and management systems may influence the force of infection. Precise knowledge of these factors may reduce dry period infections and thereby improve cow health and productivity. Recent UK research has shown that the use of internal teat sealants may play a role to reduce new dry period infections (Berry and Hillerton, 2002; Huxley et al., 2002). The high prevalence of dry period bacterial isolates is broadly similar to two studies conducted in the USA. One, a 40 cow study (Oliver and Mitchell, 1983) reported the quarter prevalence of major pathogens to be 3.8% at drying off , 15.6% before calving and 10.6% in early lactation. The second involved 160 cows without the use of antibiotic dry cow therapy (Oliver, 1988), and the quarter prevalences of major pathogens at drying off, before calving and after calving were 4.5%, 19.1% and 9.1% respectively. However, in these two studies, the most prevalent bacteria were Streptococcus spp. (other than Strep. agalactiae) followed by coliforms, whereas in the current study coliforms were most prevalent, followed by Streptococcus spp. Results in this chapter identified that some bacterial species had either synergistic or inhibitory influences on the presence of other species. This was particularly evident in the models of coagulase positive staphylococcus and Strep. uberis, in which several different 81 species influenced the probability of isolating these organisms. The reasons why one bacterial species increased the probability of isolating another species, may be that some quarters were simply prone to bacterial invasion, as discussed in Chapter Two. This could explain associations between the opportunist pathogens, Strep. uberis and E. coli. Another possibility is that in certain conditions, some combinations of micro-organisms co-exist as an ecological unit within the quarter or that there is synergy between organisms. That is, infection with one predisposes to or allows infection with another. Positive interactions between bacteria have been suggested, for example, in bacterial vaginosis in women when it is thought that a complex network of interactions may occur before establishment of disease (Pybus and Onderdonk, 1999). The risk of isolating either Strep. uberis or coagulase positive staphylococci was significantly reduced, when Corynebacterium spp. were isolated in a milk sample. This may explain why Corynebacterium spp. were associated with reduced risk of clinical mastitis in the previous Chapter; because they were associated with a decreased risk of major pathogen infections during the dry period. The risk of isolating coagulase positive staphylococci also decreased when coagulase negative staphylococci were isolated. Previous studies have reported a protective influence of these minor pathogens on major pathogen infection during lactation (Rainard and Poutrel, 1988; Mathews et al., 1991; White et al., 2001), but this has not been reported previously during the dry period. The negative association between coagulase positive and negative staphylococci needs to be interpreted with care. Although differences between gross colony features on blood agar may be clear (such as pigmentation, colour and zones of haemolysis), this is not always the case. Therefore, it is possible that on some occasions when both coagulase negative and positive staphylococci were present, they could not be differentiated on gross morphology and only one species was carried forward for identification. This would lead to an overestimate of the protective influence of coagulase negative staphylococci on coagulase positive staphylococci. If the presence of minor pathogens does reduce the likelihood of major pathogen infection, this may provide a route to reduce major pathogen infections during the dry period, and their consequences. Clarification is required in this area, however, because Corynebacterium spp. have also been reported to be associated with increased susceptibility to mastitis in some circumstances (Hogan et al., 1988; Berry and Hillerton 2002). Ecological interactions between bacterial species are probably complex. It is likely that intramammary infection and clinical outcome are to some extent determined by cow and bacterial factors, as well as environmental and management systems. More information is needed to understand the roles of each and their interactions. However, such interactions as those demonstrated here 82 have been shown, theoretically, to potentially confound attempts to control intra-mammary infection and mastitis (White et al, 2001). In most statistical models, increased parity was associated with an increased risk of bacterial isolation. Increasing parity has been reported previously as a risk factor for new dry period infections (Ward and Shultz, 1974; Oliver, 1987;) and this suggests that anatomical or intramammary defence mechanisms deteriorate with age. Bacterial identification in this study was carried out using recommended methods for bovine mastitis (National Mastitis Council, 1999) but a limitation of the data was that some bacteria were only identified to genus level. For example, over 95% of coagulase positive staphylococci in bovine milk have been reported to be Staph. aureus but Staphylococcus intermedius and Staphylococcus hyicus may have been responsible for some infections (Capurro et al., 1999). Therefore, although interactions were found between bacteria, the exact species involved was not always known. Despite a variety of research studies that have reported that dry period bacterial intramammary infections have a detrimental effect on the health and production of cows, our results suggest that in commercial UK dairy herds, there remains an important risk from bacterial intramammary infection in the dry period. Further studies on farm, cow and bacterial factors that influence this risk would be beneficial to the UK dairy industry. 83 Chapter 4: Somatic Cell Concentrations in Milk Protect and Predict Clinical Mastitis 4.1. Chapter summary The relationship between somatic cell concentrations in milk and subsequent, naturally occurring, clinical mastitis in dairy cows was investigated. Data originated from a prospective study carried out on three commercial dairy herds in south-west England. Milk samples from four quarters of all cows were collected to measure quarter somatic cell counts (QSCC) at approximately monthly intervals, for 12 months, using a standardised electronic counting procedure. Clinical mastitis was identified by trained herdsmen. Two methods of analysis were used. Firstly, cows with clinical mastitis were selected and a matched analysis used to make a comparison between affected and unaffected quarters of the same cow. For the second analysis, all cows in the herds were used and quarters with and without clinical mastitis compared using a Bayesian generalized linear mixed model. The results of both within cow and between cow analysis identified that quarters with a QSCC in the range 41 – 100,000 cells/ml had the lowest risk of clinical mastitis during the next month. Quarters with a QSCC > 200,000 cells/ml were at the greatest risk of clinical mastitis in the next month. There was a reduced risk of clinical mastitis between one and two months later in quarters with a SCC of 81,000 – 150,000 cells/ml compared with quarters above or below this level. The between cow analysis identified a further reduced risk of clinical mastitis between two and three months later in quarters with a QSCC 61,000 – 150,000 cells/ml, compared to other quarters. It appears that low concentrations of somatic cell in milk are associated with increased risk of clinical mastitis, and that high concentrations are indicative of immunological mobilisation against infection. These two processes combine to produce an apparent protective effect of intermediate leukocyte concentration. The variation in risk 84 between quarters of affected cows suggests that local quarter immunological events, rather than solely whole cow factors, have an important influence on the risk of clinical mastitis. Elucidating the immune mechanisms behind these findings, may be of great benefit in the future prevention of clinical mastitis. 4.2 Aims This chapter presents further analysis of the data examined by Peeler et al. (2003). The hypothesis that a low concentration of leukocytes in milk (measured as the somatic cell count) is associated with an increased risk of clinical mastitis in dairy cows, was further investigated. The particular aim was to investigate whether the level of QSCC influenced the risk of naturally occurring clinical mastitis in the next four months. 4.3 Materials and methods Data collection has been recently described (Peeler et al., 2003). 4.3.1 Herd selection Three commercial dairy herds participated in the study, each with 120 to 180 Holstein/Friesian cows. Herds were selected on location (south-west England) and owner compliance. The incidence rate of clinical mastitis during the study period was 55 quarter cases per 100 cow years. The monthly bulk milk SCC ranged from 60,000 cells/ml to 200,000 cells/ml. All three herds grazed grass from April to October and were housed for the remaining months in either straw-bedded cubicles or straw yards. Annual herd milk yields ranged from 6000 to 7500kg per cow. 4.3.2 Milk samples and clinical mastitis Quarter milk samples were collected at a morning milking by Dr Edmund Peeler, approximately monthly, for 12 months, starting in February 1999. Following routine teat preparation by the herdsman, the teats were dry wiped with an individual paper towel and the first three strippings of foremilk discarded. A 30 ml sample of milk was taken into a universal tube containing the preservative 2-bromo-2-nitropropane-1,3-diol (Bronopol, Knoll, Ludwigschafen, Germany). Milk samples were identified by quarter and cow and submitted to an accredited, commercial company (On Merit, Newbury, Berkshire, UK) for automatic somatic cell counting. The electronic cell counter was standardised using recognised European cell count standard samples (Centre D’etude et de controle des analyses en industrie laitiere, France) and checked for re-calibration after every 20 measurements. 85 Clinical mastitis was identified by trained herdsmen on each farm on the basis of visual changes to the milk (clots or watery secretion) or changes to the mammary gland (heat, redness, swelling). An aseptic milk sample was taken, by the herdsman, for bacterial culture from cases of clinical mastitis, before treatment. The samples were frozen (-180C) and submitted to an accredited laboratory (Veterinary Laboratories Agency, Langford, Bristol, UK) for bacteriological culture, within 5 weeks of collection. Milk samples (0.01ml milk per plate) were cultured on blood, Edwards and MacConkeys agar. The plates were incubated for 24 hours at 370C and if no growth was found, incubation continued for a further 24 hours. A sample of milk was also incubated separately for 6 hours, and if there was no growth from the original sample, the incubated milk was cultured. Bacterial species were identified using recommended techniques, as described in Chapter Two. Herds were visited by the author fortnightly throughout the period of data collection as a part of a routine health/fertility program. Health and fertility data were recorded on all the herds at Orchard Veterinary Group (Wirrall Park, Glastonbury) and stored in the DAISY software programme. Information for each cow was extracted from the veterinary computer records, such as calving dates and clinical mastitis history. 4.3.3 Data analysis Initial data entry was performed using Microsoft Access (Microsoft Corp, USA). Univariable analysis was carried out using Microsoft Excel 2000 (Microsoft Corp. USA) and modelling using EGRET (Vs 2.0.3, Anon, 1999), MLwiN (Vs 1.10.0007, Rasbash et al., 1999) and WinBUGS (Vs 1.3, Spiegelhalter et al., 2000). Two methods of analysis were used, retrospectively. Firstly patterns of QSCC were investigated in quarters of cows with clinical mastitis and a comparison made between affected and unaffected quarters within cows. Using this matching procedure, cow factors, such as parity, stage of lactation, season, systemic immune function and nutritional status were controlled for implicitly (Model 4.1). Secondly patterns of QSCC were compared in quarters of all cows, with and without clinical mastitis, whilst controlling for the autocorrelation structure of QSCC, within and between quarters and cows. MCMC with Gibbs sampling was again used to obtain parameter estimates (Model 4.2). 4.3.4. Model 4.1 – Conditional logistic regression analysis Quarters that had clinical mastitis were case quarters and the unaffected quarters of the same cow at the same time, were their matched controls. When a cow had a second case of clinical mastitis, this was defined as a new matched ‘risk set’ of quarters. A second case of 86 clinical mastitis was identified when it occurred greater than seven days after the first case and also after the next monthly QSCC reading, so as not to replicate the data point. QSCC in quarters before clinical mastitis were compared with QSCC in unaffected quarters over four consecutive monthly readings. The consecutive monthly QSCC readings were labelled as times m = -1 (QSCC in the monthly reading before clinical mastitis), m = -2 (QSCC in the monthly reading before m = -1), m = -3 (QSCC in the monthly reading before m = -2), and m = -4 (QSCC in the monthly reading before m = -3). When QSCC readings were not available, because clinical mastitis occurred too soon after calving, those that were available were used, and earlier months were recorded as missing. Quarters with clinical mastitis and no QSCC reading after calving, were omitted (n = 67). QSCC were initially grouped into the following nine categories (000’scells/ml); 0 - 20, 21 - 40, 41 - 60, 61 - 80, 81 – 100, 101 - 150, 151 - 200, 201 – 400 and >400. Conditional logistic regression using relative (multiplicative) risk was used (Hosmer and Lemeshow, 1989; Anon, 1999), with the occurrence of clinical mastitis as a binary outcome (present or absent). All nine categories of QSCC at the four recordings before clinical mastitis were modelled as categorical variables and these were combined into three groups in the final model, on the basis of similar odds of clinical mastitis. The mean, median, standard deviation and coefficient of variation (standard deviation / mean) of the previous two, three and four SCC readings, were also explored as covariates. Model construction was exploratory and covariates were left in the model when there was a significant reduction in deviance, computed from a likelihood ratio statistic of p = 0.05. Quarter position (ie. right hind, left hind, right fore, or left fore) was included as a fixed covariate when this was found to confound the relationship between QSCC and clinical mastitis (Hosmer and Lemeshow, 1989). Interactions between covariates were tested and were left in the model when there was a significant improvement in the likelihood ratio statistic (p = 0.05). The logistic model was specified in conventional form: pij = (exp (aj + x’ ij ß )) / (1 + exp (aj + x’ ij ß )) (4.1) where pij was the fitted probability that quarter i in matched set j developed mastitis, aj was the baseline effect in the jth matched set of quarters. x’ ij was the (transposed) column vector of p covariates (x1…….xp). ß was the column vector of unknown regression coefficients associated with the covariates (ß1…….ßp). 87 Scientific interest focused on estimating the ß vector representing the loge(odds ratio) associated with each covariate, and because model fitting was based upon the conventional conditional likelihood (Clayton and Hills, 1993), the baseline effects within matched sets cancelled out of the calculation. Model fit was judged by assessment of Pearson residuals and patterns of delta betas for each covariate, (McCullagh and Nelder, 1989, Anon, 1999). The data were re-analysed with points producing large positive and negative delta betas omitted, to investigate whether parameter estimates were changed by their omission. 4.3.5. Model 4.2 - Analysis of quarters in all cows QSCC in quarters before clinical mastitis were compared with QSCC in all quarters without clinical mastitis over a four month period. Monthly QSCC readings of all cows were labelled as times m = -1 to m = -4, as for Model 4.1. When QSCC readings were not available, because clinical mastitis occurred too soon after calving, those that were available were used, and earlier months were modelled as a category ‘dry’. Quarters with clinical mastitis and no QSCC reading after calving were not used in analysis. Modelling was based upon a Bayesian generalised linear mixed model (GLMM) (Breslow and Clayton, 1993; Burton et al., 1999) with clinical mastitis as a binary response variable. The hierarchical model structure reflected variation between repeated measures of QSCC within quarter over time (level 1), between quarters within cow (level 2) and between cows (level 3). Model exploration was performed with the QSCC categories and patterns, as described for Model 4.1. Categories were combined in the final model based on a similar risk (odds) of clinical mastitis. The fixed covariates farm, parity, quarter position, month of lactation and month of year were tested to control for their possible confounding influence in the model. Parameter estimates were obtained using MCMC with Gibbs sampling in WinBUGS (Vs 1.3, Spiegelhalter et al., 2000), as described in Chapter One. The GLMM for the Bernoulli response was specified in a standard manner (Zeger and Karim, 1991; Burton et al., 1999) as: logit(µijk) = a + ß’1ijkX1ijk + ß’2jkX2jk + ß’3kX3k + vk + ujk (4.2) Clinical mastitisijk ~ Bernoulli distribution (µijk) where 88 the subscripts i, j and k denote the ith QSCC reading, the jth quarter and the kth cow respectively. Clinical mastitisijk = the binary response variable [1 = Clinical mastitis, 0 = not Clinical mastitis] denoting response in the period following the ith QSCC reading in the jth quarter of the kth cow. µijk = the fitted probability of clinical mastitis following QSCC reading i in quarter j of cow k. a = regression intercept X1ijk = vector of covariates associated with QSCC reading i of quarter j of cow k. ß’1ijk = vector of coefficients for X1ijk. X2jk = vector of quarter-level exposures for quarter j of cow k. ß’2jk = vector of coefficients for X2jk. X3k = vector of cow-level exposures for cow k. ß’3k = vector of coefficients for X3k. vk = random effect reflecting residual variation between cows. ujk = random effect reflecting residual variation between quarters, within cows. Modelling strategies and convergence have been described in Chapter One. Chains were run for 70,000 iterations each after burn in and the posterior means and credibility intervals of parameters were derived from these iterations. The model parameter distributions were assessed using kernel density plots. Model fit was assessed using Pearson residuals as described in Chapter One. Outlying points were investigated to discover if they were associated with any particular covariate pattern and if they had an important influence on covariate coefficients. 4.4. Results A total of 12,696 QSCC readings were used from 446 cows. Sixty-seven cases of clinical mastitis occurred before the first QSCC recording of lactation and therefore were not available for modelling. One hundred and twenty two cases of clinical mastitis were used in the models and the distribution of these cases during lactation is presented in Figure 4.1, below: 89 Figure 4.1. The occurrence of clinical mastitis during lactation in quarters used for models of QSCC (n =122). Results of bacterial culture have been reported previously (Peeler, 2001). Over 50% of clinical cases were caused by E. coli (n = 42) or Strep. uberis (n = 24). Less than 5% of the other cases of clinical mastitis were associated with any one pathogen. Figure 4.2, below, illustrates the proportion of quarters with clinical mastitis at different levels of QSCC, for four consecutive monthly QSCC readings. 0 5 10 15 20 25 30 1 2 3 4 5 6 7 8 9 10 11 Month of lactation in which clinical mastitis occurred Number of cases 90 Figure 4.2. Bar charts a, b, c and d illustrate univariable analysis of the proportion of quarters with clinical mastitis in different categories of QSCC: a. Risk of clinical mastitis 0 – 1 month after the QSCC reading b. Risk of clinical mastitis 1 - 2 month after the QSCC reading 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 0-20 21-40 41-60 61-80 81-100 101- 150 151- 200 201- 400 >400 Quarter somatic cell count at m -1 % Quarters with clinical mastitis 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 0-20 21-40 41-60 61-80 81- 100 101- 150 151- 200 201- 400 >400 Quarter somatic cell counts at m -2 % Quarters with clinical mastitis 91 c. Risk of clinical mastitis 2 - 3 month after the QSCC reading d. Risk of clinical mastitis 3 - 4 month after the QSCC reading 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 0-20 21-40 41-60 61-80 81-100 101- 150 151- 200 201- 400 >400 Quarter somatic cell counts at m -3 % Quarters with clinical mastitis 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 0-20 21-40 41-60 61-80 81-100 101- 150 151- 200 201- 400 >400 Quarter somatic cell counts at m -4 % Quarters with clinical mastitis 92 4.4.1. Model 4.1: Conditional logistic analysis On four occasions, two quarters from one cow got mastitis simultaneously. On each occasion, both quarters were defined as case quarters and matched with the two unaffected quarters as controls – this is dealt with appropriately in the conditional likelihood. QSCC were initially modelled in the nine specified categories and after initial model exploration, based on similar risk of clinical mastitis, the categories were grouped as: At m = -1 - QSCC categories (per ml): = 40,000, 41,000 - 100,000, > 100,000. At m = -2 - QSCC categories (per ml): = 80,000, 81,000 – 150,000, > 150,000. At m = -3 - QSCC categories (per ml): = 60,000, 61,000 – 150,000, > 150,000. At m = -4 - QSCC categories (per ml): = 60,000, 61,000 – 150,000, 101,000 – 200,000, >200,000. The distributional descriptors of SCC (mean, median, standard deviation and coefficient of variation) did not remain in the model. Results of the conditional logistic regression (Model 4.1) are presented in Table 4.1, below. Quarters with QSCC 41,000-100,000 cells/ml, had a reduced risk of clinical mastitis at m = -1, compared with QSCC = 40,000 cells/ml (OR = 0.31, 95% confidence intervals = 0.10 – 0.96). Conversely, at m = -1, quarters with QSCC >100,000 cells/ml, had an increased risk of clinical mastitis (OR = 2.16, 95% confidence intervals = 1.06 - 4.40), compared with QSCC = 40,000 cells/ml. Quarters with QSCC 81,000 – 150,000 cells/ml, had a reduced risk of clinical mastitis at m = -2, compared with QSCC = 80,000 cells/ml. Analysis of delta-betas and Pearson residuals were consistent with a good model fit. The plots of Pearson residuals are presented below (Figure 4.3) and the graphs of deltabetas are provided in Appendix 3. No outlying values were found to have an important biological effect on the model. 93 Table 4.1. Model 4.1: Conditional logistic regression model for clinical mastitis. All cows selected had clinical mastitis, and unaffected quarters were matched with mastitic quarters within cow, at the time of a clinical case. Variable Odds Ratio 95% C.I. Lower-Upper LRS .2 p-value Number matched sets used = 78. Response variable – Quarter with clinical mastitis = 1, without clinical mastitis = 0. Left front quarter Reference category Right front quarter 0.39 0.17 0.90 0.01 Left hind quarter 1.03 0.54 1.95 Right hind quarter 1.19 0.64 2.22 M = -1 QSCC <40,000 cells/ml Reference category M = -1 QSCC 41-100,000 cells/ml 0.31 0.10 0.96 <0.01 M = -1 QSCC >100,000 cells/ml 2.16 1.06 4.40 <0.01 M = -2 QSCC <80,000 cells/ml Reference category M = -2 QSCC 81 -150,000 cells/ml 0.15 0.03 0.79 <0.01 M = -2 QSCC > 150,000 cells/ml 1.00 0.38 2.68 Key to Table 4.1: C.I. – confidence interval, LRS .2 p-value - Likelihood ratio statistic significance probability, QSCC – quarter somatic cell count, M = -1 – QSCC in the month before risk of clinical mastitis, M = -2 – QSCC between one and two months before risk of clinical mastitis. Figure 4.3. Graphs of Pearson Residuals for Model 4.1: a. Pearson residuals plotted against fitted values, and b. Aggregates of Pearson residuals in ascending quintiles plotted against fitted values. a. -3 -2 -1 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 Fitted Value Pearson Residual 94 b. 4.4.2. Model 4.2: Analysis of quarters in all cows Following initial model exploration, quarters were aggregated into the following QSCC categories; At m = -1 - QSCC categories (per ml) : = 40,000, 41,000- 100,000, 100 –150,000, 151 – 200,000, > 200,000. At m = -2 - QSCC categories (per ml) : = 80,000, 81,000 - 150,000, > 150,000, 'dry'. At m = -3 - QSCC categories (per ml) : = 60,000, 61,000 – 150,000, > 150,000, 'dry'. At m = -4 - QSCC categories (per ml) : = 60,000, 61,000 – 150,000, 101 – 200,000, > 200,000, 'dry' The distributional descriptors of SCC (mean, median, standard deviation and coefficient of variation) did not remain in the model. The final model (Model 4.2) is presented in Table 4.2, below and the WinBUGS code for this model is provided in Appendix 4. Since the stage of lactation was missing / misrecorded for 59 data points, the number of QSCC readings used in the final model was 12637. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 Residuals aggregated into ascending quintiles Mean Pearson Residual 95 Table 4.2. MODEL 4.2: Bernoulli GLMM of clinical mastitis using MCMC with Gibbs sampling. Variable Coefficient Odds Ratio 95% Credibility Interval lower upper Response variable – Quarter with clinical mastitis = 1, without clinical mastitis = 0 n - QSCC = 12637, n – clinical mastitis = 122 Intercept value -5.20 Farm 1 Reference Farm 2 0.39 0.21 0.70 Farm 3 1.15 0.77 1.73 Right hind quarter Reference Left hind quarter 0.94 0.60 1.49 Right fore Quarter 0.39 0.21 0.70 Left fore quarter 0.71 0.43 1.17 DIM 0-30, 61-90, >150 Reference DIM31-60 2.46 1.37 4.38 DIM 91-120 2.49 1.37 4.35 DIM 121-150 1.96 1.01 3.63 M = -1 QSCC < 41,000 cells/ml Reference M = -1 QSCC 41 – 100,000 cells/ml 0.42 0.16 0.94 M = -1 QSCC 100 - 150,000 cells/ml 0.96 0.29 2.51 M = -1 QSCC 151-200,000 cells/ml 1.64 0.49 4.38 M = -1 QSCC > 200,000 cells/ml 4.12 2.55 6.56 M = -2 QSCC < 81,000 cells/ml Reference M = -2 QSCC 81 – 150,000 cells/ml 0.23 0.04 0.90 M = -2 QSCC > 150,000 cells/ml 0.92 0.49 1.69 M = -2 QSCC dry 1.95 1.10 3.51 M = -3 QSCC < 61,000 cells/ml Reference M = -3 QSCC 61 – 150,000 cells/ml 0.25 0.04 0.98 M = -3 QSCC > 150,000 cells/ml 0.46 0.17 1.22 M = -3 QSCC dry 1.19 0.64 2.51 Between cow variance 0.12 0.00 0.59 Between quarter variance 0.11 0.001 0.70 Key to Table 4.2: DIM - days in milk, QSCC – quarter somatic cell count, M = -1 – QSCC in the month before risk of clinical mastitis, M = -2 – QSCC between one and two months before risk of clinical mastitis, M = -3 – QSCC between two and three months before risk of clinical mastitis. 96 Kernel densities for the model parameters were Normally distributed (see Appendix 4). Having accounted for the effect of farm, time of year, stage of lactation, position of quarter and the effects of clustering of QSCC readings, the level of QSCC systematically influenced the risk of clinical mastitis for the following three months. The relationship between QSCC and clinical mastitis is summarised below in Figure 4.4: Figure 4.4. Summary of the relationship between quarter somatic cell count and the risk of clinical mastitis, over a three month period, calculated from Model 4.2. Shaded cells were significantly different to the reference category within each column. Quarter somatic cell count category Odds of clinical mastitis in the next month (m = -1) Odds of clinical mastitis between one and two months later (m = -2) Odds of clinical mastitis between two and three months later (m = -3) = 40,000 cells/ml 1.00 (reference) 41,000-60,000 cells/ml 1.00 (reference) 61,000-80,000 cells/ml 1.00 (reference) 81,000-100,000 cells/ml 0.42 101,000-150,000 cells/ml 0.96 0.23 0.25 151,000-200,000 cells/ml 1.64 > 200,000 cells/ml 4.12 0.92 0.46 Variation in the underlying risk of clinical mastitis between quarters within cows (variance = 0.11) was similar to that between cows (variance = 0.12). However, the mixing of Markov Chains for the random effect variances was poor (i.e. chains moved unevenly through the parameter space, (Gilks et al., 1995)). The techniques used to investigate this problem were described in Chapter One, and these suggested that the final parameter estimates were robust. A graph illustrating the Pearson residuals plotted against fitted value and means of deciles of the Pearson residuals in categories in ascending fitted value are shown below (Figure 4.5). The groups of residuals approximated to zero and showed no systematic relationship with fitted value. This was consistent with a good model fit. A discussion of Bernoulli residual analysis, using this Model 4.2 as an example, is given in Chapter Seven. 97 Figure 4.5. Graphs of Pearson Residuals for Model 4.2: a. Pearson residuals plotted against fitted values, and b. Aggregates of Pearson residuals in ascending quintiles plotted against fitted values. a. b. -5 0 5 10 15 20 25 0 0.05 0.1 0.15 Fitted Value Pearson residual -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 Aggregated groups (of equal sizes) in order of ascending fitted values Mean of aggregated Pearson residuals 98 4.5. Discussion This chapter focused on the relationship between quarter somatic cell concentration in milk and the risk of subsequent clinical mastitis. Findings indicate that intermediate levels of QSCC resulted in the lowest risk of clinical mastitis. This was true both when a comparison was made between quarters of all cows in the study and also when only the quarters of cows that got mastitis were compared. Explanation of this result may be twofold. First, either leukocytes in milk themselves provide protection against clinical mastitis, or they may be associated with other unknown factors that reduce the risk of clinical mastitis. It is possible that a larger resident population of macrophages and neutrophils in the uninfected mammary gland milk is advantageous to impede bacterial multiplication in the first hours of infection, before leukocyte migration commences. This is consistent with the actions of these cells because both types non-specifically phagocytose invading bacteria (Sordillo et al., 1997). It is also possible that the presence of leukocytes in the mammary gland increases the speed of additional neutrophil recruitment (van Werven, 1999) or is associated with other immune events. Consequently, low leukocyte concentration is likely to result in increased susceptibility to infection. Second, it is not surprising that quarters with QSCC > 200,000 cells/ml were found to have an increased risk of clinical mastitis in the next month (Model 4.2). It has been established that QSCC > 200,000 cells/ml are usually indicative of bacterial infections with major pathogens (Brolund, 1985; Schepers et al., 1997). Therefore these quarters are likely to be at increased risk of clinical mastitis because the raised QSCC either represents the early stages of an infection, or it represents a sub-clinical infection that may recrudesce and become a clinical case. So the apparent protective effect of intermediate leukocyte concentration may be a consequence of two processes that show both low and high leukocyte concentrations as increasing risk of clinical mastitis: one because immunological cells are protective and one because immunological cells are a marker of infection. The results also suggest that local quarter immune factors exert an important influence on the risk of clinical mastitis. This was particularly clear from the distinct differences in QSCC found between quarters of cows with clinical mastitis. The differences in leukocyte concentration between quarters could be caused by environmental components, such as variation in previous bacterial challenge. It has been reported that intramammary infection with the minor pathogen Corynebacterium bovis can lead to an average increase in QSCC of approximately 40,000 cells/ml (LeVan et al., 1985) and also that minor pathogens can reduce 99 the risk of clinical mastitis (Rainard and Poutrel, 1988; Lam et al., 1997; White et al., 2001; Green et al., 2002). This may be a link between QSCC and reduced risk of clinical mastitis. The findings in this chapter contrast with another longitudinal, observational study of QSCC, that reported no change in risk of clinical mastitis from low QSCC in the month before clinical mastitis (Zadoks et al., 2001). There were important differences between the two field studies. In the research reported by Zadoks et al (2001), the three herds used had herd bulk milk SCC in the range 200,000-300,000 cells/ml. In contrast, herds in this study were 80,000-200,000 cells/ml during the study period. Given these findings, there may have been relatively few quarters in the Zadoks et al (2001) study that were in the lowest SCC categories and this could have prevented detection of the effect we found. This raises the issue that herds with different bulk milk SCC are likely to have different patterns of cow and quarter SCC within the herd, and therefore have different proportions of quarters and cows in each risk category. This phenomenon has been described previously (Beaudeau et al., 2002). Also in the present study, the majority of clinical mastitis was caused by E. coli and Strep. uberis, whereas in the study reported by Zadoks et al (2001), Strep. uberis or Staph. aureus were the pathogens encountered. There could be pathogen differences in the influence of QSCC on clinical mastitis. A final difference between these two studies was the statistical approach used. The use of MCMC with Gibbs sampling prevented the problems found previously with non-convergence (Zadoks et al., 2001) and allowed correlations at each hierarchical level of the data to be accounted for. The study by Beaudeau et al (2002) reported that the incidence of clinical mastitis in 121 French herds increased as the proportion of cows with a CSCC > 250,000 cells/ml or < 50,000 cells/ml increased. Therefore the proportion of quarters in these herds with high and low QSCC would also have increased as incidence of clinical mastitis increased, and this agrees with the findings of this research. These results, and the findings of previous experimental studies are entirely consistent with the hypothesis that quarters with lower levels of leukocyte concentrations in milk are at an increased risk of developing infection leading to clinical mastitis. High QSCC are indicators of infection, so that they predict mastitis in the next month. The consequence is that quarters with intermediate QSCC are least likely to develop mastitis, because they have a higher level of protection, but are uninfected. The results suggest that the somatic cell concentration in milk acts as both an indicator of and protector against infection (Figure 4.6, below). Consequently, a continued industry drive towards reduction in SCC could increasingly result in enhanced susceptibility to mastitis in individual quarters and cows. 100 Figure 4.6. Schematic representation of the hypothesis: Reduced quarter somatic cell count (QSCC) is causally related to increased risk of acquiring an infection (continuous line). Increased QSCC is indicative of a current infection (dashed line). The combination of these two processes results in the risk of clinical infection (dotted line) being lowest for intermediate levels of QSCC. = Likelihood of clinical mastitis in next month because of presence of infection = Risk of establishment of infection and therefore clinical mastitis (i.e. vulnerability) = Apparent risk of mastitis in next month as a combination of real risk of future infection and consequence of current infection QSCC Risk of clinical mastitis 101 Chapter 5: Variance components of quarter somatic cell counts in three commercial dairy herds 5.1. Chapter summary Patterns of quarter somatic cell counts (n = 12696) were investigated in the three commercial dairy herds described in Chapter Four, to examine variance components and movements between different cell count levels. Following univariable analysis, generalised linear mixed models (GLMM) of log transformed QSCC were constructed and parameters estimated using MCMC. Significant variation in QSCC occurred with quarter position, parity of cow, month of lactation, month of year, the occurrence of clinical mastitis and an interaction between parity and month of lactation. Most residual variation occurred between readings within quarters, rather than between quarters or between cow. Movements of quarters between nine ascending categories of QSCC was investigated using a transition matrix and a GLMM of QSCC changes. Most QSCC readings were in the lowest QSCC categories (0 - 40,000 cells/ml) and the majority remained in this range at the next monthly recording. There was also evidence of stability in the middle and high ranges of QSCC between consecutive monthly recordings. This is relevant following the findings from Chapter Four. It may explain why quarters were at reduced risk of clinical mastitis for up to three consecutive months; because the low risk quarters were more likely to remain in the intermediate low risk QSCC categories for clinical mastitis over time, compared to other quarters. 5.2. Introduction In the previous chapter, the level of quarter somatic cell count (QSCC) was found to be associated with the subsequent risk of clinical mastitis. Somatic cell counts are generally measured for individual cows rather than quarters (in a milk sample pooled from all four quarters), and relatively little research has been conducted on quarter SCC. It is possible that in the future, as rapid diagnostic techniques improve, individual quarter somatic cell counts 102 will be measured during the milking process and therefore understanding the dynamics of QSCC will become important. The dynamics and variability of quarter somatic cell counts have not been investigated in detail in UK dairy herds. The aims of this chapter were: • To describe patterns of QSCC in three commercial UK dairy herds. • To assess variance components for QSCC, including the apportionment of variation within quarters, between quarters and between cows. • To investigate movements of QSCC, with reference to how quarters move in and out of the risk categories identified in Chapter Four. 5.3. The data Sample collection and QSCC estimation were described in Chapter Four. Over 13,000 QSCC samples were collected in a one year period but 12696 QSCC records carried sufficient detail (e.g. cow details such as parity and month of lactation) to be useful for analysis. A log (base 10) transformation was made of QSCC to convert the data to an approximately Normal distribution, as previously suggested for SCC records (Ali and Shook, 1981). The transformation was assessed visually using a kernal density plot. 5.4. Variance components of QSCC: Descriptive and univariable analysis 5.4.1. Denominators QSCC readings (n = 12696) were analysed from 1783 quarters of 446 cows. The number of QSCC recordings, divided by farm, taken from each quarter, cow, month of lactation, month of year and parity of cow are shown below (Tables 5.1 to 5.4): Table 5.1. The number of cows, quarters and QSCC readings grouped by farm. Farm Number cows Number quarters sampled Number QSCC samples 1 153 667 4379 2 126 504 3452 3 167 612 4865 Totals 446 1783 12696 103 Table 5.2. The number of QSCC readings obtained from each farm grouped by month of lactation. Farm Lactation Month 1 2 3 4 5 6 7 8 9 >10 Unrecorded Total 1 373 477 439 434 422 406 415 416 338 630 29 4379 2 393 368 356 343 299 296 294 327 304 464 8 3452 3 409 440 431 435 440 394 423 456 462 953 22 4865 Total 1175 1285 1226 1212 1161 1096 1132 1199 1104 2047 59 12696 Table 5.3. The number of QSCC readings grouped by month of sampling. Farm Month of Year (1 = January, 12 = December) 1 2 3 4 5 6 7 8 9 10 11 12 Total 1 390 402 396 417 396 412 378 384 379 0 410 415 4379 2 303 316 316 318 292 277 330 345 0 340 329 286 3452 3 441 785 824 391 373 370 0 390 409 463 419 0 4865 Total 1134 1503 1536 1126 1061 1059 708 1119 788 803 1158 701 12696 Table 5.4. The number of QSCC readings grouped by parity of cow. Farm Parity of cow 1 2 3 4 5 6 7 8+ Total 1 863 722 1018 570 493 326 184 203 4379 2 827 640 756 408 268 242 123 188 3452 3 1425 1257 873 818 313 104 32 43 4865 Total 3115 2619 2647 1796 1074 672 339 434 12696 5.4.2. Raw data A scatter plot of log QSCC against days in milk is illustrated in Figure 5.1 below and a histogram illustrating that the log QSCC distribution was approximately Normal, but with a slight right skew, is shown below in Figure 5.2. 104 Figure 5.1. Scatter plot of log10 QSCC (cells / ml) against days in milk illustrating the raw data (n = 12637). Figure 5.2. Histogram illustrating the distribution of the log QSCC data (n = 12696) around the mean (set at zero). -3 -2 -1 0 1 2 3 Log QSCC: Deviations from the mean (mean set at 0) 105 5.4.3. Univariable analysis QSCC Univariable analysis and graphics were carried out in Microsoft Excel (Excel 97, Microsoft Corp) and Minitab (Version 13.3, Minitab inc, 2000). Analysis of variance (ANOVA) was used to compare log QSCC within each of the following categorised variables: .. Farm. .. Month of sample collection (January to December). .. Month of lactation (defined in 30 day categories, starting from the date of calving). .. Month of calving. .. Parity of cow. .. Quarter position (right fore, right hind, left fore, left hind). .. Whether the QSCC reading was 30 days before or after a case of clinical mastitis in that quarter. .. Whether the QSCC reading was in a quarter that had clinical mastitis at any time during the sampling period. .. Whether the QSCC reading was in a quarter that had clinical mastitis at any time during the lactation. .. Whether the QSCC reading was in a quarter that had clinical mastitis more than once during the lactation. Characteristics of QSCC and log QSCC distributions are show in Table 5.5, below: Table 5.5. Descriptive statistics of QSCC readings grouped by farm. Farm Arithmetic mean QSCC (000’s/ml) Median QSCC (000’s/ml) Mean log QSCC Geometric mean QSCC (000’s/ml) Standard deviation log QSCC 1 142.9 21 4.38 23.98 0.74 2 117.2 17 4.32 21.01 0.66 3 129.1 19 4.39 24.35 0.67 Totals 130.6 19 4.37 23.27 0.69 Univariable analysis identified that log QSCC varied significantly (p < 0.05) between farms, between parities, between months of lactation, between months of calving, between month of the year, between quarter position and between quarters with and without clinical mastitis. The means and standard deviations of log QSCC for each variable are displayed graphically below, in Figures 5.3 to 5.10. 106 Figure 5.3. Mean, and one standard deviation (depicted with a continuous line) of log10 QSCC (cells / ml) for each farm (n = 12696). Figure 5.4. Mean, and one standard deviation (depicted with a continuous line) of log10 QSCC (cells / ml) for each month of lactation (n = 12637). 3 3.5 4 4.5 5 5.5 1 2 3 4 5 6 7 8 9 10+ Lactation Month Log QSCC 3.0 3.5 4.0 4.5 5.0 5.5 1 2 3 Farm Log QSCC 107 Figure 5.5. Mean, and standard deviation (depicted with a continuous line), log10 QSCC (cells / ml) for cows of different calving months (n = 12696). Figure 5.6. Mean, and standard deviation (depicted with a continuous line), log10 QSCC (cells / ml) for cows of different parity (n = 12696). 3 3.5 4 4.5 5 5.5 6 2 3 4 5 6 7 8+ Parity LogQSCC 0 0.5 1 1.5 2 2.5 3 181 days into lactation. Log QSCC increased with increasing parity. Since quarters of cows of fourth or greater parity had similar coefficients, these parities were aggregated and four categories were included in the final model. There was an additional increase (interaction) in log QSCC in third and fourth parity cows, in late (> 210 days) lactation. Log QSCC was significantly lower in samples taken in January and February and higher in October and November, than in samples taken in other months. Hind quarters had significantly higher log QSCC than fore quarters. Log QSCC was significantly higher in quarters up to 30 days before clinical mastitis than unaffected quarters and greater still in quarters up to 30 days after clinical mastitis than unaffected quarters. Quarters from cows of first parity with clinical mastitis did not have significantly higher log QSCC over lactation as a whole, (having controlled for increased log QSCC 30 days either side of clinical mastitis), than quarters without clinical mastitis. However, quarters from cows of more than first parity with clinical mastitis had increased log QSCC during lactation as a whole, even having accounted for increased log QSCC 30 days either side of clinical mastitis. Most residual variation in Model 5.1 occurred between QSCC readings, within quarter (variance = 0.269). This was approximately double the sum of the variance at quarter level (0.066) and cow level (0.073). Complex variation was tested in the model (i.e. whether there was random slope variation) but none was identified. The intra-class correlations calculated from Equations 5.3 and 5.4 were; ICCcow = 0.073 / (0.073 + 0.066 + 0.269) = 0.18 ICCquarter = 0.073 + 0.066 / (0.073 + 0.066 + 0.269) = 0.34 The r2 value for this model was 0.28, therefore covariates in this model explained approximately 28% of the total variation in log QSCC. 113 Table 5.6. Model 5.1: Generalised linear mixed model incorporating variance components of log QSCC; all readings included. Variable Coefficient 95% Credibility Interval lower upper Response variable – Log Quarter Somatic Cell Count (n = 12637) Intercept value 4.14 1.08 1.20 Fore quarters Reference Right hind quarter 0.10 0.06 0.14 Left hind quarter 0.12 0.09 0.16 Months of sampling = March to September and December Reference Month of sampling = January -0.22 -0.25 -0.18 Month of sampling = February -0.24 -0.27 -0.21 Month of sampling = October 0.11 0.07 0.14 Month of sampling = November 0.10 0.06 0.13 Days in milk = 1 - 30 Reference Days in milk = 31 - 60 -0.31 -0.35 -0.26 Days in milk = 61 - 90 -0.22 -0.27 -0.18 Days in milk = 91 - 120 -0.15 -0.20 -0.11 Days in milk = 121 - 150 -0.06 -0.10 -0.02 Days in milk = 151 - 180 0.02 -0.02 0.07 Days in milk = 181 - 210 0.13 0.08 0.17 Days in milk = >210 0.12 0.08 0.17 Parity = 1 Reference Parity = 2 0.20 0.15 0.25 Parity = 3 0.20 0.13 0.26 Parity > 3 0.31 0.25 0.38 Interaction – Parity >3 x Days in milk = >210 0.22 0.17 0.28 Interaction – Parity 3 x Days in milk = >210 0.21 0.15 0.27 Log QSCC reading not 30 days before clinical mastitis Reference Log QSCC reading within 30 days before clinical mastitis 0.24 0.14 0.34 Log QSCC reading not 30 days after clinical mastitis Reference Log QSCC reading within 30 days after clinical mastitis 0.52 0.43 0.62 Log QSCC from a quarter without clinical mastitis Reference Log QSCC reading in a quarter of cow parity 2 with clinical mastitis at any time during the study period 0.18 0.001 0.36 Log QSCC reading in a quarter of cow parity 3 with clinical mastitis at any time during the study period 0.23 0.02 0.45 Log QSCC reading in a quarter of cow parity > 3 with clinical mastitis at any time during the sampling period 0.41 0.26 0.56 Between cow variance 0.073 0.060 0.087 Between quarter within cow variance 0.066 0.058 0.075 Between reading within quarter variance 0.269 0.267 0.272 114 5.5.3. Model 5.1. - Graphic representations. Parameters from Model 5.1 were used to calculate adjusted mean QSCC values for different parities, lactation months and for quarters with and without clinical mastitis. This was done by adding the intercept value (model mean), to the fixed effect coefficients. For example to derive the mean log QSCC for cows of parity 3 in lactation month 4, the intercept was added to the mean coefficients of these fixed effects. The results are shown graphically below for different parities (Figure 5.11), for quarters with and without clinical mastitis during the study period (Figure 5.12), and quarters within 30 days of clinical mastitis (Figure 5.13). Figure 5.11. Geometric mean QSCC during lactation in quarters from cows of different parities, (Model 5.1). 0 10 20 30 40 50 60 70 1 2 3 4 5 6 7 8+ Month of lactation Geometric mean QSCC (000s / ml) Parity 1 Parity 2 Parity 3 Parity 4+ 115 Figure 5.12. Geometric mean QSCC in quarters from cows of different parities, with and without clinical mastitis during the study period, (Model 5.1). Figure 5.13. Geometric mean QSCC in quarters up to 30 days before or up to 30 days after clinical mastitis, compared with other QSCC readings, (Model 5.1). 0 5 10 15 20 25 30 35 40 45 50 1 2 3 4 5 6 7 8+ Month of lactation Geometric mean QSCC (000's / ml) No Clinical Mastitis Clinical Mastitis in Parity 2 Clinical Mastitis in Parity 3 Clinical Mastitis in Parity 4+ 0 10 20 30 40 50 60 70 1 2 3 4 5 6 7 8+ Month of lactation Geometric mean QSCC (000s / ml) No Clinical Mastitis QSCC within 30 days before Clinical Mastitis QSCC within 30 days after Clinical Mastitis 116 5.5.4. Model 5.1 - Goodness of fit. The mean of level one residuals in Model 5.1 was 0.0002 and the standard deviation of standardised residuals was 1.000001. The plots of level one standardised residuals indicated that there were few outliers (94.4% of residuals were < +2 or > -2, see Figure 5.14 below). Investigation of residuals indicated that large values (> +2 or < -2) were not associated with any particular covariate or covariate pattern. Omission of data points with large residuals did not affect the model. Therefore, investigations of residuals suggested the model was of good fit. Figure 5.14. Histogram of level one standardised residuals from Model 5.1 in descending (positive residuals) or ascending (negative residuals) order of magnitude. The residual plots of level two and level three standardised Bayesian residuals are shown below, for quarter effects (Figure 5.15) and cow effects (Figure 5.16). There was a small right skew in these residuals. However, repeating the model first with the quarters with outlying positive quarter effects omitted (six quarters) and then cows with outlying positive cow effects omitted (six cows), did not result in significant changes in parameter estimates. -6 -4 -2 0 2 4 6 Residuals in order of magnitude Standardised residuals 117 Figure 5.15. Histogram of level two (between quarter) standardised Bayesian residuals from Model 5.1 in descending (positive residuals) or ascending (negative residuals) order of magnitude. Figure 5.16. Histogram of level three (between cow) standardised Bayesian residuals from Model 5.1 in descending (positive residuals) or ascending (negative residuals) order of magnitude. -6 -4 -2 0 2 4 6 Residuals in order of magnitude Quarter level residuals -3 -2 -1 0 1 2 3 4 Residuals in order of magnitude Cow level residuals 118 5.5.5. Model 5.2 - Generalised linear mixed model of log QSCC in quarters that did not exceeded 100,000 cells / ml. In order to investigate variance components of low cell count quarters (i.e. those unlikely to be infected with a major pathogen (Scheppers et al., 1997)), the modelling process described above, was repeated for quarters that did not exceed a QSCC of 100,000 cells / ml for the whole study period. Therefore, Model 5.2 took the form: Log QSCC ~ normal distribution (mean = µ ijk, variance = s2 ijk) µijk = a + ß’1ijkX’1ijk + ß’2jkX’2jk + ß’3kX’3k + vk + ujk+ eijk (5.6) where the parameters were as described for Model 5.1. The final model (Model 5.2) is presented below (Table 5.7). The number of QSCC readings used for this model was 5608 and these came from 861 quarters of 343 cows. Once again, herd was excluded from the model because it was not significant as a fixed effect and it did not influence other parameter coefficients. Log QSCC in hind quarters tended to be higher than in the fore quarters, although significance was marginal in the case of the left hind quarter. The influence of parity and lactation month on log QSCC was similar to that in Model 5.1, although the coefficients were smaller in magnitude. Log QSCC generally increased with increasing parity and was lowest between days 31 and 120 of lactation. Parity 3 remained in the model as a fixed effect (even though significance was marginal) because it was a lower order term to the interaction ‘Parity 3 x days in milk > 210’. Quarters with clinical mastitis (n = 18) during the study period had a significantly higher mean log QSCC than unaffected quarters. However, clinical mastitis within 30 days of a QSCC reading did not significantly influence QSCC in this model. The influence of clinical mastitis was not split into different parities, as in Model 5.1, because there were insufficient cases of clinical mastitis per parity to obtain meaningful results. The random effect variances were smaller than for Model 5.1 (because QSCC with less variation were selected for this model), but most variation remained at the bottom level, between readings within quarter. In contrast to Model 5.1, the variation between cows was approximately three times the variation between quarters. Complex variation was again tested in the model (i.e. random slope variation) but none was identified. The intra-class correlations for Model 5.2 were therefore; ICCcow = 0.035 / (0.035 + 0.011 + 0.121) = 0.21 119 ICCquarter = 0.035 + 0.011 / (0.035 + 0.011 + 0.121) = 0.28 The r2 value for this model was 0.27, therefore covariates in this model explained 27% of the total variation in log QSCC. Adjusted mean log QSCC values for different parities during lactation, calculated from Model 5.2, are shown graphically below (Figure 5.17): Figure 5.17. Geometric mean QSCC during lactation in quarters from cows of different parities, calculated from Model 5.2. 0 5 10 15 20 25 30 1 2 3 4 5 6 7 8+ Month of lactation Geometric mean QSCC (000's / ml) Parity 1 Parity 2 Parity 3 Parity 4+ 120 Table 5.7. Model 5.2: Generalised linear mixed model incorporating variance components of log QSCC; readings only included from quarters in which the QSCC did not exceed 100,000 cells / ml. Variable Coefficient 95% Credibility Interval lower upper Response variable – Log Quarter Somatic Cell Count in quarters that did not exceed 100,000 / ml (343 cows, 861 quarters, 5608 QSCC readings). Intercept value 3.98 Fore quarters Reference Right hind quarter 0.03 0.003 0.07 Left hind quarter 0.03 -0.01 0.06 Months of sampling = March to September and December Reference Month of sampling = January -0.18 -0.21 -0.14 Month of sampling = February -0.26 -0.29 -0.23 Month of sampling = October 0.09 0.05 0.13 Month of sampling = November 0.09 0.06 0.12 Days in milk = 1 - 30 Reference Days in milk = 31 - 60 -0.18 -0.22 -0.14 Days in milk = 61 - 90 -0.13 -0.17 -0.09 Days in milk = 91 - 120 -0.08 -0.12 -0.04 Days in milk = 121 - 150 -0.01 -0.06 0.03 Days in milk = 151 - 180 0.06 0.02 0.11 Days in milk = 181 - 210 0.11 0.06 0.16 Days in milk = >210 0.17 0.13 0.21 Parity = 1 Reference Parity = 2 0.11 0.07 0.15 Parity = 3 0.04 -0.02 0.09 Parity > 3 0.09 0.03 0.15 Interaction – Parity 4 x Days in milk = >210 0.15 0.09 0.21 Interaction – Parity 3 x Days in milk = >210 0.18 0.12 0.25 Log QSCC in quarters without clinical mastitis Log QSCC reading in a quarters with clinical mastitis at least once during the study period 0.19 0.08 0.30 Between cow variance 0.035 0.028 0.044 Between quarter within cow variance 0.011 0.008 0.016 Between reading within quarter variance 0.121 0.120 0.123 121 5.5.6. Model 5.2 goodness of fit. The mean of level one residuals for Model 5.2 was –0.0004 and the standard deviation of standardised residuals was 1.000. The plots of level one standardised residuals is shown below (Figure 5.18) and 94.6% of residuals were < +2 or > -2. Investigations of residuals again suggested the model was of good fit. Similarly, investigations of higher level residuals indicated a good model fit (Figures 5.19 and 5.20). Figure 5.18. Histogram of level one standardised residuals from Model 5.2 in descending (positive residuals) or ascending (negative residuals) order of magnitude. Figure 5.19. Histogram of level two (quarter) standardised Bayesian residuals from Model 5.2 in descending (positive residuals) or ascending (negative residuals) order of magnitude. -8 -6 -4 -2 0 2 4 6 8 Residuals in order of magnitude Quarter level residuals -6 -4 -2 0 2 4 6 Residuals in order of magnitude Standardised residuals 122 Figure 5.20. Histogram of level three (cow) standardised Bayesian residuals from Model 5.2 in descending (positive residuals) or ascending (negative residuals) order of magnitude. 5.6. Analysis of monthly changes in quarter somatic cell counts between categories. 5.6.1. QSCC transition matrix To investigate movements of quarters between the different categories of QSCC each month, a transition matrix was calculated. The probability of a quarter in a given QSCC category changing to another category at the next recording was calculated, and results presented in a matrix format. The nine categories of QSCC that were originally modelled in relation to clinical mastitis in the Chapter Four, were further investigated using this approach. The categories were (000’s cells/ml); 0 - 20, 21 - 40, 41 - 60, 61 - 80, 81 – 100, 101 - 150, 151 - 200, 201 – 400 and > 400. The matrix was calculated for all consecutive monthly QSCC readings within a lactation, for all quarters. Results are presented in tabular and graphical format. The transition matrix is shown below (Table 5.8). Over 80% of quarters = 40,000 cells/ml, remained = 40,000 cells/ml at the next recording. Quarters 41,000-100,000 cells/ml tended to move to a lower rather than to a higher QSCC at the next recording. However, a greater proportion (33.5%) of these quarters remained 41,000-100,000 cells/ml, than quarters >100,000 cells/ml (16.9%) or quarters = 40,000 cells/ml (12.2%). 22.7% of quarters with a QSCC > 150,000 cells/ml moved to = 40,000 cells/ml in the next month and 54.9% of quarters with a QSCC > 150,000 cells/ml remained > 150,000 cells/ml in the next month. The matrix -6 -4 -2 0 2 4 6 8 Residuals in order of magnitude Cow level residuals 123 was repeated for cows of parity 1, 2, 3 and >3, but since the general patterns described were similar for all parities, results are not shown. Table 5.8. Transition matrices of quarter somatic cell count movements between categories during lactation. The numbers in bold face indicate quarters moving into the QSCC categories identified as low risk in Chapter Four (41,000 – 100,000/ml.). Transition matrix (a): Cells give the proportion of quarters moving from one QSCC category to another Category of QSCC at the following monthly recording n 0-20 21-40 41-60 61-80 81-100 101- 150 151- 200 201- 400 >400 0-20 5629 0.73 0.14 0.05 0.02 0.01 0.02 0.01 0.01 0.01 21-40 1536 0.35 0.26 0.13 0.08 0.05 0.05 0.02 0.03 0.02 41-60 767 0.23 0.21 0.16 0.10 0.08 0.11 0.04 0.05 0.03 61-80 440 0.24 0.16 0.13 0.12 0.10 0.11 0.05 0.05 0.05 81-100 296 0.17 0.11 0.15 0.09 0.10 0.15 0.07 0.09 0.06 101-150 422 0.16 0.11 0.09 0.08 0.10 0.16 0.09 0.11 0.09 150-200 234 0.14 0.09 0.08 0.06 0.09 0.15 0.07 0.22 0.11 201-400 442 0.13 0.07 0.06 0.03 0.04 0.10 0.11 0.22 0.23 Category of QSCC at a monthly recording >400 461 0.19 0.06 0.03 0.02 0.02 0.06 0.05 0.20 0.36 Transition matrix (b) (denominators): Cells give the numbers of quarters moving from one QSCC category to another Category of QSCC at the following monthly recording n 0-20 21-40 41-60 61-80 81-100 101- 150 151- 200 201- 400 >400 0-20 5629 4081 788 297 117 61 92 47 69 77 21-40 1536 537 401 202 122 77 83 33 43 38 41-60 767 176 162 121 75 59 82 33 36 23 61-80 440 104 71 55 51 42 48 24 22 23 81-100 296 51 34 44 26 30 43 22 27 19 101-150 422 67 48 40 35 42 66 37 47 40 150-200 234 32 20 18 15 21 36 16 51 25 201-400 442 58 31 25 15 19 45 49 98 102 Category of QSCC at a monthly recording >400 461 89 28 15 8 11 27 25 91 167 124 Transition matrix (a) is represented graphically, below. Firstly, the matrix is illustrated using a three dimensional area plot (Figure 5.21). Secondly the proportion of quarters that moved into the lowest risk QSCC category for clinical mastitis, (41,000 – 100,000 cells / ml), from different QSCC categories, is illustrated (Figure 5.22). These graphs illustrate a degree of stability between consecutive QSCC readings, with low QSCC tending to remain low, and high QSCC tending to remain high. Intermediate QSCC (41,000 – 150,000 cells/ml) were the most likely group to be in the same intermediate range at the next monthly recording. Figure 5.21. Illustration of movements of quarters between somatic cell count categories at consecutive monthly recordings. 0-20 21-40 41-60 61-80 81-100 101-150 151-200 201-400 >4000-20 41-60 81-100 151-20 0 >400 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 Proportion of quarters QSCC category at one monthly recording (000s/ml) QSCC category at next monthly recording (000s/ml) 125 Figure 5.22. Illustration of movements of quarters between QSCC categories at different risk of clinical mastitis in the next month. A QSCC of 41 – 100,000/ml was identified in Chapter Four as the category at least risk of clinical mastitis in the following month. 5.6.2. Categories of QSCC in different lactation months. The proportion of QSCC readings in different months of lactation, for each of the nine QSCC categories is presented below, in Figure 5.23. In Figure 5.24, the graph is repeated with the categories between 0 to 40,000 cell/ml, 41,000 to 100,000 cell/ml and 101,000 and 200,000 cells/ml combined. The first ten months of lactation were used for these graphs because the number of readings in each category reduced quickly after this time. The proportion of readings 0 – 20,000 cells/ml peaked in month two at 73.0%, coinciding with the month of lowest overall mean QSCC, and then gradually declined to just under 40% by month ten of lactation. The proportion of readings in all other categories (20 to >400,000 cells/ml) was lowest in month two and then gradually increased during the rest of lactation. In all months, over 50% of QSCC were between 0 and 40,000 cells/ml. Between 10% and 30% of QSCC readings were between 41,000 and 100,000 cells/ml and less than 10% were 101,000 – 200,000 cells/ml. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0-20 21-40 41-60 61-80 81-100 101-150 151-200 201-400 >400 Current Quarter SCC category Proportion in SCC category in next month 0 - 40,000/ml 41 - 100,000/ml > 100,000/ml 126 Figure 5.23. Proportion of QSCC in nine categories (000’s cells/ml) during the first ten months of lactation (n = 11381). Figure 5.24. Proportion of QSCC in four categories (000’s cells/ml) during the first ten months of lactation (n = 11381). 0% 10% 20% 30% 40% 50% 60% 70% 80% 1 2 3 4 5 6 7 8 9 10 Lactation Month Proportion in each category 0 - 20 21 - 40 41- 60 61 - 80 81 - 100 101 - 150 151 - 200 201 - 400 > 400 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 1 2 3 4 5 6 7 8 9 10 Lactation Month Proportion in each category 0 - 40 41 - 100 101 - 200 > 200 127 5.6.3. Model 5.3 – Generalised linear mixed model of QSCC transitions between categories. The movements between QSCC categories at consecutive recordings were investigated further with a generalised linear mixed model incorporating previous QSCC categories. The QSCC category with the lowest risk of clinical mastitis in the next month, identified in Chapter Four (QSCC = 41,000 – 100,000 cells / ml), was the centre of interest. This was used to define a Bernoulli response variable (quarter in the low risk QSCC category = 1, quarter not in this QSCC category = 0). Previous QSCC categories were assessed as explanatory variables and the fixed covariates farm, parity, quarter position, month of lactation and month of year were tested to control for their possible confounding influence. The modelling strategy and assessment of model fit followed the Bayesian generalised linear mixed approach described in Chapter One. Therefore, the form of the model was: logit(µijk) = a + ß’1ijkX1ijk + ß’2jkX2jk + ß’3kX3k + vk + ujk (5.7) QSCC {41 – 100,000/ml}ijk ~ Bernoulli distribution (µijk) where the subscripts i, j and k denote the ith QSCC reading, the jth quarter and the kth cow respectively QSCC {41 – 100,000/ml}ijk = the binary response variable [1 = QSCC between 41 – 100,000/ml , 0 = other QSCC readings] denoting the ith QSCC reading in the jth quarter of the kth cow. µijk = the fitted probability for QSCC reading i in quarter j of cow k. a = regression intercept X1ijk = vector of covariates associated with QSCC reading i of quarter j of cow k. ß’1ijk = vector of coefficients for X1ijk. X2jk = vector of quarter-level exposures for quarter j of cow k. ß’2jk = vector of coefficients for X2jk. X3k = vector of cow-level exposures for cow k. ß’3k = vector of coefficients for X3k. vk = random effect reflecting residual variation between cows. ujk = random effect reflecting residual variation between quarters, within cows. 128 Final parameter estimates were obtained using MCMC and Gibbs sampling, using the methods described in Chapter One. Explanatory covariates and interactions between significant covariates remained in the models when the 95% credibility intervals for the odds ratio did not include 1.00. Thirty thousand iterations were used after burn-in to estimate parameters. The final model of QSCC movements (Model 5.3) is shown in Table 5.9. below. The WinBUGS code for this model and kernal density plots are provided in Appendix 6. Having controlled for the confounding effects of farm, quarter position and month of lactation, quarters were most likely to have a QSCC 41-100,000/ml at the next recording if they had a QSCC between 40,000 and 100,000/ml at the previous monthly recording. Quarters = 20,000/ml were least likely to move to the 41,000 – 100,000/ml category. The interaction terms in this model indicate that quarters with QSCC > 400,000/ml in lactation months greater than five were also unlikely to move into QSCC category 40,000 to 100,000/ml at the next monthly recording. More random variation occurred between cows than between quarters within cows. 129 Table 5.9. MODEL 5.3: Generalised linear mixed model of movements of quarters into the lowest risk QSCC category for clinical mastitis in the next month (41,000-100,000 cells / ml). Coefficient Odds Ratio 95% Credibility Interval lower upper Response variable - quarter in the low risk range of QSCC (41-100,000/ml) at a test day recording. Intercept value -3.31 0.16 0.24 Farm 1 Reference Farm 2 0.73 0.59 0.89 Farm 3 1.07 0.89 1.30 Lactation month 2 Reference Lactation month 3 2.09 1.52 2.83 Lactation month 4 1.89 1.36 2.59 Lactation month 5 2.12 1.55 2.89 Lactation month 6 3.24 2.39 4.36 Lactation month 7 3.07 2.26 4.08 Lactation month 8 3.23 2.37 4.35 Lactation month > 8 3.58 2.73 4.63 Previous month QSCC categories: 1-20,000/ml Reference 21-40,000/ml 3.29 2.79 3.87 41-60,000/ml 3.73 3.04 4.59 61-80,000/ml 3.66 2.83 4.72 81-100,000/ml 3.80 2.83 5.07 101-150,000/ml 3.35 2.60 4.33 151-200,000/ml 2.73 1.93 3.84 201-400,000/ml 1.34 0.98 1.82 >400,000/ml 1.79 1.09 2.87 Interactions: {Lactation month > 8} * {Previous month QSCC categories >400,000/ml} 0.18 0.06 0.46 Lactation month 8} * {Previous month QSCC categories >400,000/ml} 0.05 0.00 0.35 Lactation month 7} * {Previous month QSCC categories >400,000/ml} 0.15 0.02 0.68 Lactation month 6} * {Previous month QSCC categories >400,000/ml} 0.26 0.06 0.90 Between cow variance 0.28 0.18 0.39 Between quarter, within cow, variance 0.06 0.002 0.19 130 Model 5.3 parameter distributions were assessed using kernel density plots. Model fit was assessed graphically by plotting Pearson residuals against fitted values (McCullagh and Nelder, 1989) and by calculating the mean of aggregations of these residuals, as described in Chapter One. Pearson residuals plotted against fitted values for Model 5.3 and means of Pearson residuals in equal deciles of ascending fitted value Figure (5.25), are shown below. These were consistent with a good model fit (see Chapter Seven). Figure 5.25. Graphs of Pearson Residuals for Model 5.3: a. Pearson residuals plotted against fitted values, and b. Deciles of Pearson residuals in ten equal groups in order of ascending fitted value. a. b. -2 -1 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 Fitted Value Pearson Residual -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 Mean Residuals in Decile Aggregates Pearson Residual 131 5.7 Discussion 5.7.1. Month of Lactation The patterns of QSCC found during lactation were similar to those described for CSCC (Dohoo and Meek, 1982) and QSCC (Broland, 1985; Wever and Emanuelson, 1989; Schepers et al. 1997; Laevens et al., 1997). After controlling for other covariates such as month of year, quarter position and clinical mastitis, QSCC decreased between month one and month two of lactation and then gradually increased through the next months of lactation. It has been reported that the effect of stage of lactation arises from the influence of infected quarters (Eberhart et al.,1979; Laevens et al., 1997) although this remains controversial because others report the effect remains after controlling for infection status (Broland, 1985, Schepers, 1997). It is notable that in quarters that remained below 101,000 cells/ml (Model 5.2), the effect of lactation month on QSCC in the later lactation months was of a similar magnitude to that in Model 5.1. This implies that the effect of stage of lactation does not occur simply because of the presence of high SCC quarters. Further evidence comes from the analysis of QSCC in categories. The proportion of quarters < 21,000 cell / ml constantly decreased after the second month of lactation, whereas the proportion of quarters in higher categories increased. Therefore, the overall mean increase in QSCC towards the end of lactation was a result of a general increase in all categories of QSCC, not just the result of a large increase in few quarters. 5.7.2. Parity QSCC increased with parity and this also agrees with previous reports (Dohoo and Meek, 1982, Broland, 1985; Schepers et al., 1997; Laevens et al., 1997). Most of this previous research suggests that the increase is a feature of increasing intramammary infection with age, rather than an innate physiological effect. This would agree with findings in Chapters One and Two of this thesis, with clinical and sub-clinical major pathogen isolations increasing with parity. The effect of parity on QSCC in quarters that remained below 100,000 cells / ml (Model 5.2), was much smaller than in all quarters (Model 5.1). This also suggests that parity was having a greater effect in quarters with some high QSCC readings and these quarters were most likely to have bacterial infections. Both models of log QSCC indicated that there was an added influence of parity in late lactation. Quarters in cows of greater than second parity, had a sharper increase in QSCC when more than 210 days in milk. The influence of an interaction between age and lactation month on QSCC has been previously reported (Schepers et al., 1997), and could either be a result of milk yield reducing more quickly at the end of lactation in older cows or increased susceptibility to intramammary infection, in older cows at the end of lactation. 132 5.7.3. Time of year After accounting for stage of lactation, variation in QSCC was identified between month of sample collection, and seasonal variation has been previously described (Dohoo and Meek, 1982; Broland, 1985; Wever and Emanuelson, 1989). The reasons for this variation cannot be ascertained in this study, but it may have resulted from differences in the force of infection at different times of year, or from differences in immune status. It is notable that January and February were the months with lowest QSCC. These winter months are associated with housing in the UK and are often considered a time of increased environmental challenge. Therefore, the reduction in QSCC may have been caused by a seasonal effect on immune function. It has been reported that winter, being an energetically demanding period, is a time of substantial physiological stress and results in impaired immune status (Nelson and Demas, 1996). It is possible therefore, that the reduction in QSCC in January and February is a marker of reduced immune capability rather than a reduction in environmental challenge. The mean QSCC was highest in October and November. Similarly, this could represent an improvement in immune status or an increase in response to sub-clinical bacterial challenge. If changes in mean QSCC could represent either an alteration in immune status or a response to bacterial challenge, it is difficult to interpret changes when QSCC is modelled as a continuous response variable. The variability could arise from either sub-clinical bacterial challenge or a change in immune status. Month of sampling was retained in the final models (Models 5.1 and 5.2), but not calving month. This is not surprising since month of calving is correlated to the month of sampling and the month of lactation, both of which were in the final models. This indicates that the variation in QSCC was more closely associated with month of sampling and month of lactation, than with calving month. 5.7.4. Quarter position Quarter position has not always been included as a fixed effect in previous models of QSCC (Broland, 1985; Wever and Emanuelson, 1989; Laevens et al., 1997) although it has in some (Schepers et al., 1997). In this study, hind quarters were found to have higher QSCC than fore quarters, and this may have been because sub-clinical intramammary infections were more frequent in hind quarters. The inclusion of quarter as both a fixed and random effect could have resulted in over-specification of the models. However, the models converged well and fit was good, so both parameters were included. 133 5.7.5. Clinical mastitis affecting QSCC As expected and as previously reported (Schepers et al.,, 1997), QSCC increased in quarters with clinical mastitis. In this study, the increase after a clinical case was higher than before. The previous chapter demonstrated that the QSCC in the month before clinical mastitis was likely to be either high (> 200,000 cells/ml) or low (<41,000 cells/ml). The higher values cause the mean effect on QSCC (measured in Model 5.1) to be increased before clinical mastitis. The reason QSCC was higher within 30 days after a case of clinical mastitis, than 30 days before, is likely to be because all mastitic quarters had a raised QSCC during the recovery phase, whereas not all did prior to clinical mastitis. Separate to this effect, mean QSCC were also increased in all the recordings taken from quarters that contracted clinical mastitis during the sampling period. This probably occurred either because QSCC remained high during a prolonged recovery phase (> 30 days) or because infections were not cured and a chronic sub-clinical inflammatory response was being measured. Interestingly, repeated quarter cases of clinical mastitis were tested in the models as a fixed effect but these were not associated with a significant additional increase in QSCC. 5.7.6. Variation in hierarchical levels Having accounted for variation caused by the fixed effects, residual variation was greatest between readings within each quarter, than between quarters or between cows. This is confirmed by the intra-class correlations (ICC). In Model 5.1, the ICC for readings within quarters was 0.34, which means that approximately two thirds of the residual variation occurred between readings within quarter. In Model 5.2, the ICC for readings within quarters was of a similar order of magnitude at 0.28. This concurs with earlier research on QSCC that found bacteriological status was the most important cause of variation in QSCC (Broland, 1985; Laevens et al., 1997; Schepers et al., 1997). Since bacteriological status can change over time (due to cures and new infections), variation between readings would be expected to be large. However, since sub-clinical bacteriological status was not measured, variation at level one cannot be differentiated between bacterial infection, measurement error or other causes. In two similar types of analyses that did include bacteriological status (Broland, 1985; Schepers et al., 1997), the variation explained by the models were approximately 40% and 50% respectively, compared with a little under 30% in this study. This difference could be attributable to the knowledge of sub-clinical infection status. The intra class correlations suggest that events over time had a greater impact on the QSCC than factors associated with particular quarters or cows. The effect of cow was more important, however, in the low QSCC model (Model 5.2) than in Model 5.1. This may 134 be because higher QSCC were ruled out, and cow factors influenced the ‘baseline’ QSCC. Variation between cows was also greater than that between quarters in Model 5.3, suggesting that cow factors more than quarter factors were important to determine whether a QSCC was in the range 41,000 – 100,000 cells / ml. 5.7.7. QSCC in categories Most QSCC readings were in the lowest QSCC categories (0 - 40,000 cells/ml) and the transition matrix indicated that the great majority remained in this range at the next monthly recording. This implies that a QSCC 0 – 40,000 cells/ml was a stable and ‘normal’ (where the majority existed) category of QSCC, although interestingly, not the category at least risk of clinical mastitis. However, the transition matrix, graphical plots (Figures 5.21 and 5.22) and transition SCC model (Model 5.3, Table 5.9) also indicated a degree of stability in the middle and high ranges of QSCC between consecutive monthly recordings. Quarters with a QSCC 41,000 – 100,000 cells / ml were over 3.5 times the odds of being 41,000 – 100,000 cells / ml at the next monthly recording compared to quarters <41,000 cells / ml. This is particularly relevant following the findings from Chapter Four. It may explain why quarters were at reduced risk of clinical mastitis for up to three consecutive months; because the low risk quarters were more likely to remain in the central low risk QSCC categories for clinical mastitis over time, compared to other quarters. The general stability of QSCC within broad categories (high, medium or low) needs to be considered alongside the variance components of Model 5.1. Although most overall variation in QSCC was identified between readings rather than between quarters or cows, some stability in QSCC still existed when categories were analysed. The variation identified between readings within quarter, may not always have been great enough for a quarter to move between biologically important QSCC categories in consecutive months. The standard deviation of log QSCC at the lowest (between reading) level in Model 5.1 was; Square root {0.269} = 0.52 Therefore, the average deviation from the intercept value, due to variation arising between readings was; 4.14 (intercept) +/- 0.52 = 3.62 to 4.66 Converting this to geometric mean QSCC gives (000’s cells / ml); 135 13,804 (intercept) +/- one standard deviation = 4,169 to 45,709 Therefore, although most variation was identified between readings, this average deviation from the mean is relatively small and quarters may often not change between the biologically important QSCC categories identified in Chapter Four. This demonstrates the importance of being able to recognise and understand categories of QSCC with biological meaning. The effectiveness of immune defences, therefore, may not only depend on cow factors, such as genetic and nutritional components, but may also be significantly influenced by local quarter events over time. The reasons why intermediate levels of QSCC protect against clinical mastitis, the reasons why some quarters appear to maintain an intermediate level of QSCC and investigations into the cell types and function in intermediate QSCC quarters, would all make excellent areas for continued research. 136 Chapter 6: Somatic Cell Count Distributions during Lactation Predict Clinical Mastitis. 6.1. Chapter summary. Somatic cell count records during lactation were investigated with the purpose of identifying distributional characteristics (mean and measures of variation) that were most closely associated with clinical mastitis. Three separate data-sets were used, one containing quarter somatic cell counts (n = 1444) and two cow somatic cell counts (n = 933 and 11825). Clinical mastitis was defined as a binary outcome, present or absent, for each lactation and somatic cell counts were log (base 10) transformed. A generalised linear mixed model within a Bayesian framework was used for analysis. Parameters were estimated using MCMC with Gibbs sampling. Results from the three data-sets were similar. Increased maximum and standard deviation log SCC during lactation, rather than increased geometric mean, were the best overall indicators of clinical mastitis. Distributions of SCC were also investigated separately for different mastitis pathogens. Increased maximum log SCC was associated with clinical mastitis caused by all pathogen types. Increased standard deviation log SCC was associated with Staph. aureus and Strep. uberis clinical mastitis and increased coefficient of variation log SCC (standard deviation divided by mean) was associated with E. coli clinical mastitis. Increased geometric mean lactation SCC was associated with an increased risk of Staph. aureus clinical mastitis but a reduced risk of E. coli clinical mastitis. These results suggest that using measures of variation and maximum SCC would enhance the accuracy of predicting clinical mastitis, compared with geometric mean SCC, and therefore improve genetic programs that aim to select for clinical mastitis resistance. The results are also consistent with low SCC increasing susceptibility to some mastitis pathogens. 137 6.2. Aims. As described in Chapter One, it may be possible to improve the prediction of clinical mastitis occurrence in a lactation by using characteristics of SCC distributions, other than the lactation mean. This would be of interest for programs that use SCC as a proxy for clinical mastitis, for genetic evaluation. The aim of this chapter was to investigate SCC distributions during lactation with the purpose of identifying the characteristics most closely associated with clinical mastitis (CM). 6.3. Materials and methods. Quarter SCC (QSCC) or cow SCC (CSCC) from three separate data-sets were investigated in the chapter. In each set of data, lactations with and without CM were identified from prospectively collected records. 6.3.1. Data-Set One. These data comprised the QSCC readings and clinical mastitis records from the three commercial dairy herds described in Chapters Four and Five. 6.3.2. Data-Set Two. Data from five commercial dairy herds in Gloucestershire, UK, comprised this data-set and data collection has been described previously (Hedges et al., 2001). The herds contained between 100 and 250 cows each and had bulk milk SCC in the range 100,000/ml – 250,000/ml. CSCC were measured from pooled quarter milk samples taken from each cow, approximately monthly, between June 1997 and April 1999, as a part of a national commercial milk recording program (National Milk Records, Chippenham, UK). CM was identified and recorded prospectively by the herdsmen. 6.3.3. Data-Set Three. These data came from 274 Dutch dairy herds. The herds participated in a national SCC recording scheme and have been described previously by Barkema et al. (1998). CSCC was measured every three to four weeks and CM was identified and recorded by the herdsmen. Concurrent CM and SCC records were available for analysis from December 1992 until June 1994. Aseptic milk samples were collected from cases of CM (Barkema et al., 1998) and bacterial culture and identification carried out using standard techniques (Harmon et al., 1990). 138 6.3.4. Analysis. In data-sets two and three, complete lactations that had a minimum of five SCC readings were used for analysis. A lactation started on the date of calving and ended either at the date of drying off or of culling. In data-set one, because data collection was only performed for one year, lactations with five or more SCC readings were included, whether or not lactations were whole. CM was defined as a Bernoulli outcome, present or absent, for each lactation. Therefore, a lactation with CM had one or more clinical episodes. For pathogen-specific analysis in data-set three, a lactation was defined as having a case of CM caused by a specific pathogen when all the cases during that lactation were caused by that one pathogen. Lactations with mixed causes of CM were omitted from the pathogen specific analysis. Individual quarter and cow somatic cell counts, were log (base 10) transformed to normalise the data (Ali and Shook, 1980). The lactation characteristics of SCC investigated were minimum, maximum, mean, standard deviation, variance and coefficient of variation (standard deviation / mean) of log-transformed SCC and these were calculated for each quarter or cow lactation. These SCC characteristics were compared between lactations with and without CM. A further comparison was made between lactations with specific bacterial causes of CM and unaffected lactations. 6.3.5. Modelling strategy. A generalised linear mixed model (GLMM) (Breslow and Clayton, 1993; Burton et al., 1999) within a Bayesian framework was used for modelling CM, as described in Chapter One. Models were specified in the following manner (Zeger and Karim, 1991; Burton et al., 1999): logit(µij) = a + ß’1ij X1ij + ß’2jX2j…… + vj (6.1) CMij ~ Bernoulli distribution where the subscripts i, and j denote the ith (lowest) level data points clustered within the jth (second) level respectively. i and j were either quarter-lactations within cows (data-set one) cowlactations within cows (data-set two) or cow-lactations within farms (data-set three). CMij = the binary response denoting mastitis in the ith lactation of the jth cluster (cow or herd). µij = the fitted probability of CM in the ith lactation of the jth cluster. a = intercept 139 X1ij = vector of covariates associated with lactation i within cluster j. ß’1ij = transposed vector of coefficients for X1ij. X2j = vector of j-level exposures for each cluster, j. ß’2j = transposed vector of coefficients for X2j. vj = random effect reflecting residual variation between clusters j. Interest centred on the relationship between minimum, maximum, mean, standard deviation, variance and coefficient of variation log SCC and CM. These covariates were initially modelled in quintiles of increasing magnitude and only included as continuous variables when the relationship with CM was linear. Interactions were tested between significant covariates. Farm (data-sets one and two), parity, calving month, mean days in milk of SCC recordings and quarter position (data-set one), were modelled as fixed effects in the models and included if they influenced the relationship between SCC and CM (Hosmer and Lemeshow, 1989). In a few instances in data-sets one and three, cows contributed more than one lactation to the analysis, because they were dried off and calved again within the period of data collection. Since this second lactation was a rare event, a binary variable was introduced for ‘second lactation’ and modelled as a fixed effect. In data-set two, second lactations during the study were modelled as random variables, because their frequency was relatively high. In data-set three, farm was fitted as a random effect. Final models were constructed using Markov Chain Monte Carlo with Gibbs sampling and the methods for model building and convergence were described in Chapter One. Chains were each run for a minimum of 7,000 iterations after ‘burn-in’ and the posterior means and credibility intervals of parameters derived from these iterations. An example of the WinBUGS code for one of the GLMM constructed in this chapter, along with the kernal density plots, is provided in Appendix 7. Model fit was assessed from Pearson residuals as described in Chapters One and these methods are discussed in Chapter Seven. 6.4. Results. Data-Set One A total of 1444 quarter-lactations, from 353 cows, were used for analysis. CM occurred in 100 (6.9%) quarter-lactations from 82 (23.3%) cows. The mean number of QSCC records per quarter-lactation was 6.67. Data-set two 140 Nine hundred and thirty two cow-lactations from 733 cows were used for analysis. CM occurred in 128 (13.7%) cow-lactations from 118 (16.1%) cows. The mean number of QSCC records per lactation was 7.59. Data-set three A total, 11,825 cow-lactations from 11,673 cows were included in the analysis. CM occurred in 1994 (16.9%) cow-lactations from 1993 (17.1%) cows. The mean number of QSCC records per lactation was 9.85. Pathogen-specific models were constructed for clinical mastitis caused by Staph. aureus (n = 206), Strep. dysgalactiae (n = 96), Strep. uberis (n = 81), E. coli (n = 310) and clinical mastitis associated with no bacterial growth (n = 242). 6.4.1. Description of SCC distributions in lactations with and without clinical mastitis. Features of SCC distributions in lactations with and without CM are shown in Tables 6.1 and 6.2 below. Quarter SCC in data-set one tended to be lower and more variable during lactation than cow SCC in data-sets two and three. The effect of CM on SCC, however, was similar in the three data-sets. Overall, lactations with CM had numerically higher mean, minimum, maximum, standard deviation, variance and coefficient of variation of log SCC than lactations without CM. The increase in maximum, standard deviation and variance of log SCC was proportionately greater, than in mean or minimum log SCC. SCC characteristics during lactations associated with different mastitis pathogens are presented in Table 6.3 and Figure 6.1, below. There was a numerical increase in maximum, standard deviation and variance log SCC in lactations associated with all pathogenspecific CM, compared with unaffected lactations. There was also an increase in mean and minimum lactation log SCC associated with all pathogen-specific CM, although this increase was relatively small for CM associated with E. coli or no bacterial growth. 141 Table 6.1. Numbers in the table describe the antilog of the mean log transformed SCC parameters. Data-set 1 Data-set 2 Data-set 3 No CM n = (1344) CM (n = 100) No CM (n = 804) CM (n = 128) No CM (n = 9831) CM (n = 1994) Mean lactation SCC 22776 39995 54515 100800 81935 148738 Minimum lactation SCC 5558 6961 20585 27182 26830 38752 Maximum SCC 104630 299167 172935 614567 266168 701071 Key to Table 6.1: CM – clinical mastitis Table 6.2. Log SCC distributions between lactations with and without clinical mastitis. Data-set 1 Data-set 2 Data-set 3 No CM n = 1344 CM n = 100 % diff No CM n = 804 CM n = 128 % diff No CM n = 9831 CM n = 1994 % diff Mean log SCC 4.36 4.60 5.6% 4.74 5.00 5.6% 4.91 5.17 5.3% Minimum log SCC 3.74 3.84 2.6% 4.31 4.43 2.8% 4.43 4.59 3.6% Maximum log SCC 5.02 5.48 9.1% 5.24 5.79 10.5% 5.43 5.85 7.8% Standard deviation log SCC 0.46 0.59 27.4% 0.30 0.44 47.6% 0.30 0.38 26.6% Variance log SCC 0.26 0.43 67.5% 0.13 0.26 105.0% 0.11 0.17 59.4% Coefficient of variation log SCC 0.11 0.13 6.5% 0.06 0.09 40.4% 0.07 0.09 22.9% Key to Table 6.2: CM – clinical mastitis, % diff – percentage difference between lactations with and without clinical mastitis 142 Table 6.3. Log SCC distributions in lactations with and without clinical mastitis caused by specific pathogens (data-set three). Pathogen-specific clinical mastitis No CM E. coli No Growth Strep. uberis Strep. dysgal Staph. aureus n 9831 310 242 81 96 206 Mean Mean % Mean % Mean % Mean % Mean % Mean log SCC 4.91 4.99 1.6 5.00 1.8 5.22 6.3 5.26 7.0 5.36 9.1 Minimum log SCC 4.43 4.47 0.9 4.45 0.6 4.65 5.0 4.66 5.0 4.75 7.2 Maximum log SCC 5.43 5.70 5.0 5.65 4.2 5.90 8.7 5.93 9.3 5.96 9.8 Standard deviation log SCC 0.30 0.37 21.6 0.36 20.0 0.38 24.1 0.39 30.1 0.38 24.9 Variance log SCC 0.11 0.16 48.0 0.16 43.7 0.17 51.7 0.18 67.6 0.17 57.1 Coefficient of variation log SCC 0.07 0.08 17.1 0.08 19.7 0.08 19.1 0.09 24.6 0.08 18.4 Key to Table 6.3: CM – Clinical Mastitis, Strep. dysgal – Streptococcus dysgalactiae. %– percentage difference between lactations with and without clinical mastitis 143 Figure 6.1. Bar chart illustrating the proportional differences in lactation log SCC characteristics (data-set three), between lactations with pathogen-specific causes of clinical mastitis and lactations without clinical mastitis. Key to Figure 6.1: mean – geometric mean lactation SCC, min – minimum lactation log SCC, max – maximum lactation log SCC, sd – standard deviation lactation log SCC, var – variance lactation log SCC, cofv – coefficient of variation lactation log SCC. 6.4.2. Models of all Clinical Mastitis The models for all CM (Models 6.1, 6.2 and 6.3) are presented in Table 6.4, below. Having controlled for confounding covariates, an increase in maximum and standard deviation log SCC was associated with an increased probability of CM in all three data-sets. An increase in minimum log SCC was associated with an increased risk of CM in data-set one (Model 6.1). The mean log SCC was not retained in any of the models. There were no significant interaction terms and analysis of Pearson residuals and outliers, suggested the models were of good fit (see Figure 6.2, below). Table 6.4. Generalised linear mixed models for all clinical mastitis in data-sets one, two and three. Parameters were estimated using Markov Chain Monte Carlo with Gibbs Sampling (overleaf). 144 Table 6.4. Coefficient Odds Ratio 95% Credibility Intervals Lower Upper Model 6.1 – Response is quarter clinical mastitis (n = 100) in 1444 quarter-lactations (353 cows) Intercept -3.02 Farm 1 Reference Farm 2 0.23 0.10 0.50 Farm 3 0.96 0.55 1.69 Mean days in milk of SCC recordings (per day) 0.99 0.99 1.00 Maximum log SCC = 5.78 (600,000/ml) Reference Maximum log SCC > 5.78 (600,000/ml) 2.31 1.04 5.21 Minimum log SCC (unit increase) 1.72 0.96 3.14 Standard deviation log SCC (unit increase) 5.41 1.20 24.85 Between cow variance 0.98 0.08 2.25 Model 6.2 – Response is cow clinical mastitis (n = 128) in 932 cow-lactations (733 cows) Intercept -7.58 Farms 2 and 5 Reference Farm 1 3.30 1.17 10.11 Farm3 5.40 2.11 16.79 Farm4 5.97 2.34 18.32 Maximum log SCC < 5.32 (210,000/ml) Reference Maximum log SCC 5.32 – 5.65 (210,000 – 450,000/ml) 3.52 1.34 11.93 Maximum log SCC > 5.65 (450,000/ml) 7.63 2.72 28.42 Standard deviation log SCC (0.10 increase) 1.49 1.18 1.93 Between cow variance 0.82 0.38 1.36 Model 6.3 – Response is cow clinical mastitis (n = 1994) in 11825 cow-lactations (11673 cows) Intercept -10.80 Parity > 1 Reference Parity 1 0.68 0.60 0.78 Calving in months February to December Reference Calving in January 0.77 0.62 0.96 Maximum log SCC (unit increase) 5.08 4.54 5.76 Standard deviation log SCC = 0.422 Reference Standard deviation log SCC > 0.422 1.18 1.03 1.34 First lactation in study Reference Second lactation in study 0.06 0.02 0.17 Between farm variance 0.56 0.43 0.72 145 Figure 6.2. Graphs of Pearson residuals for Models 6.1, 6.2 and 6.3. The graphs illustrate Pearson residuals plotted against fitted values, and aggregates of Pearson residuals in order of ascending fitted values, for each model. Model 6.1 – Residual plots. Model 6.2 – Residual plots. -4 -2 0 2 4 6 8 10 12 14 16 0 0.2 0.4 0.6 0.8 1 Fitted value Pearson residual -2 -1 0 1 2 3 4 5 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Fitted value Pearson residual -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4 5 Five aggregated groups in order of ascending fitted value Mean Pearson residual 146 Model 6.3 – Residual plots. -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4 5 Five aggregated groups in order of ascending fitted value Mean Pearson residual -4 -2 0 2 4 6 8 10 12 14 0 0.2 0.4 0.6 0.8 1 Fitted value Pearson residual -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 Ten aggregated groups in order of ascending fitted value Mean Pearson residual 147 6.4.3. Models of Pathogen-Specific Clinical Mastitis. The final models are presented in Tables 6.5 and 6.6 below. Having controlled for confounding covariates, maximum log SCC was the parameter most consistently associated with CM and it was positively associated with CM in all pathogen-specific models. Increased variability of log SCC (measured as either standard deviation or coefficient of variation) was associated with an increased likelihood of CM in the Staph. aureus , E. coli and Strep. uberis models. Increasing mean log SCC was associated with an increased probability of clinical mastitis associated with Staph. aureus but with a reduced probability of CM associated with E. coli or no bacterial growth. An increase in minimum SCC was associated with an increased likelihood of clinical E. coli and Strep. uberis mastitis. There were no significant interactions in these models and analysis of Pearson residuals (see Figure 6.3, below) and outlying values, also suggested the models fitted well. 148 Table 6.5. Generalised linear mixed models of SCC distributional characteristics for Staph. aureus , Strep. dysgalactiae and Strep. uberis clinical mastitis in data-set three. Parameters were estimated using Markov Chain Monte Carlo with Gibbs Sampling. Coefficient Odds Ratio 95% Credibility Intervals Lower Upper Model 6.4 – Staph. aureus clinical mastitis n = (206) Intercept -15.47 Parity 2 and > 3 Reference Parity 1 1.61 1.10 2.34 Parity 3 1.70 1.17 2.44 Mean log SCC (unit increase) 7.53 4.46 12.92 Maximum log SCC < 5.56 (360,000/ml) Reference Maximum log SCC = 5.56 – 5.97 (360,000 – 930,000/ml) 2.05 1.25 3.34 Maximum log SCC = 5.97 (930,000/ml) 2.63 1.42 4.82 Standard deviation log SCC = 0.422 Reference Standard deviation log SCC > 0.422 1.91 1.33 2.74 First lactation in study Reference Second lactation in study 0.08 0.00 0.55 Between farm variance 0.84 0.40 1.42 Model 6.5 – Strep. dysgalactiae clinical mastitis (n = 96) Intercept -6.10 Parity 1, 2 and >3 Reference Parity 3 0.47 0.23 0.88 Maximum log SCC < 5.56 (360,000/ml) Reference Maximum log SCC = 5.56 – 5.97 (360,000 – 930,000/ml) 5.47 3.04 10.07 Maximum log SCC > 5.97 (930,000/ml) 8.21 4.77 14.69 Between farm variance 0.57 0.02 1.27 Model 6.6 – Strep. uberis clinical mastitis (n = 81) Intercept -6.16 Calving in months other than March, and August Reference Calving in March 2.00 1.00 3.73 Calving in May Calving in August Maximum log SCC = 5.97 (930,000/ml) Reference Maximum log SCC > 5.97 (930,000/ml) 2.28 1.26 4.15 Minimum log SCC = 4.79 (62,000/ml) Reference Minimum log SCC > 4.79 (62,000/ml) 2.86 1.60 5.01 Standard deviation log SCC < 0.326 Reference Standard deviation log SCC = 0.326 - 0.422 1.97 1.09 3.49 Standard deviation log SCC > 0.422 2.54 1.30 4.87 Between farm variance 0.36 0.00 1.17 149 Table 6.6. Generalised linear mixed models of SCC distributional characteristics for Escherichia coli, and no growth clinical mastitis in data-set three. Parameters were estimated using Markov Chain Monte Carlo with Gibbs Sampling. Coefficient Odds Ratio 95% Credibility Intervals Lower Upper Model 6.7 – E. coli clinical mastitis (n = 310) Intercept -4.56 Parity > 1 Reference Parity 1 0.47 0.34 0.65 Calving September to July Reference Calving in August 1.43 0.99 2.03 Mean days in milk of SCC readings (per day) 0.996 0.992 1.000 Mean log SCC (unit increase) 0.16 0.08 0.26 Maximum log SCC (unit increase) 7.11 5.10 10.05 Minimum log SCC = 4.11 (13,000/ml) Reference Minimum log SCC < 4.11 1(3,000/ml) 0.59 0.40 0.84 Coefficient of variation = 0.0985 Reference Coefficient of variation > 0.0985 1.20 0.82 1.73 Between farm variance 0.46 0.23 0.76 Model 6.8 – Clinical mastitis associated with no bacterial growth (n = 242) Intercept -7.76 Calving in March to January Reference Calving in February 1.60 1.01 2.47 First lactation in study Reference Second lactation in study 0.30 0.05 1.13 Parity > 1 Reference Parity 1 0.69 0.49 0.94 Mean log SCC (unit increase) 0.45 0.29 0.73 Maximum log SCC (unit increase) 4.07 2.77 6.06 Between farm variance 0.77 0.42 1.23 150 Figure 6.3. Graphs of Pearson Residuals for Models 6.4 to 6.8. The graphs illustrate Pearson residuals plotted against fitted values, and aggregates of Pearson residuals in ascending deciles plotted against fitted values, for each model. Model 6.4 – Residual plots. Model 6.5 – Residual plots. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 Ten aggregated groups in order of ascending fitted value Mean Pearson residual -2 0 2 4 6 8 10 12 14 16 18 0 0.02 0.04 0.06 0.08 0.1 Fitted value Pearson residual -2 0 2 4 6 8 10 12 14 16 18 0 0.1 0.2 0.3 0.4 0.5 Fitted value Pearson residual 151 Model 6.6 – Residual plots. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 Ten aggregated groups in order of ascending fitted value Mean Pearson residual 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 Ten aggregated groups in order of ascending fitted value Mean Pearson residual -5 0 5 10 15 20 0 0.02 0.04 0.06 0.08 0.1 0.12 Fitted value Pearson residual 152 Model 6.7 – Residual plots. Model 6.8 – Residual plots. -4 -2 0 2 4 6 8 10 12 14 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Fitted value Pearson residual -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 Ten aggregated groups in order of ascending fitted value Mean Pearson residual -2 0 2 4 6 8 10 12 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Fitted value Pearson residual 153 6.5. Discussion. Somatic cell counts are a useful measure of udder health, because they are widely recorded and accessible for appraisal. The importance of these results is that they suggests some limitations of using lactation mean log SCC as an indicator of CM, although the trait is currently widely used in genetic evaluation programs (Swanson et al., 1998; Mark et al., 2002). Making better use of patterns or distributions of SCC records may therefore improve genetic programs that aim to select for CM resistance. Furthermore, pathogen differences in distributions of SCC associated with CM have implications for local mastitis control. It may be possible to identify farms or periods of time when some SCC patterns (and hence pathogens) predominate, and therefore indicate the areas of control that should be addressed. Results from this analysis suggest that maximum and standard deviation of lactation log SCC improve the prediction of CM compared with using geometric mean SCC. The results were consistent across the three data-sets, despite the differences between lactation definition (whole or part lactations used), SCC sample type (quarter or cow), geographical location (UK or The Netherlands) or the size of data-set (n = 932 to n=11825). Maximum and standard deviation log SCC were more closely associated with CM than mean log SCC. This may be because these characteristics more accurately describe the effect of clinical intramammary infections on SCC. SCC rises dramatically following bacterial infection (Shuster et al., 1996; van Werven, 1999) and may return to normal in days or weeks (Milner et al., 1997). Therefore the impact of infection on maximum SCC is likely to be greater than that on mean SCC because the mean is influenced by all SCC readings during lactation, many of which may be taken when there is no inflammatory process. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 Ten aggregated groups in order of ascending fitted value Mean Pearson residual 154 Increased standard deviation of SCC during lactation was also associated with CM. Variability in SCC during lactation may occur if there is a recrudescence of an initial infection, a new infection later in lactation or it could be caused by a series of smaller challenges (and therefore SCC responses) in susceptible quarters. Again, these features are more likely to be accurately described by variability in SCC than mean or individual test day SCC. From these results, modelling variation may improve the accuracy of identifying cows with CM. This warrants continued investigation. The differences in SCC distributions between pathogens in data-set three indicate there were clear differences in the behaviour of organisms causing CM. There was a negative association between mean log SCC and CM in the E. coli and “no growth” CM models. This shows, that after accounting for the maximum SCC during lactation, cows that were more likely to get these types of CM had a lower mean lactation SCC than cows that did not get CM. This contrasts with the Staph. aureus model, in which increased mean log SCC increased the odds of CM. There were similarities between the E. coli and “no growth” CM models with a positive correlation between maximum log SCC and CM and a negative correlation between mean log SCC and CM. This may have occurred because a significant proportion of “no growth” CM were caused by E. coli, with the bacteria not being detected by culture (Zorah et al, 1993). Having controlled for other SCC characteristics, a minimum log SCC > 13,000/ml was also associated with an increased probability of E. coli CM. Therefore, a generally low SCC level over lactation was associated with an increased risk of E. coli CM, but not a single low SCC. Chapter Four of this thesis and other studies (Schukken et al., 1999; van Werven 1999; Suriyasathaporn et al., 2000; Peeler et al., 2003) have reported that low SCC are associated with an increased rate or severity of CM. Results from this chapter tend to support the contention that low SCC may predispose to CM. The Strep. dysgalactiae CM model contained only one SCC characteristic, maximum log SCC. Therefore, other than one high SCC, the distributions of SCC during lactation were not different from those of unaffected cows for this pathogen. The effect of parity on the risk of CM varied for different mastitis pathogens. The risk of E. coli CM was reduced in the first lactation, whereas this was not the case for Staph. aureus CM, when cows of parity one and three were at the greatest risk. For CM associated with Strep. dysgalactiae, parity three cows were at reduced risk of CM compared with other cows. The effects of parity and calving season in data-set three are difficult to explain, but imply that the transmission dynamics were very different between pathogens in these herds. For this study, however, we were concerned with controlling for these processes, thus ensuring that parameter estimates for the SCC variables were unbiased. 155 Possible methodological sources of error in these data arise from the diagnosis of CM and the accuracy of SCC recording. It is possible that CM could have been underrecorded during data collection, but is unlikely to have been over-recorded. Misclassification of lactations would generally result in fewer differences in SCC being detected between lactations with and without CM rather than falsely enhancing the differences found. The prospective nature of data collection would have helped to minimise the possibility of incorrect recording. The SCC data were dependent upon the accuracy of the electronic counting methods employed by each laboratory. SCC from all three data-sets were estimated by laboratories that were accredited for data collection for national SCC statistics and therefore provide data of equivalent accuracy to those currently used for bull evaluations. It was beyond the scope of this study to assess the reliability of these methods. However, poor accuracy of SCC estimation would, again, have tended to reduce rather than enhance the differences found between lactations with and without CM. 156 Chapter 7 General Discussion and Conclusions 7.1 Discussion 7.1.1. Clinical mastitis Despite widespread recognition of its importance and a considerable research effort, clinical mastitis remains one of the most serious production diseases of dairy cows. The incidence rate of clinical mastitis appears to have changed little in the UK over the past 15 years. There are possible explanations for this lack of improvement in clinical mastitis rates. First, it may be that sufficient knowledge exists to reduce the incidence but that control measures are not being efficiently implemented on farms. This could arise through faults in education, motivation and quantity or skill of the labour force. Second, it may be that current research has not provided the necessary knowledge to improve clinical mastitis in UK conditions. A large scale intervention study to carefully assess the effectiveness of properly implemented control measures would be required to assess which of these two possibilities is true. The research reported in this thesis has highlighted factors that may be useful to improve the control of clinical mastitis. In Chapter Two, bacterial isolates identified during the late dry-calving period were associated with increased risk of clinical mastitis. Caution in interpretation of the results is necessary because cause and effect cannot be ascertained from this type of study; it may be that the association arose from a population of generally susceptible quarters. However, previous research that has followed strains from the dry period to clinical cases of mastitis using microbiological techniques, suggests that at least in some instances the bacteria remain in the mammary gland and subsequently cause mastitis (Bradley and Green, 2000). Moreover, dry cow antibiotic treatments have been shown to reduce clinical mastitis during lactation (Bradley and Green, 2001c), another indicator that preventing dry period infections can reduce clinical mastitis in the next lactation. A further caution with interpreting results in Chapter Two, is that the research was conducted on six dairy units in one geographical region. Therefore, the findings may not be applicable to the general UK 157 dairy farm population. There is usually a trade-off in research projects between using the funding for less-detailed but wider ranging studies or smaller more detailed work. In Chapters Two and Three of this thesis, the required level of detail dictated that only six herds in one locality could be used. Despite these limitations, the results suggest that improved management of dry cows could result in reduced dry period infections and therefore reduced levels of clinical mastitis. The proportion of clinical cases in this study that were associated with presence of the same pathogen in the previous dry period was nearly 40%. This suggests that large improvements in the control of clinical mastitis may be possible if these dry period infections were more effectively prevented. Management strategies to achieve this should be tested in future research studies and then the affect of specific management changes on clinical mastitis could be identified. Further research is also required to improve the understanding of associations between bacterial species. In Chapter Three of the thesis there was evidence of both positive and negative associations between species during the dry period. Most work on bacterial interactions in bovine mastitis have been carried out either experimentally, during lactation or theoretically using mathematical modelling. In most instances it has been suggested that minor pathogens can play a role in preventing major pathogen infections. It is now necessary to expand this area of knowledge in order to reap benefits in the field. For example, understanding whether protective effects are reliant on certain strains of minor pathogens or the timing and persistence of minor pathogen infection. Methods of allowing and controlling colonisation with appropriate strains of minor pathogens will be essential for practical field applications. Furthermore, minor pathogens will influence the quarter, and hence herd somatic cell counts, and so repercussions for the herd in loss of milk value needs to be evaluated. There are significant hurdles to clear before minor pathogens can be used on farm to reliably have a beneficial effect. However, current research and the need for improved, non-antibiotic methods to control mastitis, suggest that an increased research effort in this direction could be valuable. As described earlier in this thesis, the link between minor pathogens and reduced probability of clinical mastitis could be through a small increase in somatic cell count. Whether this is the case or not, results from Chapter Five indicated that quarters with intermediate range somatic cell counts were at the least risk of clinical mastitis. This raises some intriguing questions such as which cell types are responsible for the protection, can we influence their levels in the mammary gland, and what genetic or environmental influences dictate intermediate cell concentrations? Analysis in Chapters Four and Five suggested that there was important variation within quarters, and therefore control of these mechanisms may 158 be, at least to some extent, local. This implies that environmental factors affecting individual quarters may be of greater importance than genetic determinants that would influence the ‘whole cow’. This concurs with the relatively low heritability of clinical mastitis, estimated at around 0.05 (Emanuelson et al., 1988), and suggests that mastitis research into genetic resistance may be of limited value. Currently there are no practical ways of using quarter SCC information on farm to aid in the control of mastitis. Future research will be important to enhance the understanding of the mechanisms behind intermediate SCC and protection against clinical mastitis. Despite possible limitations of genetic selection against clinical mastitis, results of Chapter Six suggests that there may at least be better methods than those currently used, for clinical mastitis selection. In most countries lactation mean SCC is used as a proxy for clinical mastitis in cows. Common sense suggests this must be a crude indicator, because SCC is sometimes raised for a short time only. These results showed that other measures of SCC distributions could be more useful than lactation mean, and this should be examined using other large data-sets for validation. Further research would also be required to assess the performance of bull’s offspring in terms of these SCC traits, to allow incorporation into genetic selection indices. It is a common conception in the UK farming industry, however, that in due course selecting for ‘genetic resistance’ will eradicate mastitis. Whilst in the long term, improvements should certainly be made, it is likely that the environmental component influencing the probability of mastitis will continue to play a large role and further research efforts in this area will be important. 7.1.2. Statistical methods During this thesis, most hypotheses were tested in a Bayesian framework with parameters estimated using MCMC with Gibbs sampling. Although the method was used because it was felt that parameter estimates would be accurate for the types of statistical models used, it became apparent that there were both advantages and disadvantages of using this approach. An important benefit of using MCMC, and the software WinBUGS, was the flexibility allowed for model building. For instance, models could be constructed in which parameters were either estimated (with distributional assumptions allowed to vary) or set at particular values. Model convergence and fit could be compared between the different models and an improved understanding of the data gained. Such flexibility allows the biological processes rather than mathematical constraints, to lead the modelling. Another benefit found with using MCMC was that visual assessment of the Markov Chains was very helpful to identify model suitability and stability. Poor mixing or 159 convergence implied models may have been mis-specified or over-parameterised, and a critical reassessment made. Most problems with chain mixing were encountered with the random effect variances in the Bernoulli and Cox proportional hazards models. The strategies used to resolve poor mixing were described in Chapter One, Section 1.4.2.3, and were considered successful. There were disadvantages of using MCMC for parameter estimation. Most important was the time for model construction and completion. The code written in WinBUGS had to be precise and error messages and reasons for failure were often unclear. Models generally took hours rather than minutes to converge and therefore initial model exploration and the continual changing of covariates was laborious. For this reason, much initial model exploration was carried out using PQL in MLwiN. Another potential disadvantage was that it was possible to fit inappropriate models and care had to be taken that the models constructed were appropriate for the data and hypotheses being investigated. An exploratory approach to model building, rather than a regimented forward or backward stepwise method was used throughout the research. Repeatedly adding covariates back to a model after it had been up-dated, helped to improve the understanding of relationships between variables or groups of variables. Correlations between explanatory covariates were also examined by investigating interaction terms, although these were rarely found to be statistically significant. Another area of model building that was found to be important was investigating the shape of relationships between explanatory and response variables. This was carried out by initially grouping continuous explanatory covariates into five or more categories and assessing the direction and magnitude of the relationship with the response variable. A decision was then made as to whether the relationship was linear or nonlinear and therefore how best to include the explanatory covariate in the model. Examples of this were categorising cows by parity, categorising QSCC by month of lactation, and modelling lactation SCC distributional characteristics either as linear or categorical covariates. Goodness of fit of Bernoulli GLMM provided another area of interest that developed as the research proceeded. Many texts offer only sparse advice on the subject (e.g. Snijders and Bosker, 1999; Schukken et al., 2003) and it is an area of ongoing research. An underlying element of assessing goodness of fit in all GLMM is to discover outlying data points, covariate patterns or higher level units and to check their influence/leverage on the model. For Bernoulli models, plots of standardised lowest level Pearson residuals were used (see Chapter One, section 1.4.3.3). This was initially carried out subjectively, by visual assessment, and several methods were used to attempt to improve on this subjective assessment. An example is given below using the data from Model 4.2 (Chapter Four). 160 Figure 7.1a shows that a graphic representation of the residuals in order of observation number gives little information on adequacy of fit, although it does indicate that there were few cases of clinical mastitis (positive residuals, n = 122) amongst many unaffected (control) readings (n = 12,515). From plot (a) it is difficult to evaluate whether the few large positive residuals were ‘balanced’ by numerous small negative residuals with a similar fitted probability. Plotting the residuals in order of fitted value (Figure 7.1 b and c) indicated that the ratio of cases to controls remained approximately correct as fitted value increased, because the aggregate means were close to zero. Figure 7.1 Pearson residuals from Model 4.2, Chapter 4: a. Pearson residuals plotted against observation number, b. Pearson residuals plotted in ascending order of fitted value and c. Aggregate means of Pearson residuals plotted in ascending order of fitted value. a. b. c. -5 0 5 10 15 20 25 Observation number Pearson residual -5 0 5 10 15 20 25 0.000 0.050 0.100 0.150 Fitted Value Pearson residual -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 Aggregated groups (of equal sizes) in order of ascending fitted values Mean of aggregated Pearson residuals 161 In order to investigate further whether the aggregate means in graph 7.1 c did differ from zero, further statistical tests were investigated. The mean and 95% confidence interval of the mean were calculated for each aggregate of Pearson residuals, and this is illustrated below, in Figure 7.2a. The 95% confidence interval for the mean was also calculated on a rolling basis, for cumulative, ascending sets of Pearson residuals (sets of 3000 in this example) and this is illustrated in Figure 7.2b. These graphs suggest possible slight deviation from the expected ratio of cases to controls, with aggregates one and five having a confidence interval that did not include zero. The data values used to calculate the mean and construct these confidence intervals do not necessarily have a Normal distribution, and in this research outcomes Y=1 were generally sparse. This suggests that estimates of the 95% confidence intervals of the aggregate means have to be viewed with caution. An alternative approach to model fit was also used, a method based on the principles of the Hosmer- Lemeshow Statistic (Hosmer and Lemeshow, 1989). The number of outcomes Y=1 and Y=0 were calculated for each aggregated set of Pearson residuals. The observed number of outcomes in each aggregate was compared to the expected number (the expected number of Y=1 being the sum of the fitted values of each aggregate). An example of this approach for Model 4.2 is presented graphically below, (Figure 7.3). The graph confirms that there were proportionately largest differences between observed and expected numbers in aggregates one, four and five. However, in aggregate one, the difference was nil (observed) and one (expected) out of 1264 data points. Similarly in deciles four and five, the differences were 2 (observed) and 5.1 (expected) and 2 (observed) and 6.4 (expected) respectively, out of 1264 data points. None of these individual differences was significant using a .2 test (p > 0.1), suggesting that the deviation of the model from the expected pattern may have been unimportant. The main reason to assess model fit was to ensure that inferences made from the statistical models were safe. Particular difficulty arose from the data in this research because, for Bernoulli models, the proportion of outcomes Y=1 was often very small. Therefore, the ‘average’ (null) model fit approached zero and the expected number of outcomes Y=1 became very small at very low fitted values. If model fit is assumed to be adequate unless it is found that the model differs significantly from an expected ‘good’ fit, sufficient numbers are needed to allow a true difference to be identified. One way of helping with this issue is to combine aggregates of residuals, to increase the number of expected outcomes Y=1. The graphical approaches described in this example provided a method of assessing model fit and moreover gave an indicator of the areas of data that did not fit the model, and that needed further investigation. 162 Figure 7.2. Pearson residuals from Model 4.2, Chapter 4: a. Mean and 95% confidence intervals of the aggregated groups of Pearson residuals, and b. 95% confidence intervals for rolling groups of 3000 Pearson residuals in ascending order of fitted value. a. b. Figure 7.3. Model 4.2, Chapter 4: Observed and expected number of cases in each of ten aggregates of Pearson residuals. -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 1 2 3 4 5 6 7 8 9 10 Aggregated groups (of equal sizes) in order of ascending fitted values Mean and 95% C.I. of Pearson residuals 0 10 20 30 40 50 60 < 0.0015 to 0.0022 to 0.003 to 0.006 to 0.006 to 0.007 to 0.010 to 0.014 to 0.020 to 0.140 Model fitted value Number of cases of clinical mastitis Observed number of cases Expected number of cases -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.0017 0.0018 0.0020 0.0022 0.0025 0.0029 0.0034 0.0039 0.0041 0.0044 0.0047 0.0050 0.0054 0.0058 0.0062 0.0067 0.0071 0.0080 0.0089 0.0098 0.0108 0.0118 0.0132 0.0145 0.0159 0.0174 Fitted value 95% Confidence interval for mean Pearson residuals in rolling aggregates of 3000 163 Assessing goodness of fit of higher level units in the hierarchical Bernoulli models also presented difficulties, although if the bottom level residuals did not suggest deviations then it was unlikely that higher level units would cause problems. Therefore, poor fit of higher level units was partially identified through investigation of clusters of poorly fitting lower level units. The higher level Bayesian residuals for this example (between quarters within cow, and between cows) are shown graphically in Figure 7.4 below. Higher level residuals tended to reflect the distribution of the data and this is likely when there are relatively few lower level units for each higher level unit. In this example, there were seven quarters with large residuals and these were quarters that had more than one case of clinical mastitis, and that were therefore most different from the ‘average quarter’. A similar effect was seen for cow (level three) residuals. Omission of each of the seven quarters or cows with largest residuals, however, did not alter the biological inferences made from the model and suggested that clustering of points within the data was not resulting in biased parameter estimates. Calculation of an overall ‘goodness of fit’ statistic that incorporates fit at each level of the Bernoulli GLMM and allows easy identification of outlying points would be a useful subject for future research. 164 Figure 7.4. Higher level Bayesian residuals from Model 4.2: a. Unstandardised level two residuals (between quarters) plotted against observation number, and b. Unstandardised level three residuals (between cows) plotted against observation number. a. b. -0.010 -0.005 0.000 0.005 0.010 0.015 0.020 Observation number Unstandardised residual -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Observation number Unstandardised residual 165 7.2. Conclusions. 7.2.1. Chapter Two. The results from this chapter demonstrated that bacterial infection during the dry period was an important influence on subsequent clinical mastitis. • Infections with major pathogens in the late dry and post calving period increased the risk of clinical mastitis and this mastitis occurred at a greater rate after calving than mastitis not associated with dry period infections. • Isolation of Corynebacterium spp. was associated with both an increase and a decrease in clinical mastitis, depending on the timing of infection. • There was evidence of quarter susceptibility to infection or the possibility that infection with one organism may lead to clinical mastitis with another. • Future research on preventing dry period infections, the protective effects of Corynebacterium spp., quarter susceptibility and interactions between consecutive infections with different bacteria may improve our ability to reduce clinical mastitis. 7.2.2. Chapter Three. • Significant differences in the prevalence of infection during the dry period occurred between farms and in different calving months, suggesting the level of infection was dependent on external conditions. • The probability of isolating E. coli or Strep. uberis significantly increased when the other organism was cultured in a milk sample; this was also true of coagulase positive staphylococci and Strep. uberis. • When Corynebacteria spp. were isolated in a milk sample, the probability of isolating coagulase positive staphylococci or Strep. uberis significantly decreased and when coagulase negative staphylococci were isolated there was a reduced probability of coagulase positive staphylococci being cultured. • The role of interactions between bacterial infections of the bovine udder during the dry period requires further research. 7.2.3. Chapter Four. • Quarters with intermediate levels of leukocytes in milk, measured as a somatic cell count, had a reduced risk of clinical mastitis for up to three months. • Compared to quarters with QSCC = 40,000 cells/ml, QSCC 41,000 – 100,000 cells/ml had a reduced risk of clinical mastitis, in the following month, and QSCC > 200,000 cells/ml an increased risk of clinical mastitis. 166 • Between one and two months later, quarters with QSCC 81,000 – 150,000 cells/ml had a lower risk of clinical mastitis than quarters = 80,000 cells/ml. • Between two and three months later, quarters with QSCC 61,000 – 150,000 cells/ml had a lower risk of clinical mastitis than quarters = 60,000 cells/ml. • Understanding the reasons why intermediate ranges of QSCC are associated with a reduced risk of clinical mastitis may lead to improved methods to prevent clinical mastitis in dairy herds. • The results provide a further caution against a continual drive to the lowest possible SCC within the dairy industry. 7.2.4. Chapter Five. • Generalised linear mixed models used to assess variance components of QSCC identified that significant variation occurred with; • quarter position • parity of cow • month of lactation • month of year • the occurrence of clinical mastitis • an interaction between parity and month of lactation • Most residual variation occurred between readings within quarters, rather than between quarters or between cows. • Most QSCC readings were in the lowest QSCC categories (0 - 40,000 cells/ml) and the majority remained in this range at the next monthly recording • There was evidence of stability in the low, middle and high ranges of QSCC between consecutive monthly recordings • These findings were relevant following the results from Chapter Four. It may explain why quarters were at reduced risk of clinical mastitis for up to three consecutive months; because, despite variation within quarters, the low risk quarters were more likely to remain in the central low risk QSCC categories for CM over time, compared with other quarters. 7.2.5. Chapter Six. • Characteristics of SCC distributions over lactation were investigated to assess their association with clinical mastitis. 167 • When all pathogens were considered together, results indicated that maximum and standard deviation of log SCC were the best indicators of CM, rather than mean log SCC. Results were consistent across three different sets of data. • Pathogen-specific models indicated that maximum log SCC was consistently positively associated with CM, but that other SCC characteristics differed between pathogens. • The models of E. coli and “no growth” CM had similar SCC features, including both types showing an increased risk with reducing lactation mean log SCC. 7.2.6. Statistical approaches. • The use of MCMC provided a useful platform for estimating parameters in hierarchical Bernoulli models. • The main advantage of using MCMC was the flexibility allowed in the approach to modelling. The main disadvantage was that the technique was computer intensive and model exploration was extremely slow. • Goodness of fit of multilevel Bernoulli models was explored. This is an area that would benefit from more research to provide a robust statistical basis for goodness of fit to be tested at each level. 168 References and Bibliography Ali, A. K. A. and G. E. Shook. 1980. An optimum transformation for somatic cell count concentration in milk. J. Dairy Sci. 63:487-490. Anon. 1999. Egret for Windows Version 2.0.3. User Manual. Cytel Software Corporation, USA. Anon. 2001. Veterinary Investigation Surveillance Report. London, Veterinary Laboratories Agency. Barkema, H.W., Y.H. Schukken, T.J. Lam, M.L. Beiboer, G. Benedictus, A. Brand. 1998. Management practices associated with low, medium, and high somatic cell counts in bulk milk. J. Dairy Sci. 81:1917-27. Beaudeau, F., H. Seegers, C. Fourichon, and P. Hortet. 1998. Association between milk somatic cell counts up to 400,000 cells/ml and clinical mastitis in French Holstein cows. Vet. Rec. 143(25): 685-687. Beaudeau, F., C. Fourichon, H. Seegers and N. Bareille. 2002. Risk of clinical mastitis in dairy herds with a high proportion of low individual milk somatic cell counts. Prev. Vet. Med. 53: 43-54. Berry, E.A. 1998. Mastitis incidence in straw yards and cubicles. Vet. Rec. 142: 517-8. Berry, E.A. and J.E. Hillerton. 2002 The effect of an intramammary teat seal on new intramammary infections. Journal of Dairy Science. 85, 2512-20. Blowey R. and P. Edmondson. 1995. Mastitis Control in Dairy Herds. Farming Press Books, Wharfedale Road, Ipswich, UK. Boerlin P., P. Kuhnert, D. Hussy, M. Schaellibaum. 2003. Methods for identification of Staphylococcus aureus isolates in cases of bovine mastitis. J. Clin. Microbiol. 41: 767-71. Booth, J. M. 1997. Progress in mastitis control - an evolving problem. Proc. British Mastitis Conference. pp. 3-9. Bradley A. J. and M. J. Green. 2000. A study of the incidence and significance of intramammary enterobacterial infections acquired during the dry period. J. Dairy Sci. 83: 1957-1965. Bradley A. J. and M. J. Green. 2001a. Clinical mastitis in a cohort of Somerset dairy herds. Vet. Rec. 148: 683-86. Bradley A. J. and M. J.Green. 2001b. Adaptation of Escherichia coli to the bovine mammary gland. J. Clinical Microbiol. 39: 1845-9. Bradley A. J. and M. J. Green. 2001c. An investigation of the impact of intramammary antibiotic dry cow therapy on clinical coliform mastitis. J. Dairy Sci. 84, 1632-9. Bradley, A. 2002. Bovine mastitis: An evolving disease. The Vet. Journal. 163: 1-13. 169 Bramley A.J. 1975. Infection of the udder with coagulase-negative micrococci and Corynebacterium bovis. Seminar of mastitis control procedings. IDF. p377. Bramley A.J. 1976. Variations in the susceptibility of lactating and non-lactating bovine udders to infection when infused with Escherichia coli. J. Dairy Res. 43:205-211. Bramley A.J. 1978. The effect of Staphylococcus epidermidis infection of the lactating bovine udder on its susceptibility to infection with Streptococcus agalactiae or Escherichia coli. Br. Vet. J. 134:146. Breslow N.E. and, D.G. Clayton 1993. Approximate inference in generalized linear mixed models. J. Am. Statistical Assoc. 88:9-25. Brolund, L. 1985. Cell counts in bovine milk: causes of variation and applicability for diagnosis of sub-clinical mastitis. Acta Vet. Scand. 80: 1. Brooks B.W., D.A. Barnum and A.H. Meek. 1983. An observational study of Corynebacterium bovis in selected Ontario dairy herds. Can J Comp Med. 47:1 73-8 Brooks B.W. and D.A. Barnum. 1984a. The susceptibility of bovine udder quarters colonised with Corynebacterium bovis to experimental infection with Staphylococcus aureus or Streptococcus agalactiae. Can J Comp Med. 48:146 Brooks B.W. and D.A. Barnum. 1984b. Characterization of strains of Corynebacterium bovis. Can. J. Comp. Med. 48:2 230-232. Brooks, S.P. and A. Gelman. 1998. Alternative methods for monitoring convergence of iterative simulations. J. Computational and Graphical Statistics. 7: 434-455. Browne, W.J. and D. Draper. 2003. A comparison of Bayesian and likelihood-based methods for fitting multilevel models. Submitted. www.maths.nottingham.ac.uk/personal/pmzxjb/bill.html Buelow K.L., C.B. Thomas, W.J. Goodger, K.V. Norland and M.T. Collins. 1996. Effect of milk sample collection strategy on the sensitivity and specificity of bacteriologic culture with somatic cell count for detection of Coagulase positive Staphylococci intramammary infection in dairy cattle. Prev. Vet. Med. 26:1-8 Burton PR, K. Tiller, L.C. Gurrin, A.W. Musk, W.O.C.M. Cookson and L.J Palmer 1999. Genetic variance components analysis for binary phenotypes using generalized linear mixed models (GLMMs) and Gibbs sampling. Genetic Epidemiology 17:118-140 Caldwell D. E. and J.W. Costerton. 1996. Are bacterial biofilms constrained to Darwins concept of evolution through natural selection? Microbiologia 12: 347-58 Capurro A., C. Concha, L. Nilsson, K. Ostensson. 1999. Identification of coagulase-positive staphylococci isolated from bovine milk. Acta Vet. Scand. 40:315-21 Clayton, D. and M. Hills. 1993. Statistical Models in Epidemiology. Oxford University Press, Oxford. 170 Coffey, E.M., W.E. Vinson, and R.E. Pearson. 1986. Somatic cell counts and infection rates for cows of varying somatic cell count in initial test of first lactation. J. Dairy Sci. 69: 552- 555. Collett, D. 1994. Modelling survival data in medical research. CRC Press LLC, 2000 NW, Florida, USA. Curtis R., P.G. Hendy, D.J. Watson, A.M.Harris, A.M. Davis, and M.J. Marshall. 1977. A cerate containing cephalonium for the prophylaxis of dry udder infections in dairy cows. Vet. Rec. 100:557-560. Dalhoff, A. 1982. Influence of Escherichia coli on Streptococcus faecalis in mixed cultures and experimental animal infections. Eur. J. Clin. Microbiol. 1:17-21. Davey M.E. and G.A.O’Toole. 2000. Microbial biofilms: from ecology to molecular genetics. Microbiol Mol. Biol. Rev. 2000. 64(4): 847-67. de Haas, Y., H. W. Barkema and R.F. Veerkamp. 2002. The effect of pathogen-specific clinical mastitis on the lactation curve for somatic cell count. J. Dairy Sci. 85:1314-1323. Deluyker, H.A., J.M. Gay and L.D.Weaver. 1993. Inter-relationships of somatic cell count, mastitis, and milk yield in a low somatic cell count herd. J. Dairy Sci. 76: 3445-52. Doane, R.M., S.P Oliver, R.D.Walker and E.P. Shull. 1987. Experimental infection of lactating bovine mammary glands with Streptococcus uberis in quarters colonised by Corynebacterium bovis. Am. J. Vet. Res. 48:749. Dodd F.H., and T.K. Griffin. 1975. The role of antibiotic treatment at drying off in the control mastitis. Proc IDF Seminar on mastitis control. IDF Bulletin 85 282. Dodd, F.H. 1983. Mastitis - progress on control. J Dairy Sci. 66:1773. Dodd, F.H., D.R. Westgarth, F.K. Neave, and R.G. Kingwill. 1969. Mastitis - The strategy of control. J. Dairy Sci. 52:689. Dohoo, I.R. and A.H. Meek. 1982. Somatic cell counts in bovine milk. Can. Vet. J. 23: 119- 125. Dohoo, I.R., W. Martin, and H.Stryhn. 2003. Veterinary Epidemiologic Research. AVC Inc. Charlottetown, Prince Edward Island, Canada. Dopfer, D., H.W. Barkema, T.J. Lam, Y.H. Schukken and W. Gaastra.1999. Recurrent clinical mastitis caused by Escherichia coli in dairy cows. J. Dairy Sci. 82: 80-5. Eberhart R.J. 1986. Management of dry cows to reduce mastitis. J. Dairy Sci. 69:1721-1732. Eberhart, R.J. and J.M. Buckalew. 1977. Intramammary infections in a dairy herd with a low incidence of Streptococcus agalactiae and Staphylococcus aureus infections. J. Am. Vet. Med. Assoc. 171: 630-34. Eberhart, R.J. H.C. Gilmore, L.J. Hutchinson and S.B. Spencer. 1979. Somatic cell counts in DHI samples. Proc Nat Mast Counc. p32-40. 171 Emanuelson, U., B. Danell and J. Philipsson. 1988. Genetic parameters for clinical mastitis, somatic cell counts and milk production estimated by multiple-trait restricted maximum likelihood. J. Dairy Sci. 71:467-476. Erskine, R.J. and R.J.Eberhart. 1988. Comparison of duplicate and single quarter milk samples for the identification of intramammary infections. J. Dairy Sci. 71:854. FAWC. 1997. Report on the Welfare of Dairy Cattle. Farm Animal Welfare Council, Tolworth. p32-34. Gilks, W.R., S. Richardson and D.J. Spiegelhalter. 1995. Markov Chain Monte Carlo in practice. Chapman and Hall, London, UK. Goldstein, H. 1995. Multilevel Statistical Models (2nd edition). Edward Arnold, London, UK. Gonzales, R.N., J. S Cullor, D.E. Jasper, T.B. Farver, R.B. Bushnell, and M.N Oliver. 1989. Prevention of clinical coliform mastitis in dairy cows by a mutant Escherichia coli vaccine. J. Dairy Sci. 53: 301-5. Green, M. J., L. E. Green, and P. J. Cripps. 1996. Low bulk milk somatic cell counts and endotoxin-associated (toxic) mastitis. Vet. Rec.138: 305-6. Green, M. J., and A. J. Bradley. 1998. Coliform Mastitis - An Evolvong Problem Cattle Practice. 6:91-94. Green M. J., L. E. Green, G. F. Medley, Y. H. Schukken and A. J. Bradley. 2002. Influence of Dry Period Bacterial Intramammary Infection on Clinical Mastitis in Dairy Cows. J. Dairy Sci. 85: 2589-2599. Green M.J., L. E. Green, Y. H. Schukken, A. J. Bradley, E. J. Peeler, H. W. Barkema, Y. de Haas, V. J. Hedges, and G. F. Medley. 2003a. Somatic Cell Count Distributions during Lactation Predict Clinical Mastitis. J. Dairy Sci. (in press). Green, M.J., P. R. Burton, L. E. Green, Y. H. Schukken, A. J. Bradley, E J. Peeler, and G. F. Medley. 2003b. Patterns of somatic cells in milk and the risk of clinical mastitis in dairy cows. Prev. Vet. Med. (accepted subject to minor revisions). Green M. J., L. E. Green, A. J. Bradley, P. R. Burton, Y. H. Schukken and G. F. Medley. 2003c. Bacterial isolates in the dry bovine mammary gland: Prevalence and Associations. Vet. Rec. (submitted) Grega T. and Szarek J. 1985. Relationship of teat canal size to milkability and udder health in three breeds. Zeszyty Naukowe Akademii Rolniczej w Krakowie No 191. Zootechnika 23:3-11. Grindal, R.J., A.W. Walton and J. E. Hillerton. 1991. Influence of milk flow rate and teat canal length on new intramammary infection in dairy cows. J. Dairy Res. 58:383-388. Harmon R.J., W.L. Crist, R.W. Hemken, B.E. Langlois. 1986. Prevalence of minor udder pathogens after intramammary dry treatment. J. Dairy Sci. 69:3 843-9. Harmon, R. J., R. J. Eberhart, D. E. Jasper, B. E. Langlois, and R. A. Wilson. 1990. Microbiological procedures for the diagnosis of bovine udder infection. Nat. Mastitis Counc. Inc., Arlington, VA. 172 Hedges, V. J., R.W. Blowey, A.J. Packington, C.J. O'Callaghan and L.E. Green. 2001. A longitudinal field trial of the effect of biotin on lameness in dairy cows. J. Dairy Sci. 84:1969- 75. Hill, A. W., A. L. Shears, and K. G. Hibbit. 1979. The pathogenesis of experimental Escherichia coli mastitis in newly calved dairy cows. Res Vet. Sci. 26: 97-101. Hill A. W. 1981. Factors influencing the outcome of Escherichia coli mastitis in dairy cows. Res.Vet. Sci. 31: 107-112. Hogan J.S., K.L. Smith, D.A. Todhunter, and P.S. Schoenberger. 1988. Rate of environmental mastitis in quarters infected with Corynebacterium bovis and Staphylococcus species. J. Dairy Sci. 71: 2520. Hosmer D.W. and S. Lemeshow. 1989. Applied Logistic Regression. John Wiley and Sons Inc. New York. USA. Huxley, J.N., M.J. Green, L.E. Green and A.J. Bradley. 2002 Evaluation of the efficacy of an internal teat sealer during the dry period. Journal of Dairy Science. 85: 551-61. International dairy federation mastitis expert group. 1987. Bovine mastitis: Definitions and guidelines for diagnosis. IDF bulletin 211/1987. Jasper D.E., J.D. Dellinger and R.B. Bushnell. 1974. Agreement of duplicate samples of milk for the evaluation of quarter infections. Am J Vet Res. 35:1371 Kay, S.J., K.A. Collins, J.C. Anderson and A.J. Grant. 1977. The effect of intergroup movement of dairy cows on bulk milk somatic cell numbers. J. Dairy Res. 44: 589-593. Kingwill, R.G., F.K.Neave, F.H Dodd, T.K.Griffin, D.R.Westgarth and C.D.Wilson. 1970. The effect of a mastitis control system on levels of subclinical and clinical mastitis in two years. Vet. Rec. 87: 94-100. Kleinbaum D G., 1994. Logistic Regression. Statistics in Health Sciences. Springer Verlag New York Inc. Kossaibati M. A. and Esslemont R. J. 1996. DAISY Report no 4: Wastage in Dairy Herds. Kossaibati, M. A., and R. J. Esslemont. 1997. The costs of production diseases in dairy herds in England . Vet. Journal. 154:41-51. Kossaibati, M. A., M. Hovi, and R. J. Esslemont 1998. Incidence of clinical mastitis in dairy herds in England. Vet Rec. 143: 649-53. Kossaibati, M. A. 2000. The costs of clinical mastitis in UK dairy herds. Cattle Practice 8, 323-8. Laevens, H., H Deluker, Y.H. Schukken, L. de Meulemeester, R. Vandermeersch, E de Muelenaere and A. de Kriuf. 1997. Influence of parity and stage of lactation on the somatic cell count in bacteriologically negative dairy cows. J. Dairy Sci. 80: 3219-3226. 173 Lam, T.J., L.J. Lipman, Y.H. Schukken, W. Gaastra and A.Brand. 1996. Epidemiological characteristics of bovine clinical mastitis caused by Staphylococcus aureus and Escherichia coli studied by DNA fingerprinting. Am. J. Vet. Res. 57: 39-42. Lam T.J., Y.H. Schukken, J.H. van Vliet, F.J. Grommers, M.J. Tielen and A Brand. 1997. Effect of natural infection with minor pathogens on susceptibility to natural infection with major pathogens in the bovine mammary gland. Am. J. Vet. Res. 58:1, 17-22 . Lee, C.S., F.B. Wooding and P. Kemp. 1980. Identification properties, and differential counts of cell populations using electron microscopy of dry cow secretions, colostrum and milk from normal cows. J. Dairy Sci. 47: 39-50. LeVan P.L. R.J. Eberhart, E.M. Kesler 1985. Effects of natural intramammary Corynebacterium bovis infection on milk yield and composition. J. Dairy Sci. 68:3329-36. Linde C., O. Holmberg, and G Anstrom. 1980. The interference between coagulase negativestaphylococci and Corynebacterium bovis and the common udder pathogens in the lactating cow. Nord. Veterinaermed. 32:552. Lund, M.S., J. Jensen and P.H. Petersen. 1999. Estimation of genetic and phenotypic parameters for clinical mastitis, somatic cell production deviance and protein yield. J. Dairy Sci. 82:1045-1051. Mark, T., W.F. Fikse, U. Emanuelson and J.Philipsson. 2002. International genetic evaluations of Holstein sires for milk somatic cell count and clinical mastitis. J. Dairy Sci. 85: 2384-2392. Mathews K.R., R. J. Harmon and B.E. Langlois. 1991. Effect of naturally occurring coagulase-negative staphylococci infections on new infections by mastitis pathogens in the bovine. J.Dairy Sci. 74:1855-59. McCullagh P., and J.A. Nelder. 1989. Generalized linear models. 2nd Edition. Chapman and Hall, Oxford, UK. McDermott J.J. and Y.H. Schukken. 1994. A review of methods used to adjust for cluster effects in explanatory epidemiological studies of animal populations. Prev. Vet. Med. 18:155- 173. McDonald, J. S. and A. J. Anderson. 1981. Experimental intramammary infection of the dairy cow with Escherichia coli during the non-lactating period Am. J.Vet. Res. 42:229-231. Milner, P., K. L. Page, and J.E. Hillerton. 1997. The effects of early antibiotic treatment following diagnosis of mastitis detected by a change in the electrical conductivity of milk. J. Dairy Sci. 80:859-63. Miltenburg, J.D., D.de Lange, A.P. Crauwels, J.H. Bongers, M.J. Tielen, Y.H. Schukken and A.R. Elbers. 1996. Incidence of clinical mastitis in a random sample of dairy herds in the Southern Netherlands. Vet. Rec. 139: 204-7. Ministry of Agriculture and Fisheries. 1953. Report on animal health services 1949-1951 p44. Mrode, R. A., and G. J. T. Swanson. 1996. Genetic and statistical properties of somatic cell count and its suitability as an indirect means for reducing the incidence of mastitis in dairy cattle. Animal Breeding Abstracts, 64(11), 847-857. 174 National Institute for Research in Dairying. 1957. Annual Report. National Mastitis Council. 1999. Laboratory Handbook on Bovine Mastitis. National Mastitis Council Inc. Madison, WI, USA. Natzke R.P. 1982. The role of therapy in mastitis control. Proc. NMC 21st annual meeting p125. Neave F.K., F.H. Dodd, and E. Henriques. 1950. Udder infections in the dry period. J. Dairy Res. 17:37-49 Neave F.K., F.H. Dodd and R.G. Kingwill. 1966. A method of controlling udder disease. Vet. Rec. 78:521-23. Nelson R. J., and G.E. Demas. 1996. Seasonal changes in immune function. The quarterly review of biology. 71: 511-548. Ngatia T.A., N.E Jensen and B.B. Berg. 1991. Changes in the bovine udder naturally infected with Corynebacterium bovis. Br. Vet. J.147:5 463-8. Oliver J., K.F. Neave, and M.E. Sharpe. 1962. Prevention of infection of the dry udder. J.Dairy Res. 29:95-102. Oliver S.P., and Michell B.A. 1983. Susceptibility of bovine mammary gland to infections during the dry period. J.Dairy Sci 66:5 1162-6. Oliver S.P. 1987. Influence of dry period number on rates of intramammary infection during physiological transitions of the bovine mammary gland. J.Dairy Sci. 70(suppl 1): 242. Oliver S.P. 1988. Frequency of isolation of environmental mastitis-causing pathogens and incidence of new intramammary infection during the non-lactating period. Am. J.Vet. Res. 49:11 1789-1793. Oliver S.P. and L.M. Sordillo. 1988. Udder health in the periparturient period. J.Dairy Sci. 71: 2584-2606. Oliver S.P., and V.K Juneja. 1990. Growth of Corynebacteriun bovis in mammary secretions during physiological transitions of the bovine mammary gland. J.Dairy Sci. 73:2 351-6. Pankey J.W., R.M. Barker, A. Twomey, and G Duirs. 1982a. A note on effectiveness of dry cow therapy in New Zealand. N.Z. Vet. J. 30:50. Pankey J.W., R.M. Barker, A. Twomey, and G Duirs. 1982b. Comparative treatment regimes against Staphylococcus aureus. N.Z. Vet J. 30:13. Pankey J.W., S.C. Nickerson, R.L. Boddie and J.S. Hogan. 1985. Effects of Corynebacteriun bovis infection on susceptibility on major mastitis pathogens. J.Dairy Sci. 68:2684. Park, Y.H., L.J. Fox, M.J. Hamilton, and W.C. Davis. 1993. Suppression of proliferative responseof BoCD4+ T lymphocytes in the mammary gland of cows with Staphylococcus aureus mastitis. Vet. Immunol. Immunopthol. 36: 137-151. 175 Parmer, K.B. and D. Machin. 1995. Survival Analysis - A practical approach. Pub. John Wiley and sons, NY, USA. Peeler E.J. 2001. Epidemiological studies of clinical mastitis in British dairy herds with bulk milk somatic cell counts of less than 150,000 cells per millilitre. PhD Thesis, University of Bristol, Langford, UK. Peeler E.J., M.J. Green, J.L. Fitzpatrick, and L.E. Green. 2002. Study of clinical mastitis in British dairy herds with bulk milk somatic cell counts less than 150,000 cells/ml. Vet. Rec. 151:170-6. Peeler, E. J., M.J. Green, J.L. Fitzpatrick and L.E. Green. 2003. The association between quarter somatic cell counts and clinical mastitis in three British dairy herds. Prev. Vet. Med. 59:169-180. Petrie A. and Watson, P. 1999. Statistics for Veterinary and Animal Science. Blackwell Sacience Ltd, Osney Mead, Oxford. Philipsson, J. G. Ral and B. Bergland. 1995. Somatic cell count as a selection criterion for mastitis resistance in dairy cattle. Livest. Prod. Sci. 41:195-200. Poutrel B., and C. Lerondelle. 1980. Protective effect in the lactating bovine mammary gland induced by coagulase-negative staphylococci against experimental Staphylococcus aureus infections. Ann. Rech.Vet. 11:327. Pybus V. and A.B. Onderdonk. 1999. Microbial interactions in the vaginal ecosystem with emphasis on the pathogenesis of bacterial vaginosis. Microbes Infect. 1(4):285-92 Quinn, P. J., M. E. Carter, B. Markey, and G. R. Carter. 1994. Clinical Veterinary Microbiology. Wolfe, London, UK. Radostits, O. M., K.E. Leslie and J. Fetrow. 1994. Herd health: Food animal production medicine. Saunders, Philadelphia, PA. USA. Rainard P., and B Poutrel. 1988. Effect of naturally occurring intramammary infections by minor pathogens on new infections by major pathogens in cattle. Am J.Vet. Res. 49: 327-9. Rasbash, J., W. Browne, H. Goldstein, M. Yang, I. Plewis, M. Healy, G. Woodhouse, D. Draper, I. Langford, and T. Lewis. 1999. A user's guide to MLwiN. Version 2, Multi-level Models Project, Institute of Education, University of London. Rosenzuaig A., and E Mayer. 1970. Observations on the effects of treatment at drying off on the incidence of sub-clinical udder infections in two dairy herds. Refu. Vet. 26:126. Rupp, R., and D. Boichard. 2000. Relationship of early first lactation somatic cell count with risk of subsequent first clinical mastitis. Livestock Prod. Sci. 62: 169-180. Schepers, A. J., T. J. G. M. Lam, Y. H. Schukken, J. B. M. Wilmink, and W. J. A. Hanekamp. 1997. Estimation of variance of components for somatic cell counts determine thresholds for uninfected quarters. J. Dairy Sci. 80: 1833-1840. 176 Schukken, Y. H., B. A. Mallard, J. C. M. Dekkers, K. E. Leslie, and M. J. Stear. 1994. Genetic Impact On the Risk of Intramammary Infection Following Staphylococcus-Aureus Challenge. J. Dairy Sci. 77: 639-647. Schukken, Y. H., K. E. Leslie, D. A. Barnum, B. A. Mallard, J. H. Lumsden, P. C. Dick, G. H. Vessie, and M. E. Kehrli. 1999. Experimental Staphylococcus aureus intramammary challenge in late lactation dairy cows: Quarter and cow effects determining the probability of infection. J. Dairy Sci. 82: 2393-2401. Schukken, Y.H., Y.T. Grohn, B. McDermott and J.J. McDermott. 2003. Analysis of correlated discreet observations: background examples and solutions. Prev. Vet. Med. 59:223-240. Schultze W.D. and H.D. Mercer. 1976. Non-lactating cow therapy with a formulation of penicillin and novobiocin: Therapeutic and prophylactic effects. Am. J. Vet. Res. 37:1275. Schultze W.D. 1983. Effects of a selective regimen of dry cow therapy on intramammary infection and on antibiotic sensitivity of surviving pathogens. J.Dairy Sci. 66:892. Sears, P.M., B.S. Smith, P.B.English, P.S. Herer and R.N. Gonzalez. 1990. Shedding patterns of Staphylococcus aureus from the bovine intramammary infections. J.Dairy Sci. 73: 2785-9. Shook, G. E. 1993. Genetic improvement of mastitis through selection on somatic cell count. Vet. Clin. North Am. Food Anim. Pract. 9:563-81. Shook, G. E. and M. M. Schutz. 1994. Selection on somatic cell score to improve resistance to mastitis in the United States. J. Dairy Sci. 77:648-58. Shuster, D. E., E. K. Lee, and M. E. Kehlri. 1996. Bacterial growth, inflammatory cytokine production, and neutrophil recruitment during coliform mastitis in cows within ten days after calving, compared with at midlactation. Am. J.Vet. Res. 57: 1569-1575. Sinkevich M.G., P.B. Parto, L.J.Bush, M.Wells, and G.D. Adams. 1974. Effectiveness of antibiotic infusion at drying off in preventing new mastitis infections in cows. Bovine Pract. 9:43. Smith A., D.R. Westgarth, M.R. Jones, F. K. Neave, F.H. Dodd and G.C. Brander. 1967a. Methods of reducing the incidence of udder infection in dry cows. Vet. Rec. 81:504-510 Smith A., F. K. Neave, F.H. Dodd and G.C. Brander. 1967b. Methods of reducing the incidence of udder infection in dry cows. Vet. Rec. 79:233. Smith A., F.H. Dodd and F. K. Neave. 1968. The effect of intramammary infection during the dry period on the milk production of the affected quarter at the start of the succeeding lactation. J.Dairy Res. 35:287-294. Smith K.L., D.A. Todhunter and Schoenberger. 1985. Environmental pathogens and intramammary infection during the dry period. J.Dairy Sci. 68:402-417. Snijders, T. and R. Bosker. 1999. Multilevel analysis: An introduction to basic and advanced multilevel modelling. SAGE publications Ltd, 6 Bonhill St, London. 177 Soltys, J. and Quinn M.T. 1999. Selective recruitment of T cell subsets to the udder during Staphylococcal and Streptococcal mastitis: Analysis of lymphocyte subsets and adhesion molecule expression. Imunology and infection. 67: 6293. Sordillo L.M., K. Shafer-Weaver, and D. DeRosa. 1997. Immunology of the Mammary Gland. J.Dairy Sci. 80:1851-1865. Spiegelhalter, D., A. Thomas, and N. Best. 2000. WinBUGS Version 1.3. MRC Biostatistics Unit, Institute of Public Health, Robinson Way, Cambridge CB2 2SR, UK. Suriyasathaporn W., Y.H. Schukken, M. Nielen, and A. Brand. 2000. Low somatic cell count: a risk factor for subsequent clinical mastitis in a dairy herd. J.Dairy Sci. 83:1248. Swanson, G. J. T., R. A. Mrode and C. M. Lindberg. 1998 Genetic progress for production plus health, welfare and profit. Animal Data Centre, Fox Talbot House, Greenways Business Park, Chippenham, Wilts, UK. Tadich, N. A., A.Carey, R. Porter, J. Ridley, M.J. Green, and L.E. Green. 1998. Case control study of risk factors for toxic mastitis in 26 dairy herds. Vet. Rec. 143: 362-5. Taylor, B.C., R.G. Keefe, J.D.Dellinger, Y. Nakamura, J.S. Cullor, and J.L. Stott. 1997. T cell populations and cytokine expression in milk derived from normal and bacteria infected bovine mammary glands. Cell. Immunol. 182:68-76. Timms, L. T. 1990. Can cell counts get too low? Dairy, Food and Environmental Sanitation. 10, 494-497. Todhunter D. A., K. L. Smith, J. S. Hogan and P. S. Schoenberger. 1991. Gram-negative bacterial infections of the mammary gland in cows. Am. J. Vet. Res. 52:184-188. Todhunter, D.A., K.L. Smith and J.S. Hogan. 1995. Environmental streptococcal intramammary infections of the bovine mammary gland. J Dairy Sci 78: 2366-74. van Werven, T. 1999. The role of leukocytes in bovine Escherichia coli mastitis. PhD thesis, University of Utrecht, The Netherlands. Vandeputtevanmessom, G., C. Burvenich, E. Roets, A. M. Massartleen, R. Heyneman, W. D. J. Kremer, and A. Brand. 1993. Classification of Newly Calved Cows Into Moderate and Severe Responders to Experimentally Induced Escherichia Coli Mastitis. J.Dairy Res. 60:19- 29. Ward G.E., and L.H. Shultz. 1974. Incidence and control of mastitis during the dry period. J.Dairy Sci. 57:1341. Weiss, W.P. J.S. Hogan, D.A. Todhunter and K.L Smith. 1997. Effect of vitamin E supplementation in diets with a low concentration of selenium on mammmary gland health of dairy cows. J. Dairy Sci. 80: 1728-37. Weller, J. I., A. Saran and Y. Zeliger. 1992. Genetic and environmental relationships among somatic cell count, bacterial infection and clinical mastitis. J. Dairy Sci. 75:2532-2540. 178 Wever P. and U. Emanuelson. 1989. Effects of systematic influences and intramammary infection on differential and total somatic cell counts in quarter milk samples from dairy cows. Acta Vet. Scand. 30:465-474. White, D. G. & Mcdermott, P. F. 2001. Emergence and transfer of antibiotic resistance. J.Dairy Sci. 84(E. Suppl.):E151-E5. White L.J., Y.H. Schukken, T.J. Lam, G.F. Medley and M.J. Chappell. 2001. A multispecies model for the transmission and control of mastitis in dairy cows. Epidemiol Infect 127: 567- 76. Wilesmith, J.W., P.G. Francis, and C.D.Wilson. 1986. Incidence of clinical mastitis in a cohort of British dairy herds. Vet. Rec. 118: 199-204. Wilson, C.D. and R.G. Kingwill. 1975. International Dairy Federation Annual Bulletin 85, p422-38. Zadoks, R. N., H.G.Allore, H.W.Barkema, O.C.Sampimon, J.Wellenberg, Y.T.Grohn and Y.H.Schukken. 2001. Cow and Quarter level risk factors for Streptococcus uberis and Staphylococcus aureus mastitis. J.Dairy Sci. 84: 2649-2663. Zadoks, R. N., B.E. Gillespie, H.W. Barkema, O.C.Sampimon, S.P. Oliver and Y.H.Schukken. 2003. Clinical, epidemiological and molecular characteristics of Streptococcus uberis infections in dairy herds. Epidemiol. Infect. 130: 335-349. Zeger SL, and Karim MR. (1991): Generalized linear models with random effects; a Gibbs sampling approach. Journal American Statistical Association. 86: 79-86. Zorah, K.T., R.C. Daniel, and A.J. Frost. 1993. Detection of bacterial antigens in milk samples from clinical cases of bovine mastitis in which culture is negative. Vet. Rec. 132:208-10. 179 Appendices WinBUGS model codes and kernal densities. Appendix 1: Example of the WinBUGS Code and kernal density plots for Survival Models in Chapter Three, based on the E. coli Model 3.1. Model { #N is number of quarters in study for(i in 1:N) { #T is number of time jumps and t is any given time for(j in 1:T) { # define those at risk = 1 if obs.t >= t and t[j] is the time of the jump #eps is just a very small slice of time Y[i,j] <- step(obs.t[i] - t[j] + eps) # also define that after entry time to be at risk E[i,j]<-step(t[j]-entry.t[i] + eps) # counting process jump = 1 if obs.t in [ t[j], t[j+1] ) # i.e. if t[j] <= obs.t < t[j+1] #below says at risk yes (Y[i, j] = 1) and obstime is between t # and t+1(step(t[j + 1] - obs.t[i] - eps) and fail = 1. dN[i, j] <- Y[i, j] * E[i,j]*step(t[j + 1] - obs.t[i] - eps) * fail[i] # ie dN[i,j] has defined an outcome for our model #we now model the mean of this outcome } } # Model for(j in 1:T) { for(i in 1:N) { dN[i, j] ~ dpois(Idt[i, j]) # Likelihood #model for poisson mean # cox linear predictor is exp(beta*Z[i]....+coweff[cow[i]]) Idt[i, j] <- Y[i, j] * E[i,j]* exp(beta.cull * cull[i]+beta.fm6 * fm6[i]+ beta.fm2*fm2[i]+beta.fm3*fm3[i]+beta.fm4*fm4[i]+beta.fm5*fm5[i]+ beta.summer*season2[i]+beta.autumn*season3[i]+ beta.winter*season4[i]+ coweff[cow[i]]) * dL0[j] # is the increment or jump in the integrated #baseline hazard function occurring during the time interval [t, t+dt) ie. how baseline hazard is effected } dL0[j] ~ dgamma(mu[j], c) mu[j] <- dL0.star[j] * c # prior mean hazard } 180 for(k in 1 : NUMCOWS) { coweff[k] ~ dnorm(0.0, taucow); } taucow ~ dgamma(0.001, 0.001) sigma2cow <- (1 / taucow) c <- 0.1 r <- 0.01 for (j in 1 : T) { dL0.star[j] <- r * (t[j + 1] - t[j]) } #other priors beta.cull ~ dnorm(0.0,0.000001); beta.fm6~ dnorm(0.0,0.000001); beta.fm2~ dnorm(0.0,0.000001); beta.fm3~ dnorm(0.0,0.000001); beta.fm4~ dnorm(0.0,0.000001); beta.fm5~ dnorm(0.0,0.000001); beta.summer~ dnorm(0.0,0.000001); beta.autumn~ dnorm(0.0,0.000001); beta.winter~ dnorm(0.0,0.000001); } Initial values list( beta.cull =0, beta.fm6=0, beta.fm2=0, beta.fm3=0, beta.fm4=0, beta.fm5=0, beta.summer=0, beta.autumn=0, beta.winter=0, dL0 = c(1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0, 1.0,1.0,1.0,1.0,1.0,1.0, 1.0,1.0, 1.0,1.0,1.0, 1.0 ), taucow = 1) Density Plots main[1]<-beta.cull; main[3]<-beta.fm6; main[4]<-beta.fm4; main[5]<-beta.fm5; main[6]<-beta.fm3; main[7]<-beta.fm2; main[9]<-beta.summer; main[10]<-beta.autumn; main[11]<-beta.winter; main[13]<-sigma2cow; 181 Parameter kernal density plots from Model 3.1. main[1] chains 1:3 sample: 81003 -1.0 0.0 1.0 2.0 0.0 0.5 1.0 1.5 2.0 main[3] chains 1:3 sample: 81003 -1.0 0.0 1.0 2.0 3.0 0.0 0.5 1.0 1.5 main[4] chains 1:3 sample: 81003 -2.0 -1.0 0.0 1.0 2.0 0.0 0.25 0.5 0.75 1.0 main[5] chains 1:3 sample: 81003 -1.0 0.0 1.0 2.0 0.0 0.5 1.0 1.5 main[6] chains 1:3 sample: 81003 -1.0 0.0 1.0 2.0 0.0 0.5 1.0 main[7] chains 1:3 sample: 81003 -4.0 -2.0 0.0 2.0 0.0 0.25 0.5 0.75 1.0 main[9] chains 1:3 sample: 81003 -1.0 0.0 1.0 2.0 0.0 0.5 1.0 1.5 main[10] chains 1:3 sample: 81003 -1.0 0.0 1.0 2.0 0.0 0.5 1.0 1.5 main[11] chains 1:3 sample: 81003 -1.0 0.0 1.0 2.0 0.0 0.5 1.0 1.5 main[13] chains 1:3 sample: 81003 -1.0 0.0 1.0 2.0 0.0 2.0 4.0 6.0 8.0 182 Appendix 2: Example of the WinBUGS Code and kernal density plots for Generalised linear Mixed Models in Chapter 3 (based on the Streptococcus uberis Model 3.5). Model { # hierarchies for(j in 1:NUMCOWS) { coweff[j]~dnorm(0,taucow); } for(k in 1:NUMQUARTERS) { quartereff[k]~dnorm(0,tauquarter); } for( i in 1 : N ) { resid[i]<-ubi[i] - mu[i]; Presid[i]<-(resid[i])/sqrt((mu[i]*(1-mu[i]))); logit(mu[i])<-alpha + beta.farm2*(fm2[i])+ beta.farm3*(fm3[i])+ beta.farm4*(fm4[i])+ beta.farm5*(fm5[i])+ beta.farm6*(fm6[i])+ beta.lac23*(lac23[i])+ beta.ca*(ca[i])+ beta.1wk*(wk1[i])+ beta.2wk*(wk2[i])+ beta.cpsi*(cpsi[i])+ beta.coli*(coli[i])+ beta.coryi*(coryi[i])+ beta.ublagi*(ublagi[i])+ coweff[cow[i]]+ quartereff[quarter[i]]; ubi[i]~dbin(mu[i],1); } #priors alpha~dnorm(0,1.0E-6); beta.farm2~dnorm(0,1.0E-6); beta.farm3~dnorm(0,1.0E-6); beta.farm4~dnorm(0,1.0E-6); beta.farm5~dnorm(0,1.0E-6); beta.farm6~dnorm(0,1.0E-6); beta.lac23~dnorm(0,1.0E-6); beta.ca~dnorm(0,1.0E-6); beta.1wk~dnorm(0,1.0E-6); beta.2wk~dnorm(0,1.0E-6); beta.cpsi~dnorm(0,1.0E-6); beta.coli~dnorm(0,1.0E-6); 183 beta.coryi~dnorm(0,1.0E-6); beta.ublagi~dnorm(0,1.0E-6); taucow~dgamma(0.001,0.001); tauquarter~dgamma(0.001,0.001); sigma2cow<-1/taucow; sigma2quarter<-1/tauquarter; # Density Plots (see below) main[1]<-alpha; main[2]<-beta.farm2; main[3]<-beta.farm3; main[4]<-beta.farm4; main[5]<-beta.farm5; main[6]<-beta.farm6; main[7]<-beta.lac23; main[8]<-beta.ca; main[9]<-beta.1wk; main[10]<-beta.2wk; main[11]<-beta.ublagi; main[12]<-beta.cpsi; main[13]<-beta.coryi; main[18]<-beta.coli; main[19]<-sigma2cow; main[20]<-sigma2quarter; } Initial Values list(alpha = 0, beta.farm2 = 0, beta.farm3 = 0, beta.farm4 = 0, beta.farm5 = 0, beta.farm6 = 0, beta.lac23= 0, beta.ca= 0, beta.1wk= 0, beta.2wk= 0, beta.ublagi= 0, beta.cpsi= 0, beta.coryi = 0, beta.coli = 0, taucow = 1, tauquarter = 1) 184 Parameter kernal density plots from Model 3.5. main[1] chains 1:3 sample: 46074 -8.0 -6.0 -4.0 0.0 0.2 0.4 0.6 0.8 main[2] chains 1:3 sample: 46074 -6.0 -4.0 -2.0 0.0 0.0 0.2 0.4 0.6 0.8 main[3] chains 1:3 sample: 46074 -4.0 -2.0 0.0 2.0 0.0 0.2 0.4 0.6 0.8 main[4] chains 1:3 sample: 46074 -4.0 -2.0 0.0 0.0 0.2 0.4 0.6 0.8 main[5] chains 1:3 sample: 46074 -6.0 -4.0 -2.0 0.0 0.0 0.2 0.4 0.6 0.8 main[6] chains 1:3 sample: 46074 -2.0 0.0 2.0 0.0 0.25 0.5 0.75 1.0 main[7] chains 1:3 sample: 46074 -4.0 -3.0 -2.0 -1.0 0.0 0.0 0.5 1.0 1.5 main[8] chains 1:3 sample: 46074 -3.0 -2.0 -1.0 0.0 0.0 0.5 1.0 1.5 main[9] chains 1:3 sample: 46074 -2.0 -1.0 0.0 1.0 0.0 0.5 1.0 1.5 main[10] chains 1:3 sample: 46074 -3.0 -2.0 -1.0 0.0 1.0 0.0 0.25 0.5 0.75 1.0 main[11] chains 1:3 sample: 46074 -2.0 0.0 2.0 0.0 0.25 0.5 0.75 1.0 main[12] chains 1:3 sample: 46074 -2.0 0.0 2.0 4.0 0.0 0.2 0.4 0.6 0.8 main[13] chains 1:3 sample: 46074 -4.0 -2.0 0.0 0.0 0.2 0.4 0.6 0.8 main[18] chains 1:3 sample: 46074 0.0 1.0 2.0 3.0 0.0 0.5 1.0 1.5 main[19] chains 1:3 sample: 46074 0.0 2.0 4.0 6.0 0.0 0.2 0.4 0.6 main[20] chains 1:3 sample: 46074 -0.2 0.0 0.2 0.4 0.0 20.0 40.0 60.0 185 Appendix 3: Graphs of Delta-betas for the seven explanatory covariates in conditional logistic regression Model 4.1, Chapter 4. -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Observation number Delta-betas for Left Hind quarter -0.15 -0.1 -0.05 0 0.05 0.1 Observation number Delta-betas for Right Fore quarter -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Observation number Delta-betas for Right Hind quarter -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 Observation number Delta-betas for QSCC m-2 = 81,000- 150,000 cells / ml -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Observation number Delta-betas for QSCC m-2 > 150,000 cells / ml -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 Observation number Delta-betas for QSCC m-1 = 41,000- 100,000 cells / ml -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Observation number Delta-betas for QSCC m-1 > 100,000 cells / ml 186 Appendix 4: WinBUGS code and parameter kernal densities for GLMM Model 4.2, Chapter 4. Model { for(c in 1:NUMCOWS) { coweff[c]~dnorm(0,taucow); } for(q in 1:NUMQUARTERS) { quartereff[q]~dnorm(0,tauquarter); } for( i in 1 : N ) { resid[i]<-MastBin[i] - mu[i]; Presid[i]<-(resid[i])/sqrt((mu[i]*(1-mu[i]))); logit(mu[i])<-alpha + beta.farm2*equals(farm[i],2)+ beta.farm3*equals(farm[i],3)+ beta.quarter2*equals(quarter[i],2)+ beta.quarter3*equals(quarter[i],3)+ beta.quarter1*equals(quarter[i],1)+ beta.lm2*(lm2[i])+ beta.lm4*(lm4[i])+ beta.lm5*(lm5[i])+ beta.lm7*(lm7[i])+ beta.presccmid*(preSCCmid[i])+ beta.predry*(predry[i])+ beta.pre2mid*(pre2mid[i])+ beta.pre2dry*(pre2dry[i])+ beta.qscc2*(bin41100[i])+ beta.qscc3*(bin101150[i])+ beta.qscc4*(bin151200[i])+ beta.qscc5*(bin200[i])+ beta.prehigh*(prehigh[i])+ beta.pre2high*(pre2high[i])+ coweff[cowid[i]]+ quartereff[quarterid[i]]; MastBin[i]~dbern(mu[i]); } #priors alpha~dnorm(0,1.0E-6); beta.farm2~dnorm(0,1.0E-6); beta.farm3~dnorm(0,1.0E-6); beta.qscc2~dnorm(0, 1.0E-6); beta.qscc3~dnorm(0, 1.0E-6); beta.qscc4~dnorm(0,1.0E-6); beta.qscc5~dnorm(0,1.0E-6); beta.quarter2~dnorm(0,1.0E-6); beta.quarter3~dnorm(0,1.0E-6); beta.quarter1~dnorm(0,1.0E-6); beta.presccmid~dnorm(0,1.0E-6); beta.preM~dnorm(0,1.0E-6); beta.lm2~dnorm(0,1.0E-6); 187 beta.lm4~dnorm(0,1.0E-6); beta.lm5~dnorm(0,1.0E-6); beta.lm7~dnorm(0,1.0E-6); beta.pre2mid~dnorm(0,1.0E-6); beta.pre2M~dnorm(0,1.0E-6); beta.prehigh~dnorm(0,1.0E-6); beta.pre2high~dnorm(0,1.0E-6); taucow~dgamma(0.001,0.001); tauquarter~dgamma(0.001,0.001); sigma2quarter<-1/tauquarter; sigma2cow<-1/taucow; muresid~dnorm(0,1.0E-6); Density Plots main[1]<-alpha; main[2]<-beta.farm2; main[3]<-beta.farm3; main[4]<-beta.quarter2; main[5]<-beta.quarter3; main[6]<-beta.quarter1; main[7]<-sigma2cow; main[8]<-sigma2quarter; main[10]<-beta.lm2; main[11]<-beta.lm4; main[12]<-beta.lm5; main[13]<-beta.lm7; main[14]<-beta.presccmid; main[15]<-beta.pre2mid; main[16]<-beta.qscc2; main[17]<-beta.qscc3; main[18]<-beta.qscc4; main[19]<-beta.qscc5; main[20]<-beta.prehigh; main[21]<-beta.pre2high; main[22]<-beta.preM; main[23]<-beta.pre2M; DATA list(NUMCOWS=446, NUMQUARTERS = 1771, N=12637) Initials list(alpha = 0, beta.farm2 = 0, beta.farm3 = 0, beta.qscc2 = 0, beta.qscc3 = 0, beta.qscc4 = 0, beta.qscc5 = 0, beta.quarter2 = 0, beta.quarter3 = 0, beta.quarter1 = 0, beta.presccmid = 0, beta.preM = 0, beta.lm2 = 0, beta.lm4 = 0, beta.lm5 = 0, beta.lm7= 0, beta.pre2M = 0, beta.pre2mid = 0, beta.prehigh = 0, beta.pre2high = 0, taucow = 4, tauquarter = 4, ) 188 Parameter kernal density plots from Model 4.2. main[1] chains 1:3 sample: 25716 -6.0 -5.5 -5.0 0.0 1.0 2.0 3.0 main[2] chains 1:3 sample: 25716 -1.5 -1.0 -0.5 0.0 1.0 2.0 3.0 4.0 main[3] chains 1:3 sample: 25716 -0.4 -0. 2 0.0 0.2 0. 4 0.0 2.0 4.0 6.0 main[4] chains 1:3 sample: 25716 -2.0 -1.5 -1.0 -0.5 0.0 1.0 2.0 3.0 main[5] chains 1:3 sample: 25716 -0.5 -0.25 0. 0 0.25 0.0 1.0 2.0 3.0 4.0 main[6] chains 1:3 sample: 25716 -1.0 -0.5 0.0 0.0 1.0 2.0 3.0 4.0 main[7] chains 1:3 sample: 25716 -0.2 0. 0 0.2 0.4 0.0 5.0 10. 0 15. 0 20. 0 main[8] chains 1:3 sample: 25716 -0.2 0.0 0. 2 0.4 0.0 2.5 5.0 7.5 10.0 main[10] chains 1: 3 sample: 25716 0.0 0.5 1.0 0.0 1.0 2.0 3.0 4.0 main[11] chains 1:3 sample: 25716 0.0 0.5 1.0 0.0 1.0 2.0 3.0 4.0 main[12] chains 1:3 sample: 25716 0.0 0.5 1.0 0.0 1.0 2.0 3.0 main[13] chains 1: 3 sample: 25716 0.0 0.5 1.0 0.0 1.0 2.0 3.0 main[14] chains 1:3 sample: 25716 -3.0 -2.0 -1.0 0.0 0.5 1.0 1.5 main[15] chains 1:3 sample: 25716 -3.0 -2.0 -1.0 0.0 0.5 1.0 1.5 main[16] chains 1: 3 sample: 25716 -2.0 -1.5 -1. 0 -0.5 0.0 1.0 2.0 3.0 main[17] chains 1:3 s ample: 25716 -1.0 0. 0 1. 0 0.0 0.5 1.0 1.5 2.0 main[18] chains 1:3 s ample: 25716 -1.0 0. 0 1. 0 0.0 0.5 1.0 1.5 2.0 main[19] chains 1:3 s ample: 25716 0.75 1.0 1.25 1. 5 1.75 0.0 1.0 2.0 3.0 4.0 main[20] chains 1:3 s ample: 25716 -0.5 0. 0 0. 5 0.0 1.0 2.0 3.0 main[18] chains 1:3 sample: 25716 -1.0 0.0 1.0 0.0 0.5 1.0 1.5 2.0 main[21] chains 1:3 sample: 25716 -2.0 - 1.5 -1.0 -0. 5 0.0 0.0 0.5 1.0 1.5 2.0 main[22] chains 1:3 s ampl e: 25716 0.0 0.25 0.5 0.75 1.0 0.0 1.0 2.0 3.0 4.0 main[19] ch ains 1 :3 s ample: 25716 0.75 1.0 1.25 1. 5 1.75 0.0 1.0 2.0 3.0 4.0 189 Appendix 5: WinBUGS code and parameter kernal densities for Model 5.1, Chapter Five. Model { for(c in 1:NUMCOWS) { coweff[c]~dnorm(0,taucow); } for(q in 1:NUMQUARTERS) { quartereff[q]~dnorm(0, tauquarter) } for( i in 1 : N ) { resid[i]<-logqscc[i] - mu[i]; logqscc[i]~dnorm(mu[i], taulogqscc); mu[i]<-alpha + beta.quarter3*(q3[i])+ beta.quarter4*(q4[i])+ beta.lm2*(lm2[i])+ beta.lm3*(lm3[i])+ beta.lm4*(lm4[i])+ beta.lm5*(lm5[i])+ beta.lm6*(lm6[i])+ beta.lm7*(lm7[i])+ beta.lm8*(lm8[i])+ beta.p4xlm8*(p4xlm8[i])+ beta.p3xlm8*(p3xlm8[i])+ beta.m1*(m1[i])+ beta.m2*(m2[i])+ beta.m10*(m10[i])+ beta.m11*(m11[i])+ beta.p2*(p2[i])+ beta.p3*(p3[i])+ beta.p4plus*(p4[i])+ beta.p2mast*(p2xmast[i])+ beta.before*(sccbeforecm[i])+ beta.p3mast*(p3xmast[i])+ beta.p4mast*(p4xmast[i]) beta.after*(sccaftercm[i])+ coweff[cow[i]]+ quartereff[quarter[i]]+ 190 } for (z in 1:1) { meanresid <- mean(resid[]); varresid<- (sd(resid[])*sd(resid[])); } #priors alpha~dnorm(0,1.0E-6); beta.quarter3~dnorm(0,1.0E-6); beta.quarter4~dnorm(0,1.0E-6); beta.lm2~dnorm(0,1.0E-6); beta.lm3~dnorm(0,1.0E-6); beta.lm4~dnorm(0,1.0E-6); beta.lm5~dnorm(0,1.0E-6); beta.lm6~dnorm(0,1.0E-6); beta.lm7~dnorm(0,1.0E-6); beta.lm8~dnorm(0,1.0E-6); beta.p4xlm8~dnorm(0,1.0E-6); beta.p3xlm8~dnorm(0,1.0E-6); beta.m1~dnorm(0,1.0E-6); beta.m2~dnorm(0,1.0E-6); beta.m10~dnorm(0,1.0E-6); beta.m11~dnorm(0,1.0E-6); beta.p2~dnorm(0,1.0E-6); beta.p3~dnorm(0,1.0E-6); beta.p4plus~dnorm(0,1.0E-6); beta.p2mast~dnorm(0,1.0E-6); beta.p3mast~dnorm(0,1.0E-6); beta.p4mast~dnorm(0,1.0E-6); beta.after~dnorm(0,1.0E-6); taucow~dgamma(0.001,0.001); tauquarter~dgamma(0.001,0.001); taulogqscc~dgamma(0.001,0.001); sigma2cow<-1/taucow; sigma2quarter<-1/tauquarter; } DATA list(NUMCOWS=443, NUMQUARTERS = 1771, N=12637) INITIALS List (alpha = 1, beta.quarter3 = 0, 191 beta.quarter4 = 0, beta.lm2 = 0, beta.lm3 = 0, beta.lm4 = 0, beta.lm5 = 0, beta.lm6 = 0, beta.lm7 = 0, beta.lm8 = 0, beta.p4xlm8 = 0, beta.p3xlm8 = 0, beta.m1 = 0, beta.m2 = 0, beta.m10 = 0, beta.m11 = 0, beta.p2 = 0, beta.p3 = 0, beta.p4plus = 0, beta.after = 0, beta.before = 0, beta.p2mast = 0, beta.p4mast = 0, taucow =1, tauquarter = 1, taulogqscc = 1) 192 Parameter kernal density plots from Model 5.1. main[1] chains 1:3 sample: 57003 1.0 1.1 1.2 0.0 5.0 10.0 15.0 main[5] chains 1:3 sample: 57003 0.0 0.05 0.1 0.15 0.0 10.0 20.0 30.0 main[6] chains 1:3 sample: 57003 0.0 0.05 0.1 0.15 0.2 0.0 10.0 20.0 30.0 main[7] chains 1:3 sample: 57003 -0.3 -0.25 -0.2 -0.15 0.0 10.0 20.0 30.0 main[8] chains 1:3 sample: 57003 -0.35 -0.3 -0.25 -0.2 0.0 10.0 20.0 30.0 main[9] chains 1:3 sample: 57003 -0.4 -0.35 -0.3 -0.25 0.0 5.0 10.0 15.0 20.0 main[10] chains 1:3 sample: 57003 -0.35 -0.3 -0.25 -0.2 -0.15 0.0 5.0 10.0 15.0 20.0 main[11] chains 1:3 sample: 57003 -0.25 -0.2 -0.15 -0.1 0.0 5.0 10.0 15.0 20.0 main[12] chains 1:3 sample: 57003 -0.2 -0.15 -0.1 -0.05 0.0 5.0 10.0 15.0 20.0 main[13] chains 1:3 sample: 57003 -0.1 0.0 0.1 0.0 5.0 10.0 15.0 20.0 main[14] chains 1:3 sample: 57003 0.0 0.05 0.1 0.15 0.2 0.0 5.0 10.0 15.0 20.0 main[15] chains 1:3 sample: 57003 0.0 0.1 0.2 0.0 5.0 10.0 15.0 20.0 main[17] chains 1:3 sample: 57003 0.1 0.2 0.3 0.0 5.0 10.0 15.0 20.0 main[18] chains 1:3 sample: 57003 0.0 0.1 0.2 0.3 0.0 5.0 10.0 15.0 main[20] chains 1:3 sample: 57003 0.0 0.1 0.2 0.0 5.0 10.0 15.0 20.0 main[22] chains 1:3 sample: 57003 0.1 0.2 0.3 0.4 0.0 5.0 10.0 15.0 main[25] chains 1:3 sample: 57003 0.0 0.05 0.1 0.15 0.0 10.0 20.0 30.0 main[26] chains 1:3 sample: 57003 0.0 0.05 0.1 0.15 0.0 10.0 20.0 30.0 main[30] chains 1:3 sample: 57003 0.0 0.2 0.4 0.0 2.0 4.0 6.0 8.0 main[31] chains 1:3 sample: 57003 0.3 0.4 0.5 0.6 0.7 0.0 2.5 5.0 7.5 10.0 main[39] chains 1:3 sample: 57003 -0.02 -0.01 0.0 0.01 0.0 25.0 50.0 75.0 100.0 main[41] chains 1:3 sample: 57003 0.26 0.265 0.27 0.275 0.0 100.0 200.0 300.0 main[42] chains 1:3 sample: 57003 0.04 0.06 0.08 0.1 0.0 20.0 40.0 60.0 main[43] chains 1:3 sample: 57003 0.04 0.05 0.06 0.07 0.08 0.0 25.0 50.0 75.0 100.0 main[52] chains 1:3 sample: 57003 -0.25 0.0 0.25 0.5 0.0 2.0 4.0 6.0 main[53] chains 1:3 sample: 57003 -0.25 0.0 0.25 0.5 0.0 1.0 2.0 3.0 4.0 193 Appendix 6: WinBUGS code and parameter kernal densities for Model 5.3, Chapter Five. Model { for(c in 1:NUMCOWS) { for(q in 1:4) { quartereff.temp[c,q]~dnorm(0,tauquarter); } quartereff.mean[c]<-mean(quartereff.temp[c,]); for(r in 1:4) { quartereff[c,r]<-quartereff.temp[c,r]-quartereff.mean[c]; } coweff[c]~dnorm(0,taucow); } for( i in 1 : N ) { resid[i]<-bin41100[i] - mu[i]; Presid[i]<-(resid[i])/sqrt((mu[i]*(1-mu[i]))); logit(mu[i])<-alpha + beta.farm2*(fm2[i])+ beta.farm3*(fm3[i])+ beta.lm9*(lm9[i])+ beta.lm3*(lm3[i])+ beta.lm4*(lm4[i])+ beta.lm5*(lm5[i])+ beta.lm6*(lm6[i])+ beta.lm7*(lm7[i])+ beta.lm8*(lm8[i])+ beta.prescc40*(preSCCcat2[i])+ beta.prescc60*(preSCCcat3[i])+ beta.prescc80*(preSCCcat4[i])+ beta.prescc100*(preSCCcat5[i])+ beta.prescc150*(preSCCcat6[i])+ beta.prescc200*(preSCCcat7[i])+ beta.prescc400*(preSCCcat8[i])+ beta.prescc1000*(preSCCcat9[i])+ beta.int1*(lm6qscc9[i])+ beta.int2*(lm7qscc9[i])+ beta.int4*(lm9qscc9[i])+ coweff[cowid[i]]+ quartereff[cowid[i],quarter[i]]; bin41100[i]~dbin(mu[i],1); } alpha~dnorm(0,1.0E-6); 194 beta.farm2~dnorm(0,1.0E-6); beta.farm3~dnorm(0,1.0E-6); beta.lm9~dnorm(0,1.0E-6); beta.lm4~dnorm(0,1.0E-6); beta.lm5~dnorm(0,1.0E-6); beta.lm7~dnorm(0,1.0E-6); beta.lm3~dnorm(0,1.0E-6); beta.lm6~dnorm(0,1.0E-6); beta.lm8~dnorm(0,1.0E-6); beta.prescc40~dnorm(0,1.0E-6); beta.prescc60~dnorm(0,1.0E-6); beta.prescc80~dnorm(0,1.0E-6); beta.prescc100~dnorm(0,1.0E-6); beta.prescc150~dnorm(0,1.0E-6); beta.prescc200~dnorm(0,1.0E-6); beta.prescc400~dnorm(0,1.0E-6); beta.prescc1000~dnorm(0,1.0E-6); beta.int1~dnorm(0,1.0E-6); beta.int2~dnorm(0,1.0E-6); beta.int3~dnorm(0,1.0E-6); beta.int4~dnorm(0,1.0E-6); taucow~dgamma(0.001,0.001); tauquarter~dgamma(0.001,0.001); sigma2between<-1/taucow; sigma2within<-1/tauquarter; sigma2quarter<-sigma2within; sigma2cow<-sigma2between-(1/4)*sigma2quarter; tau~dgamma(0.001,0.001); muresid~dnorm(0,1.0E-6); main[1]<-alpha; main[2]<-beta.farm2; main[3]<-beta.farm3; main[7]<-sigma2cow; main[8]<-sigma2quarter; main[9]<-beta.lm9; main[10]<-beta.lm3; main[11]<-beta.lm4; main[12]<-beta.lm5; main[13]<-beta.lm6; main[14]<-beta.lm7; main[15]<-beta.lm8; main[16]<-beta.prescc40; main[17]<-beta.prescc60; main[18]<-beta.prescc80; main[19]<-beta.prescc100; main[20]<-beta.prescc150; main[21]<-beta.prescc200; main[22]<-beta.prescc400; main[23]<-beta.prescc1000; main[24]<-beta.int1; main[25]<-beta.int2; main[26]<-beta.int3; main[27]<-beta.int4; } 195 DATA list(NUMCOWS=446, N=10227) INITS list(alpha = 0, beta.farm2 = 0, beta.farm3 = 0, beta.prescc40 = 0, beta.prescc60 =0, beta.prescc80 = 0, beta.prescc100 = 0, beta.prescc150 = 0, beta.prescc200 =0, beta.prescc400 = 0, beta.prescc1000 = 0, beta.lm9 = 0, beta.lm3 = 0, beta.lm4 = 0, beta.lm5 = 0, beta.lm6 = 0, beta.lm7= 0, beta.lm8 = 0, beta.int1 = 0, beta.int2 = 0, beta.int3 = 0, beta.int4 = 0, taucow = 1, tauquarter = 1 ) Parameter kernal density plots from Model 5.3. main[1] chains 1:3 sample: 62559 -3.0 -2.5 -2.0 0.0 1.0 2.0 3.0 4.0 main[2] chains 1:3 sample: 62559 -0.75 -0.5 -0.25 0.0 0.0 1.0 2.0 3.0 4.0 main[3] chains 1:3 sample: 62559 -0.5 -0.25 0.0 0.25 0.5 0.0 2.0 4.0 6.0 main[4] chains 1:3 sample: 62559 -0.6 -0.4 -0.2 0.2 0.0 2.0 4.0 6.0 main[5] chains 1:3 sample: 62559 -0.6 -0.4 -0.2 0.2 0.0 2.0 4.0 6.0 main[6] chains 1:3 sample: 62559 -0.4 -0.2 0.0 0.2 0.4 0.0 2.0 4.0 6.0 main[7] chains 1:3 sample: 62559 0.0 0.2 0.4 0.0 2.0 4.0 6.0 8.0 main[8] chains 1:3 sample: 62559 -0.1 0.0 0.1 0.2 0.3 0.0 5.0 10.0 15.0 main[9] chains 1:3 sample: 62559 -2.0 -1.5 -1.0 0.0 1.0 2.0 3.0 main[10] chains 1:3 sample: 62559 -1.5 -1.0 -0.5 0.0 1.0 2.0 3.0 4.0 main[11] chains 1:3 sample: 62559 -1.5 -1.0 -0.5 0.0 1.0 2.0 3.0 4.0 main[12] chains 1:3 sample: 62559 -1.0 -0.75 -0.5 -0.25 0.0 1.0 2.0 3.0 4.0 main[13] chains 1:3 sample: 62559 -0.75 -0.5 -0.25 0.0 0.25 0.0 1.0 2.0 3.0 4.0 main[14] chains 1:3 sample: 62559 -0.75 -0.5 -0.25 0.0 0.25 0.0 1.0 2.0 3.0 4.0 main[15] chains 1:3 sample: 62559 -0.75 -0.5 -0.25 0.0 0.25 0.0 1.0 2.0 3.0 4.0 main[16] chains 1:3 sample: 62559 0.8 1.0 1.2 1.4 0.0 2.0 4.0 6.0 main[17] chains 1:3 sample: 62559 0.75 1.0 1.25 1.5 1.75 0.0 1.0 2.0 3.0 4.0 main[18] chains 1:3 sample: 62559 0.5 1.0 1.5 0.0 1.0 2.0 3.0 4.0 main[19] chains 1:3 sample: 62559 0.5 1.0 1.5 0.0 1.0 2.0 3.0 main[20] chains 1:3 sample: 62559 0.5 1.0 1.5 0.0 1.0 2.0 3.0 4.0 main[21] chains 1:3 sample: 62559 0.0 0.5 1.0 1.5 0.0 1.0 2.0 3.0 main[22] chains 1:3 sample: 62559 -0.5 0.0 0.5 0.0 1.0 2.0 3.0 main[23] chains 1:3 sample: 62 -1.5 -1.0 -0.5 0.0 0.0 1.0 2.0 3.0 196 Appendix 7: An example of the WinBUGS code and parameter kernal densities for the GLMM constructed in Chapter Six, based on Model 6.3. Model { for(j in 1:NUMFARMS) { farmeff[j]~dnorm(0,taufarm); } for( i in 1 : N ) { resid[i]<-mast[i] - mu[i]; Presid[i]<-(resid[i])/sqrt((mu[i]*(1-mu[i]))); logit(mu[i])<-alpha + beta.p1*(p1[i])+ beta.m1*(m1[i])+ beta.max*(max[i])+ beta.sd5*(sd5[i])+ beta.twolac*(twolac[i])+ farmeff[fm[i]]; mast[i]~dbin(mu[i],1); } alpha~dnorm(0,1.0E-6); beta.p1~dnorm(0,1.0E-6); beta.m1~dnorm(0,1.0E-6); beta.sd5~dnorm(0,1.0E-6); beta.max~dnorm(0,1.0E-6); beta.twolac~dnorm(0,1.0E-6); taufarm~dgamma(0.001,0.001); sigma2farm<-1/taufarm; main[1]<-alpha; main[2]<-beta.p1; main[3]<-beta.m1; main[4]<-beta.sd5; main[5]<-beta.max; main[6]<-beta.twolac; main[15]<-sigma2farm; } DATA list(NUMFARMS=274, N=11825) INITS list(alpha = -10, beta.p1 = 0, beta.m1= 0, beta.max = 1.5, beta.sd5= 0, beta.twolac= 0,taufarm = 0.5) 197 Parameter kernal density plots from Model 6.3. main[1] chains 1:3 sample: 19557 -12.0 -11.0 -10.0 0.0 0.5 1.0 1.5 main[2] chains 1:3 sample: 19557 -0.8 -0.6 -0.4 -0.2 0.0 2.0 4.0 6.0 main[3] chains 1:3 sample: 19557 -0.75 -0.5 -0.25 0.0 0.0 1.0 2.0 3.0 4.0 main[4] chains 1:3 sample: 19557 -0.2 0.0 0.2 0.4 0.0 2.0 4.0 6.0 main[5] chains 1:3 sample: 19557 1.4 1.6 1.8 0.0 2.0 4.0 6.0 8.0 main[6] chains 1:3 sample: 19557 -6.0 -4.0 -2.0 0.0 0.2 0.4 0.6 0.8 main[15] chains 1:3 sample: 19557 0.2 0.4 0.6 0.8 0.0 2.0 4.0 6.0