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Marginal structural Cox model to estimate the causal effect of clinical mastitis on Québec dairy cow culling risk
Abstract
Health disorders, such as milk fever, displaced abomasum, or retained placenta, as well as poor reproductive performance, are known risk factors for culling in dairy cows. Clinical mastitis (CM) is one of the most influential culling risk factors. However the culling decision could be based either on the disease status or on the current milk yield, milk production being a significant confounder when modelling dairy cow culling risk. But milk yield (and somatic cell count) are time-varying confounders, which are also affected by prior CM and therefore lie on the causal pathway between the exposure of interest, CM, and the outcome, culling. Including these time-varying confounders could result in biased estimates. A marginal structural model (MSM) is a statistical technique allowing estimation of the causal effect of a time-varying exposure in the presence of time-varying covariates without conditioning on these covariates. The objective of this paper is to estimate the causal effect on culling of CM occurring between calving and 120 days in milk, using MSM to control for such time-varying confounders affected by previous exposure. A retrospective longitudinal study was conducted on data from dairy herds in the Province of Québec, Canada, by extracting health information events from the dairy herd health management software used by most Québec dairy producers and their veterinarians. The data were extracted for all lactations starting between January 1st and December 31st, 2010. A total of 3952 heifers and 8724 cows from 261 herds met the inclusion criteria and were used in the analysis. The estimated CM causal hazard ratios were 1.96 [1.57–2.44] and 1.47 [1.28–1.69] for heifers and cows, respectively, and as long as causal assumptions hold. Our findings confirm that CM was a risk factor for culling, but with a reduced effect compared to previous studies, which did not properly control for the presence of time-dependent confounders such as milk yield and somatic cell count. Cows experienced a lower risk for CM, with milk production having more influence on culling risk in cows than heifers.
... Other researchers have studied alternative early lactation periods, although none used a competing risks model. Haine et al. (2017) studied effects of CM occurring in the first 120 d of lactation, in cows of all parities. Moussavi et al. (2012) studied CM occurring between first calving and 10 days in milk (DIM; i.e., days in lactation), 10-60 DIM, and after 60 DIM. ...
... There are many studies on the effects of mastitis on bovine longevity/productive lifetime (e.g. Beaudeau et al., 1995;Haine et al., 2017;Gussmann et al., 2019), but few look at specific pathogens causing CM, or specifically on cases occurring in the earliest stage of productive lifetime. Gröhn et al. (2005) and Cha et al. (2013) have studied the effects of different pathogens on culling (the latter on death and sale separately), but not specifically occurring in early productive lifetime. ...
... This implies that the association of CM with productive lifetime is not exclusively of brief duration; it appears to persist beyond the short-term. Haine et al. (2017) fitted a marginal structural Cox model to account for time-varying exposures and covariates in estimating the effect of CM occurring in the first 120 d of lactation on subsequent culling in 12,676 cows in 261 Québec herds. First-lactation cows with CM in the first 120 DIM had a twice higher hazard of culling than did first-lactation cows that did not have CM in the first 120 DIM. ...
The objective of this observational study was to estimate effects of clinical mastitis (CM) cases caused by different pathogens (Streptococcus spp., Staphylococcus aureus, Staphylococcus spp., Escherichia coli, Klebsiella spp., and CM cases with no growth) occurring in the first 100 d in lactation 1, of a dairy cow on the future rate of occurrence of different types of CM during a cow's full lifetime. The outcomes were occurrence of Streptococcus spp., Staphylococcus aureus, Staphylococcus spp., Escherichia coli, Klebsiella spp., and CM cases with no growth, after the first 100 d of lactation 1, until a cow's removal through death or sale in that or a subsequent lactation. Data, including information on CM cases, milk production, and event dates (including death or sale dates), were collected from 14,440 cows in 5 New York State Holstein herds from January 2004 until February 2014. Generalized linear mixed models with a Poisson distribution and log link function were fit for each pathogen. The individual cow was the unit of analysis. Escherichia coli was a predictor of future occurrence of E. coli, Klebsiella spp., and CM cases with no growth. Early-occurring Klebsiella spp. was a predictor of future cases of Klebsiella spp. Cases with no growth were predictors of future occurrence of Staphylococcus spp., E. coli, Klebsiella spp., and cases with no growth. Thus, E. coli and cases with no growth occurring early in lactation 1 appear to be consistent risk factors for future cases of CM, whether cases with the same pathogen or a different pathogen. In this study, farm effects on later pathogen occurrence differed somewhat, so treatment protocol and culling strategy may play a role in the findings. Nevertheless, the findings may help farmers in managing young cows with CM in early productive life, especially those with E. coli or cases with no growth, in that they may be more susceptible to future CM cases in their later productive life, thus meriting closer attention.
... Other researchers have studied alternative early lactation periods, although none used a competing risks model. Haine et al. (2017) studied effects of CM occurring in the first 120 d of lactation, in cows of all parities. Moussavi et al. (2012) studied CM occurring between first calving and 10 days in milk (DIM; i.e., days in lactation), 10-60 DIM, and after 60 DIM. ...
... There are many studies on the effects of mastitis on bovine longevity/productive lifetime (e.g. Beaudeau et al., 1995;Haine et al., 2017;Gussmann et al., 2019), but few look at specific pathogens causing CM, or specifically on cases occurring in the earliest stage of productive lifetime. Gröhn et al. (2005) and Cha et al. (2013) have studied the effects of different pathogens on culling (the latter on death and sale separately), but not specifically occurring in early productive lifetime. ...
... This implies that the association of CM with productive lifetime is not exclusively of brief duration; it appears to persist beyond the short-term. Haine et al. (2017) fitted a marginal structural Cox model to account for time-varying exposures and covariates in estimating the effect of CM occurring in the first 120 d of lactation on subsequent culling in 12,676 cows in 261 Québec herds. First-lactation cows with CM in the first 120 DIM had a twice higher hazard of culling than did first-lactation cows that did not have CM in the first 120 DIM. ...
The objective of this observational study was to study the association between clinical mastitis (CM) (Streptococcus spp., Staphylococcus aureus, Staphylococcus spp., Escherichia coli, Klebsiella spp., cases with other treated or other not treated organisms, CM without growth) occurring in a dairy cow's first 100 days (d) of her first lactation and her total productive lifetime, ending in death or sale (for slaughter). Data were collected from 24,831 cows in 5 New York Holstein herds from 2004 to 2014. Two analytical approaches were compared. First, removals (death, sale) were treated as competing events in separate survival analyses, in proportional subdistribution hazards models. In one, death was coded as the event of interest and sale as the competing event; in another, sale was the event of interest and death the competing event. Second, traditional survival analysis (Cox proportional hazards) was conducted. In all models, the time variable was number of days from date of first calving until event (death or sale) date; if the cow was alive at study end, she was censored. Models were stratified by herd. Ten percent of cows died; 48.4 % were sold. In the competing risks analysis, E. coli and CM without growth were associated with death; the former with an increased hazard rate of death, the latter with a lower one. Streptococcus spp., Staph. aureus, Klebsiella spp., cases with other treated or untreated organisms, and CM without growth were associated with higher hazard rates of sale. The Cox proportional hazards model's hazard rates were higher than those in the competing risks model in which death was the event of interest, and resembled those in the model in which sale was the event of interest. Four additional Cox models, omitting dead or sold cows, or censoring each, were also fitted; hazard ratios were similar to the above models. Proportional subdistribution hazards models were appropriate due to competing risks (death, sale); they produce less-biased estimates. A study limitation is that while proportional subdistribution hazards models were appropriate, they have the illogical feature of keeping subjects at risk for the event of interest even after experiencing the competing event. This is, however, necessary in estimating cumulative incidence functions. Another limitation concerns pathogen variability among study farms, implying that CM decisions are farm-specific. Misclassification of 'dead' vs. 'sold' cows was also possible. Nevertheless, the findings may help in optimizing management of cows contracting specific types of CM early in productive lifetime.
... Other researchers have studied alternative early lactation periods, although none used a competing risks model. Haine et al. (2017) studied effects of CM occurring in the first 120 d of lactation, in cows of all parities. Moussavi et al. (2012) studied CM occurring between first calving and 10 days in milk (DIM; i.e., days in lactation), 10-60 DIM, and after 60 DIM. ...
... There are many studies on the effects of mastitis on bovine longevity/productive lifetime (e.g. Beaudeau et al., 1995;Haine et al., 2017;Gussmann et al., 2019), but few look at specific pathogens causing CM, or specifically on cases occurring in the earliest stage of productive lifetime. Gröhn et al. (2005) and Cha et al. (2013) have studied the effects of different pathogens on culling (the latter on death and sale separately), but not specifically occurring in early productive lifetime. ...
... This implies that the association of CM with productive lifetime is not exclusively of brief duration; it appears to persist beyond the short-term. Haine et al. (2017) fitted a marginal structural Cox model to account for time-varying exposures and covariates in estimating the effect of CM occurring in the first 120 d of lactation on subsequent culling in 12,676 cows in 261 Québec herds. First-lactation cows with CM in the first 120 DIM had a twice higher hazard of culling than did first-lactation cows that did not have CM in the first 120 DIM. ...
... The presence of mastitis associated with reduction in milk production, followed by culling costs and preventive actions (Aghamohammadi et al., 2018), in addition to greater antibiotics usage. Clinical mastitis has been reported as one of the main risk factors for early culling in Quebec dairy herds (Haine et al., 2017). Metabolic disease is another crucial factor of premature culling, as it is associated with a reduction in milk production and compromised reproductive performance (Paiano et al., 2019). ...
... Gröhn et al. (1998) also reported mastitis as the main health culling reason. According to Haine et al. (2017), clinical mastitis is a major risk factor for culling dairy cows in Quebec, analyzing herds with at least 10% incidence of clinical mastitis in lactation. Koeck et al. (2012) identified that the highest disease rate occurs in the first month of lactation, and mastitis had the highest prevalence (12.6%) in Canadian dairy herds. ...
The decision of premature culling cows directly impacts the profitability of dairy farms. A comprehensive characterization of the primary causes of culling reasons would greatly improve both management and selection objectives in dairy cattle breeding programs. Therefore, this study aimed to analyze the temporal frequencies of 34 culling reasons in Canadian Holstein cows. After data editing and quality control, records from 3,096,872 cows culled from 9,683 herds spread across Canada were used for the analyses covering the periods from 1996 to 2020. Reproductive issues were the main culling reason accounting for 23.02%, followed by milk production (20.82%), health (20.39%), conformation problems (13.69%), economic factors (13.10%), accidents (5.67%), age-related causes (1.67%), and workability (1.63%). Nearly fifty-eight percent of cows were culled after 47 months of age. The observed frequencies of culling due to economic factors were lower than expected from 1996 to 2014 and higher than expected between 2015 and 2020. Reproduction issues had the highest culling frequencies during fall (24.54%), winter (24.02%), and spring (22.51%), while health issues were the most frequent (22.51%) culling reason in the summer season. Health issues (25.50%) and milk production (27.71%) were the most frequent culling reasons in the provinces of Quebec and Ontario, respectively. Reproductive issues showed the highest frequency across climates based on the Köppen climate classification, except for Csb (Dry-summer subtropical or Mediterranean climate) and Bsk (Middle latitude steppe climate), which correspond to small regions in Canada, where production was the most frequent culling reason (29.42% and 21.56%, respectively). Reproductive and milk performance issues were the two main culling reasons in most ecozones, except in Boreal Shield and Atlantic Marine, where health issues had the highest frequencies (25.12 and 23.75%, respectively). These results will contribute to improving management practices and selective decisions to reduce involuntary culling of Holstein cows.
Lameness is a persistent and underreported health and welfare problem in the dairy industry, resulting in reduced cow performance and profitability as well as early culling. The study objectives were (1) to quantify the impact of the first instance of lameness, at different stages of lactation, on production and economic performance, and (2) to further quantify the impacts of the first instance of lameness when only cows that remain in the herd for at least 100 d in milk (DIM) and those that remain for 305 DIM are included in the analysis. A retrospective longitudinal study was conducted using pre-existing data from animal health records and Dairy Herd Improvement Association records. Data were edited based on selected inclusion criteria, yielding a data set containing records from 15,159 first-lactation Holstein cows from 120 herds with year of first calving between 2003 and 2014. Lame cows were assigned to 1 of 4 groups based on when in the lactation the first event of lameness occurred: transition (1–21 DIM), early lactation (22–100 DIM), mid-lactation (101–200 DIM), or late lactation (201+ DIM). Mid- and late-lactation lame cows were also stratified by cumulative milk yield before the lameness event. Healthy cows (i.e., no recorded lameness event) were randomly assigned for each lactation stage, with mid-lactation healthy and late-lactation healthy cows similarly stratified. Production performance (cumulative milk, fat, and protein yield) and economic performance [milk value, margin over feed cost (MOFC), and gross profit] were analyzed using a mixed model with herd as a random effect. Cumulative milk yields were 811 to 1,290 kg lower for lame cows than for healthy cows, with milk component yields undergoing similar reductions. Reductions in milk yield contributed to losses in milk value (Can$−527 to −1,083; US$−419 to $−862) and MOFC (Can$−510 to −774; US$−406 to $−616). Higher losses were reported using gross profit (Can$−753 to −1,052; US$−599 to $−837), which includes all lameness-related costs. Production and performance losses were smaller when 100 DIM and 305 DIM thresholds were applied (i.e., exclusion of cows culled before 100 and 305 DIM, respectively), however, mid- and late-lactation lame cows maintained high levels of significant losses for all 6 variables analyzed. Lameness also led to higher levels of culling, masking losses for transition and early-lactation lame cows in the 305-DIM analysis. Increasing producer understanding of the costs associated with lameness not only serves to provide insight to producers for more informed culling decisions, but may also help producers weigh the costs of adopting new methods and technologies targeted at reducing on-farm lameness.
Mastitis is a highly prevalent disease, which negatively affects cow performance, profitability, welfare, and longevity. The objectives of this study were (1) to quantify the impact of the first instance of mastitis, at different stages of lactation, on production and economic performance, and (2) to further quantify the impact of the first instance of mastitis when only cows that remain in the herd for at least 100 d in milk (DIM) and those that remain for 305 DIM are included in the analysis. A retrospective longitudinal study was conducted using data from existing animal health record files and Dairy Herd Improvement records. After editing based on selected inclusion criteria and completeness of health records, data consisted of records from first-lactation Holstein cows, from 120 herds, that calved for the first time between 2003 and 2014, inclusive. Mastitic cows were assigned to 1 of 4 groups based on when in the lactation the first event of mastitis occurred: transition (1–21 DIM), early lactation (22–100 DIM), mid lactation (101–200 DIM), or late lactation (201+ DIM). Mid-lactation and late-lactation mastitic cows were also stratified by cumulative milk yield before the mastitis event. Healthy cows (i.e., no recorded mastitis event) were randomly assigned for each lactation stage, with mid-lactation healthy and late-lactation healthy cows similarly stratified. Production performance (cumulative milk, fat, and protein yield) and economic performance [milk value, margin over feed cost (MOFC), and gross profit] were analyzed using a mixed model with herd as a random effect. Significant losses in cumulative milk yield (−382 to −989 kg) and correspondingly lower fat and protein yields were found in mastitic cows, with transition and late-lactation mastitic cows having the highest losses. Drops in production translated to significant reductions in cumulative milk value (Can$−287 to Can$−591; US$−228 to US$−470), MOFC (Can$−243 to Can$−540; US$−193 to US$−429), and gross profit (Can$−649 to Can$−908; US$−516 to US$−722) for mastitic cows at all stages. Differences between mastitic and healthy cows in the early lactation and transition stages remained for all variables in the 100-DIM analysis, but, aside from gross profit, were nonsignificant in the 305-DIM analysis. Gross profit accounted for all costs associated with mastitis and thus continued to be lower for mastitic cows at all stages, even in the 305-DIM analysis in which culled cows were omitted (Can$−485 to Can$−979; US$−386 to US$−779). The research reflects the performance implications of mastitis, providing more information upon which the producer can make informed culling decisions and maximize both herd profitability and cow longevity.
The objective of this study was to assess the association between individual metabolic diseases (MD) and multiple MD (MD+) in the transition period (±3 wk relative to calving) and the culling risk in the first 120 d in milk (DIM) in Holstein-Friesian dairy cows. Health records from a transition management facility in Germany with 1,946 calvings were analyzed in a 1-yr cohort via survival analysis and a decision tree model. The recorded MD were milk fever (MF), retained placenta (RP), metritis (METR), ketosis (KET), displaced abomasum (DA), twinning (TWIN), and clinical mastitis (MAST). The overall culling within 120 DIM was 18%. The 120 DIM culling risk for healthy cows (64.8% of the total) was 13%, whereas it was 25% for MD (24.5%) and 33% for MD+ (10.7%) cows. The 120 DIM culling risk (%) for each MD and MD+, respectively, was 34.6 and 48 for MF and MF+, 15 and 31.5 for RP and RP+, 9.4 and 22.2 for METR and METR+, 30.7 and 37.3 for KET and KET+, 56.1 and 46.8 for DA and DA+, 30.3 and 34 for TWIN and TWIN+, and 36.6 and 27.8 for MAST and MAST+. Moreover, the incidence risk (%) for each MD and MD+, respectively, was 4 and 2.6 for MF and MF+, 1 and 2.8 for RP and RP+, 8.7 and 6 for METR and METR+, 4.5 and 6.1 for KET and KET+, 0.8 and 2.4 for DA and DA+, 1.7 and 2.7 for TWIN and TWIN+, and 3.6 and 1.8 for MAST and MAST+. Setting the healthy cows as the referent, the 120 DIM hazard ratios (HR) for culling were MD 2.1, MD+ 2.9, MF 3.3, MF+ 4.6, RP+ 2.7, METR+ 1.8, KET 2.6, KET+ 3.3, DA 5.5, DA+ 4.5, TWIN 2.8, TWIN+ 3.0, MAST 3.1, and MAST+ 2.3. According to both decision tree and random forest analyses, MF was the most significant disease influencing survival, followed by DA, MAST, METR, and TWIN. In conclusion, the presence of MD or MD+ during the transition period was associated with increased culling risk in the first 120 DIM. The culling hazard was greater when an MD was complicated with another MD. In this study performed in a well-managed large farm, uncomplicated cases of RP (HR = 1.2) and METR (HR = 0.7) did not have an influence on the 120 DIM culling risk. Interestingly, both decision tree and random forest analyses pointed to MF and DA as main culling reasons in the first 120 DIM in the present dairy herd.
An epidemiological prospective study was carried out in French dairy herds with Holstein, Montbéliarde, or Normande cows and with low herd somatic cell scores. The objective was to identify dairy management practices associated with herd incidence rate of clinical mastitis. The studied herds were selected on a national basis, clinical cases were recorded through a standardized system, and a stable dairy management system existed. In the surveyed herds, mean milk yield was 7420 kg/cow per yr and mean milk somatic cell score was 2.04 (132,000 cells/mL). Overdispersion Poisson models were performed to investigate risk factors for mastitis incidence rate. From the final model, the herds with the following characteristics had lower incidence rates of clinical mastitis: 1) culling of cows with more than 3 cases of clinical mastitis within a lactation; 2) more than 2 person-years assigned to dairy herd management; 3) balanced concentrate in the cow basal diet. Moreover, herds with the following characteristics had higher incidence rates of clinical mastitis: 1) milking cows loose-housed in a straw yard; 2) no mastitis therapy performed when a single clot was observed in the milk; 3) clusters rinsed using water or soapy water after milking a cow with high somatic cell count; 4) 305-d milk yield >7435 kg; 5) herd located in the South region; 6) herd located in the North region; 7) cows with at least 1 nonfunctional quarter; and 8) premilking holding area with a slippery surface. The underlying mechanisms of some highlighted risk factors, such as milk production level and dietary management practices, should be investigated more thoroughly through international collaboration.
Propensity score methods are increasingly being used to estimate causal treatment effects in observational studies. In medical and epidemiological studies, outcomes are frequently time-to-event in nature. Propensity-score methods are often applied incorrectly when estimating the effect of treatment on time-to-event outcomes. This article describes how two different propensity score methods (matching and inverse probability of treatment weighting) can be used to estimate the measures of effect that are frequently reported in randomized controlled trials: (i) marginal survival curves, which describe survival in the population if all subjects were treated or if all subjects were untreated; and (ii) marginal hazard ratios. The use of these propensity score methods allows one to replicate the measures of effect that are commonly reported in randomized controlled trials with time-to-event outcomes: both absolute and relative reductions in the probability of an event occurring can be determined. We also provide guidance on variable selection for the propensity score model, highlight methods for assessing the balance of baseline covariates between treated and untreated subjects, and describe the implementation of a sensitivity analysis to assess the effect of unmeasured confounding variables on the estimated treatment effect when outcomes are time-to-event in nature. The methods in the paper are illustrated by estimating the effect of discharge statin prescribing on the risk of death in a sample of patients hospitalized with acute myocardial infarction. In this tutorial article, we describe and illustrate all the steps necessary to conduct a comprehensive analysis of the effect of treatment on time-to-event outcomes. © 2013 The authors. Statistics in Medicine published by John Wiley & Sons, Ltd.
Risk of culling consequent to the main health disorders occurring in the current production systems is reviewed. Survival analysis including health disorders as time-dependent variables is considered to be the most appropriate method to assess their effects because they allow a better description of the exact follow-up of disease history. Farmers preferentially consider health events in the current lactation and/or those occurring in early stages of lactation for making culling decisions. The unfavourable direct effects on culling of dystocia and udder disorders (mastitis and teat injuries) are clearly demonstrated, whereas there are variations between studies on the association between metabolic and reproductive disorders and culling. These variations may be due to differences in study designs, populations involved and methods. Consequences, in terms of estimated effect of health disorders, of methodological choices (e.g. whether or not including in the models descriptors for milk yield and/or reproductive performance) are discussed. Metabolic and reproductive disorders may act indirectly through a subsequent decrease in milk yield and reproductive performance. The impact of health disorders on longevity is on average weak, compared to the impact of low milk yield potential and poor reproductive performance. Herd characteristics (availability of heifers, quota, farmer's attitude towards risk and uncertainty...) modify the risk for a cow to be culled for a given health disorder. Aims of further studies could be (1) to interpret the meaning and to analyse the reliability of culling reasons information, (2) to evaluate the relative effect on culling of health disorders and performance (milk yield and reproduction) in different parities, (3) to investigate the role of components of the herd effect on the risk of culling.
Propensity score weighting is sensitive to model misspecification and outlying weights that can unduly influence results. The authors investigated whether trimming large weights downward can improve the performance of propensity score weighting and whether the benefits of trimming differ by propensity score estimation method. In a simulation study, the authors examined the performance of weight trimming following logistic regression, classification and regression trees (CART), boosted CART, and random forests to estimate propensity score weights. Results indicate that although misspecified logistic regression propensity score models yield increased bias and standard errors, weight trimming following logistic regression can improve the accuracy and precision of final parameter estimates. In contrast, weight trimming did not improve the performance of boosted CART and random forests. The performance of boosted CART and random forests without weight trimming was similar to the best performance obtainable by weight trimmed logistic regression estimated propensity scores. While trimming may be used to optimize propensity score weights estimated using logistic regression, the optimal level of trimming is difficult to determine. These results indicate that although trimming can improve inferences in some settings, in order to consistently improve the performance of propensity score weighting, analysts should focus on the procedures leading to the generation of weights (i.e., proper specification of the propensity score model) rather than relying on ad-hoc methods such as weight trimming.
In time-to-event analyses, artificial censoring with correction for induced selection bias using inverse probability-of-censoring weights can be used to 1) examine the natural history of a disease after effective interventions are widely available, 2) correct bias due to noncompliance with fixed or dynamic treatment regimens, and 3) estimate survival in the presence of competing risks. Artificial censoring entails censoring participants when they meet a predefined study criterion, such as exposure to an intervention, failure to comply, or the occurrence of a competing outcome. Inverse probability-of-censoring weights use measured common predictors of the artificial censoring mechanism and the outcome of interest to determine what the survival experience of the artificially censored participants would be had they never been exposed to the intervention, complied with their treatment regimen, or not developed the competing outcome. Even if all common predictors are appropriately measured and taken into account, in the context of small sample size and strong selection bias, inverse probability-of-censoring weights could fail because of violations in assumptions necessary to correct selection bias. The authors used an example from the Multicenter AIDS Cohort Study, 1984-2008, regarding estimation of long-term acquired immunodeficiency syndrome-free survival to demonstrate the impact of violations in necessary assumptions. Approaches to improve correction methods are discussed.
This study was designed to identify risk factors for intramammary infections with Streptococcus uberis and Staphylococcus aureus under field conditions. An 18-mo survey with sampling of all quarters of all lactating cows at 3-wk intervals was carried out in three Dutch dairy herds with medium bulk milk somatic cell count (200,000 to 300,000 cells/ml). Quarter milk samples were used for bacteriology and somatic cell counting. Data on parity, lactation stage, and bovine herpesvirus 4-serology were recorded for each animal. During the last year of the study, body condition score, and teat-end callosity scores were recorded at 3-wk intervals. A total of 93 new infections with Strep. uberis were detected in 22,665 observations on quarters at risk for Strep. uberis infection, and 100 new infections with Staph. aureus were detected in 22,593 observations on quarters at risk for Staph. aureus infection. Multivariable Poisson regression analysis with clustering at herd and cow level was used to identify risk factors for infection. Rate of infection with Strep. uberis was lower in first- and second-parity cows than in older cows, and depended on stage of lactation in one herd. Quarters that were infected with Arcanobacterium pyogenes or enterococci, quarters that had recovered from Strep. uberis- or Staph. aureus-infection in the past, and quarters that were exposed to another Strep. uberis infected quarter in the same cow had a higher rate of Strep. uberis infection. Teat-end callosity and infection with coagulase-negative staphylococci or corynebacteria were not significant as risk factors. Rate of Staph. aureus infection was higher in bovine herpesvirus 4-seropositive cows, in right quarters, in quarters that had recovered from Staph. aureus or Strep. uberis infection, in quarters exposed to other Staph. aureus infected quarters in the same cow, and in quarters with extremely callused teat ends. Infection with coagulase-negative staphylococci was not significant as a risk factor. The effect of infection with corynebacteria on rate of infection with Staph. aureus depended on herd, stage of lactation, and teat-end roughness. Herd level prevalence of Strep. uberis or Staph. aureus, and low quarter milk somatic cell count were not associated with an increased rate of infection for Strep. uberis or Staph. aureus.
Multivariate Imputation by Chained Equations (MICE) is the name of software for imputing incomplete multivariate data by Fully Conditional Speci cation (FCS). MICE V1.0 appeared in the year 2000 as an S-PLUS library, and in 2001 as an R package. MICE V1.0 introduced predictor selection, passive imputation and automatic pooling. This article presents MICE V2.0, which extends the functionality of MICE V1.0 in several ways. In MICE V2.0, the analysis of imputed data is made completely general, whereas the range of models under which pooling works is substantially extended. MICE V2.0 adds new functionality for imputing multilevel data, automatic predictor selection, data handling, post-processing imputed values, specialized pooling and model selection. Imputation of categorical data is improved in order to bypass problems caused by perfect prediction. Special attention to transformations, sum scores, indices and interactions using passive imputation, and to the proper setup of the predictor matrix. MICE V2.0 is freely available from CRAN as an R package mice. This article provides a hands-on, stepwise approach to using mice for solving incomplete data problems in real data.
Knowledge of reproductive risk factors for culling is useful in making insemination and culling decisions and helps motivate efforts to reduce or eliminate risk factors. The objective of this study was to describe survival and reproductive risk factors for culling in Holstein dairy herds with at least 200 cows. Results were calculated from 2,345,015 DHI lactation records from 727 herds with at least 200 cows from 2001 to 2006. Herds were located in 36 states primarily located east of the Mississippi River. Kaplan-Meier survival curves were obtained and daily hazards of culling were calculated with the actuarial method. Cox regression was performed with the GLIMMIX procedure in SAS (SAS Institute Inc., Cary, NC). The hazard of culling increased with parity number. Cows in their sixth parity had 3 times greater hazards than cows in their first parity. Medium remaining productive life for cows calving in parity 1 to 6 were 907, 697, 553, 469, 423, and 399 d, respectively. Daily hazards of culling first peaked approximately 30 d after calving and then again later in lactation, after 280 d, for older cows. Hazards for first-parity cows peaked earlier, around d 10 after calving, and the first-parity cows had lower risks of culling later in lactation than older cows. Pregnant cows had 3 to 7 times lower hazards of culling than open cows. Hazards of culling increased for cows that had greater calving difficulty, gave birth to males or twins, were in herds with shorter days to first insemination, or had longer days to conception. The possible to likely use of a synchronized breeding program increased from 21.9% in 2001 to 41.4% in 2006. Cows in herds that did not use a synchronized breeding program had slightly lower risks of culling than those in herds that at least possibly used a synchronized breeding program.
That conditioning on a common effect of exposure and outcome may cause selection, or collider-stratification, bias is not intuitive. We provide two hypothetical examples to convey concepts underlying bias due to conditioning on a collider. In the first example, fever is a common effect of influenza and consumption of a tainted egg-salad sandwich. In the second example, case-status is a common effect of a genotype and an environmental factor. In both examples, conditioning on the common effect imparts an association between two otherwise independent variables; we call this selection bias.
The incidence rate of clinical mastitis due to Escherichia coli and Staphylococcus aureus was studied in 125 herds with a low annual bulk milk somatic cell count (less than 150,000 cells/ml). Risk factors that were offered to a multivariate Poisson regression model included general management, housing, cleaning procedures, cow and cubicle cleanliness, feeds and feeding, dry cow management, milking procedures, machine milking, disease prevention, and milk production. Some differences in epidemiology between E. coli and S. aureus were observed. In the S. aureus model, more milking procedure and milking machine variables were present. The milk production, drinking water source, amount of bedding, and ventilation were other important factors in the S. aureus model. Teat disinfection was an important risk factor in the E. coli model but was much less important in the S. aureus model. Cleaning procedures were more important in the E. coli model. The main breed on the farm and percentage of cows leaking milk were other important factors in the E. coli model.
Data from a survey performed from 1986 to 1990 were analyzed to assess the effects of diseases on length of productive life of 3589 Holstein cows from 47 herds, using a proportional hazard model. The probability of a cow being culled, or hazard function, was supposed to be the product of an unspecified baseline hazard function and log-linear, time-dependent explanatory variables that possibly influence culling rate (Cox's regression). The effect of 16 health events was studied according to lactation number of occurrence. The model included adjustments for effects of herd-year-season (considered to be random), month of calving, stage of lactation, lactation number, reproductive performance, and milk production. The probability of a cow being culled increased in early and late stages of lactation in older cows, in low producing cows, and in cows with poor reproductive performance. Mastitis before the peak of lactation or during the dry period increased the risk (relative culling rate in first lactation, 1.3 and 4.0, respectively). Teat injuries and nontraumatic udder disorders had a large impact on longevity. Cows with late metritis or early abortion had poor survival. The decrease in median length of productive life could be over a standard lactation in particular cases. Expected survivor curves, computed after assumption of a priori values of covariates and their evolution over time, appear to be powerful tools for examining the effect of health disorders on length of productive life of cows.
The objective of this study was to describe the frequency of occurrence of clinical mastitis in dairy herds in Ontario. The study group consisted of 65 dairy farms involved in a 2-year observational study, which included recording all clinical mastitis cases and milk sampling of quarters with clinical mastitis. Lactational incidence risks of 9.8% for abnormal milk only, 8.2% for abnormal milk with a hard or swollen udder, and 4.4% for abnormal milk plus systemic signs of illness related to mastitis were calculated for 2840 cows and heifers. Overall, 19.8% of cows experienced one or more cases of clinical mastitis during location. Teat injuries occurred in 2.1% of lactations. Standard bacteriology was performed on pretreatment milk samples from 834 cows with clinical mastitis. The bacteria isolated were Staphylococcus aureus (6.7%), Streptococcus agalactiae (0.7%), other Streptococcus spp. (14.1%), coliforms (17.2%), gram-positive bacilli (5.5%), Corynebacterium bovis (1.7%), and other Staphylococcus spp. (28.7%). There was no growth in 17.7% of samples, and 8.3% of samples were contaminated. Clinical mastitis is a common disease in dairy cows in Ontario; approximately 1 in 5 cow lactations have at lease one episode of clinical mastitis. There is, however, considerable variation in the incidence of clinical mastitis among farms. The majority of 1st cases of clinical mastitis occur early in lactation, and the risk of clinical mastitis increases with increasing parity. Environmental, contagious, and minor pathogens were all associated with cases of clinical mastitis.
The effect of seven diseases on culling was measured in 7523 Holstein cows in New York State. The cows were from 14 herds and had calved between January 1, 1994 and December 31, 1994; all cows were followed until September 30, 1995. Survival analysis was performed using the Cox proportional hazards model to incorporate time-dependent covariates for diseases. Different intervals representing stages of lactation were considered for effects of the diseases. Five models were fitted to test how milk yield and conception status modified the effect of diseases on culling. Covariates in the models included parity, calving season, and time-dependent covariates measuring diseases, milk yield of the current lactation, and conception status. Data were stratified by herd. The seven diseases and lactational risks under consideration were milk fever (0.9%), retained placenta (9.5%), displaced abomasum (5.3%), ketosis (5.0%), metritis (4.2%), ovarian cysts (10.6%), and mastitis (14.5%). Older cows were at a much higher risk of being culled. Calving season had no effect on culling. Higher milk yield was protective against culling. Once a cow had conceived again, her risk of culling dropped sharply. In all models, mastitis was an important risk factor throughout lactation. Milk fever, retained placenta, displaced abomasum, ketosis, and ovarian cysts also significantly affected culling at different stages of lactation. Metritis had no effect on culling. The magnitude of the effects of the diseases decreased, but remained important, when milk yield and conception status were included as covariates. These results indicated that diseases have an important impact on the actual decision to cull and the timing of culling. Parity, milk yield, and conception status are also important factors in culling decisions.
A case-control study was conducted to evaluate factors measured at the udder inflammation-free state as risk factors for subsequent clinical mastitis. The factors including somatic cell count (SCC), body condition score, milk yield, percentages of milk fat and milk protein, and diseases were evaluated for their association with the results of udder inflammatory response. The results of the response were specified as presence (case) and absence (control) of clinical signs of mastitis. Data on Holstein Friesian cows calving from January 1984 to November 1996 from a commercial farm with low bulk milk SCC were used. Univariable and multivariable random-effect logistic models were used to evaluate the effect of those factors on the risk of clinical mastitis. The following variables were associated with increased odds of case versus control events in the univariable analysis: early lactation period, low SCC, high milk yield, high percentage of milk protein, high percentage of milk fat, low body condition score, retained placenta, and milk fever. For the final multivariable model of all variables used for analysis, only low SCC remained significantly associated with increased risk of subsequent clinical mastitis. The authors concluded that very low SCC during the udder inflammation-free state are associated with increased risk of clinical mastitis.
Mastitis is the most prevalent production disease in dairy herds world-wide and is responsible for several production effects. Milk yield and composition can be affected by a more or less severe short-term depression and, in case of no cure, by a long-acting effect, and, sometimes, an overlapping effect to the next lactation. Summary values in the literature for losses of milk production were proposed at 375 kg for a clinical case (5% at the lactation level) and at 0.5 kg per 2-fold increase of crude SCC of a cow. Due to the withdrawal period after treatment, composition changes in milk can almost be neglected in economic calculations. Lethality rate for clinical mastitis is very low on the average, while anticipated culling occurs more frequently after clinical and subclinical mastitis (relative risk between 1.5 and 5.0). The economics of mastitis needs to be addressed at the farm level and, per se, depends on local and regional epidemiological, managerial and economic conditions. To assess the direct economic impact of mastitis, costs (i.e. extra resource use) and losses (i.e. reduced revenues) have to be aggregated. To support decision making for udder health control, it is necessary to use a marginal approach, based on the comparison of the losses avoided and the additional costs of modified plans, compared to the existing ones.
Survival analysis in a Weibull proportional hazards model was used to evaluate the impact of somatic cell count (SCC) on the involuntary culling rate of US Holstein and Jersey cows with first calvings from 1990 to 2000. The full data set, consisting of records from 978,043 Holstein and 250,835 Jersey cows, was divided into subsets (5 for Holsteins and 3 for Jerseys) based on herd average lactation SCC values. Functional longevity (also known as herd life or length of productive life) was defined as days from first calving until culling or censoring, after correcting for milk production. Our model included the time-dependent effects of herd-year-season, parity by stage of lactation interaction, within-herd-year quintile ranking for mature equivalent production, and lactation average SCC (rounded to the nearest 50,000 cells/mL), as well as the time-independent effect of age at first calving. Parameters of the Weibull distribution, as well as variance components for herd-year-season effects, were estimated within each group of herds. Mean failure and censoring times decreased as herd average SCC increased, and a nonlinear relationship was observed between SCC and longevity in all groups. The risk of culling for Holstein cows with lactation average SCC > 700,000 cells/mL was 3.4, 2.7, or 2.3 times greater, respectively, than that of Holstein cows with SCC of 200,000 to 250,000 cells/mL in herds with low, medium, or high average SCC. Likewise, the risk of culling for Jersey cows with lactation average SCC > 700,000 cells/mL was 4.0, 2.9, or 2.2 times greater, respectively, than that of Jersey cows with SCC of 200,000 to 250,000 cells/mL in low, medium, or high SCC herds. These trends may reflect more stringent culling of high SCC cows in herds with few mastitis problems. In addition, cows with lactation average SCC <100,000 cells/mL had a slightly higher risk of culling than cows with SCC of 100,000 to 200,000 cells/mL in both breeds, particularly in herds with high average SCC, where exposure to mastitis pathogens was likely.
Replacing cows on a dairy is a major cost of operation. There is a need for the industry to adopt a more standardized approach to reporting the rate at which cows exit from the dairy, and to reporting the reasons why cows are replaced and their destination as they exit the dairy. Herd turnover rate is recommended as the preferred term for characterizing the cows exiting a dairy, in preference to herd replacement rate, culling rate, or percent exiting, all of which have served as synonyms. Herd turnover rate should be calculated as the number of cows that exit in a defined period divided by the animal time at risk for the population being characterized. The terms voluntary and involuntary culling suffer from problems of definition and their use should be discouraged. Destination should be recorded for all cows that exit the dairy and opportunities to record one or more reasons for exiting should be provided by management systems. Comparing reported reasons between dairies requires considerable caution because of differences in case definitions and recording methods. Relying upon culling records to monitor disease has been and will always be an ineffective management strategy. Dairies are encouraged to record and monitor disease events and reproductive performance and use this information as the basis for management efforts aimed at reducing the need to replace cows.
In assessing the efficacy of a time-varying treatment Marginal Structural Models (MSMs) and Structural Nested Mean Models (SNMMs) are useful in dealing with confounding by variables affected by earlier treatments. MSMs model the joint effect of treatments on the marginal mean of the potential outcome, whereas SNMMs model the joint effect of treatments on the mean of the potential outcome conditional on the treatment and covariate history. These models often consider independent subjects with noninformative time of observation.
The first two chapters extend the two classes of models to clustered observations with time-varying treatments in the presence of time-varying confounding. We formulate models with both cluster- and unit-level treatments and derive semiparametric estimators of parameters in such models. For unit-level treatments, we consider both the presence and absence of interference, namely the effect of treatment on outcomes in other units of the same cluster. For MSMs, we show that the use of unit-specific inverse probability weights and certain working correlation structures can improve the efficiency of estimators under specified conditions. The properties of the estimators are evaluated through simulations and compared with the conventional GEE regression method for clustered outcomes. To illustrate our methods, we use data from the treatment arm of a glaucoma clinical trial to compare the effectiveness of two commonly used ocular hypertension medications.
The third chapter extends SNMMs to situations with intermittent missing observations. In observational longitudinal studies, subjects often miss prescheduled visits intermittently. Previous literature has mainly focused on dealing with monotone censoring due to early dropout. Here we focus on intermittent missingness that can depend on the subjects' covariate and treatment history. We show that under certain assumptions the standard SNMMs can be used for situations where non-outcome covariates are missing intermittently. In situations where outcomes are also missing intermittently, we use a method that does not require artificially censoring the data, but requires a strict missing at random assumption. The estimators are shown to be consistent and achieve reasonable efficiency. We illustrate the method by estimating the effect of non-steroidal anti-inflammatory drugs (NSAIDs) on genitourinary pain using data from a study of chronic pelvic pain.
Conducting a clinical trial at multiple study centres raises the issue of whether and how to adjust for centre heterogeneity in the statistical analysis. In this paper, we address this issue for multicentre clinical trials with a time-to-event outcome. Based on simulations, we show that the current practice of ignoring centre heterogeneity can be seriously misleading, and we illustrate the performances of the frailty modelling approach over competing methods. A special attention is paid to the problem of misspecification of the frailty distribution. The appendix provides sample codes in R and in SAS to perform the analyses in this paper. Copyright © 2014 John Wiley & Sons, Ltd.
The ability to make strong causal inferences, based on data derived from outside of the laboratory, is largely restricted to data arising from well-designed randomized control trials. Nonetheless, a number of methods have been developed to improve our ability to make valid causal inferences from data arising from observational studies. In this paper, I review concepts of causation as a background to counterfactual causal ideas; the latter ideas are central to much of current causal theory. Confounding greatly constrains causal inferences in all observational studies. Confounding is a biased measure of effect that results when one or more variables, that are both antecedent to the exposure and associated with the outcome, are differentially distributed between the exposed and non-exposed groups. Historically, the most common approach to control confounding has been multivariable modeling; however, the limitations of this approach are discussed. My suggestions for improving causal inferences include asking better questions (relates to counterfactual ideas and "thought" trials); improving study design through the use of forward projection; and using propensity scores to identify potential confounders and enhance exchangeability, prior to seeing the outcome data. If time-dependent confounders are present (as they are in many longitudinal studies), more-advanced methods such as marginal structural models need to be implemented. Tutorials and examples are cited where possible.
In observational cohort mortality studies with prolonged periods of exposure to the agent under study, it is not uncommon for risk factors for death to be determinants of subsequent exposure. For instance, in occupational mortality studies date of termination of employment is both a determinant of future exposure (since terminated individuals receive no further exposure) and an independent risk factor for death (since disabled individuals tend to leave employment). When current risk factor status determines subsequent exposure and is determined by previous exposure, standard analyses that estimate age-specific mortality rates as a function of cumulative exposure may underestimate the true effect of exposure on mortality whether or not one adjusts for the risk factor in the analysis. This observation raises the question, which if any population parameters can be given a causal interpretation in observational mortality studies?In answer, we offer a graphical approach to the identification and computation of causal parameters in mortality studies with sustained exposure periods. This approach is shown to be equivalent to an approach in which the observational study is identified with a hypothetical double-blind randomized trial in which data on each subject's assigned treatment protocol has been erased from the data file. Causal inferences can then be made by comparing mortality as a function of treatment protocol, since, in a double-blind randomized trial missing data on treatment protocol, the association of mortality with treatment protocol can still be estimated.We reanalyze the mortality experience of a cohort of arsenic-exposed copper smelter workers with our method and compare our results with those obtained using standard methods. We find an adverse effect of arsenic exposure on all-cause and lung cancer mortality which standard methods fail to detect.
Longitudinal studies, where data are repeatedly collected on subjects over a period, are common in medical research. When estimating the effect of a time-varying treatment or exposure on an outcome of interest measured at a later time, standard methods fail to give consistent estimators in the presence of time-varying confounders if those confounders are themselves affected by the treatment. Robins and colleagues have proposed several alternative methods that, provided certain assumptions hold, avoid the problems associated with standard approaches. They include the g-computation formula, inverse probability weighted estimation of marginal structural models and g-estimation of structural nested models. In this tutorial, we give a description of each of these methods, exploring the links and differences between them and the reasons for choosing one over the others in different settings. Copyright © 2012 John Wiley & Sons, Ltd.
The subject-specific data from a longitudinal study consist of a string of numbers. These numbers represent a series of empirical measurements. Calculations are performed on these strings and causal inferences are drawn. For example, an investigator might conclude that the analysis provides strong evidence for “a direct effect of AZT on the survival of AIDS patients controlling for the intermediate variable ‐ therapy with aerosolized pentamidine”. The nature of the relationship between the sentence expressing these causal conclusions and the computer calculations performed on the strings of numbers has been obscure. Since the computer algorithms are well-defined mathematical objects, it is useful to provide formal mathematical definitions for the English sentences expressing the investigator’s causal inferences, In Robins (1986, 1987), I proposed a formal theory of counterfactual (Lewis 1973) causal inference that extended the Neyman‐Rubin‐Holland (Holland 1986) “point treatment” theory to longitudinal studies with time-varying treatments, outcomes, and covariates (concomitants). This theory translates any causal question concerning the overall (net), direct, and/or indirect effects of a possibly time-varying treatment on an outcome into a formal mathematical conjecture about event trees, referred to as causally interpreted structured tree graphs. Pearl (1995), and Spirtes, Glymour, and Schemes (hereafter SGS) (1993) recently developed a formal theory of causal inference based on causal directed acyclic graphs (DAGs). I showed that these causal DAGs are mathematically equivalent to a particular special case of my more general theory (Robins 1995). In longitudinal studies, treatment often varies over time. The standard approach to the estimation of the effect of a time-varying treatment on an outcome of interest is to model the outcome at time t as af unction of past treatment history. I have shown that this approach may be biased, whether or not one further adjusts for the past history of time-dependent
In observational studies with exposures or treatments that vary over time, standard approaches for adjustment of confounding are biased when there exist time-dependent confounders that are also affected by previous treatment. This paper introduces marginal structural models, a new class of causal models that allow for improved adjustment of confounding in those situations. The parameters of a marginal structural model can be consistently estimated using a new class of estimators, the inverse-probability-of-treatment weighted estimators.
Data from an observational study, carried out during a 4.5 year period (1986–1990), were used to quantify the effects of health disorders on the risk of culling. The study population consisted of 47 commercial Holstein dairy herds from western France, comprising 4123 cows.Logistic regression was used to assess the relationships between health disorders and early and late culling. Fourteen main health disorders with clinical signs and one subclinical disease were studied: abortion, periparturient accident, calving provided with assistance, digestive disorders, ketosis, locomotor disorders, mastitis, metritis, milk fever, cystic ovaries, respiratory disorders, retained placenta, teat injuries, non-traumatic udder disorders and status with respect to milk somatic cell count. Adjustments were made for year, month of calving, parity, breeding value for milk, best of the two first milk production records and reproductive performance. The possible effects of interactions among variables were also studied. The herd effect was taken into account using random effect models.Non-traumatic udder disorders, teat injuries, milk fever and the occurrence of both ketosis and assistance at calving were significantly associated with an increased risk of being early culled (odds ratios (OR) ranging from 1.6 to 10.3). Early and late abortion, late metritis, poor peproductive performance, retained placenta, non-traumatic udder disorders within 45 days post-partum and mastitis occurring in the first 3 months of the lactation were positively associated with a late culling (OR ranging from 1.2 to 6.6). Cows with lower breeding value for milk and higher parities were high risk groups for culling. A lower level of milk production and occurrence of both reproductive disorders and poor reproductive performance were risk factors for late culling.
Incidence of clinical mastitis was studied in 274 herds grouped in three categories by bulk milk somatic cell count (SCC). Mean incidence rate of clinical mastitis was 0.278, 0.257, and 0.252 cases per 365 cow-days at risk in herds with low (< or = 150,000), medium (150,000 to 250,000), and high (250,000 to 400,000 cells/ml) bulk milk SCC, respectively. The incidence rate of clinical mastitis was not different among the three categories. Variance in the incidence of clinical mastitis among herds increased as bulk milk SCC decreased. Clinical mastitis caused by Gram-negative pathogens, such as Escherichia coli, Klebsiella spp., or Pseudomonas spp., occurred more often in herds with a low bulk milk SCC. Clinical mastitis caused by Staphylococcus aureus, Streptococcus dysgalactiae, and Streptococcus agalactiae occurred more often in herds with a high bulk milk SCC. Systemic signs of illness caused by clinical mastitis occurred more often in herds with a low bulk milk SCC. Both overall culling rate and culling rate for clinical mastitis were not different among groups catergorized by bulk milk SCC. In herds with a high bulk milk SCC, however, more cows that produced milk with a high SCC were culled. In herds with a low bulk milk SCC, more cows were culled for teat lesions, milkability, udder shape, fertility, and character than were cows in herds with a high bulk milk SCC. In herds with a low bulk milk SCC, cows were also culled more for export and production reasons.
An essential reason to record and evaluate patterns of cow somatic cell count (SCC) within a dairy herd is to help in making clinical decisions on the control of mastitis. An understanding of when new infections occur and how patterns of infection influence herd bulk milk somatic cell count (BMSCC) are critical when implementing mastitis control because it enables advisors to target specific problem areas. The objective of this research was to evaluate individual cow SCC patterns in terms of their contribution to BMSCC. Data collected in 2128 herds from England and Wales between 2004 and 2006 were used. Cows were categorised as having a low, medium or high SCC based on thresholds of 100,000 cells/mL and 200,000 cells/mL. Movements between these categories in consecutive months, before or after 30 days in milk, in primiparous (heifers) and multiparous cows (cows) were used to predict BMSCC. From these categories, new variables representing different SCC patterns, were calculated and included in different models: the medium SCC category was grouped with either the low or the high category, and the denominator was either the total number of cows recorded during the herd-year or the number of cows eligible for a particular transition. Model fitting and predictions were carried out in a Bayesian framework. A random sample of 1500 herds was used for parameter estimation and the remaining 628 herds for model validation. Heifers were more likely to remain at, or to move to, a low SCC than cows. A transition threshold of 100,000 cells/mL for heifers resulted in a poorer model fit and predictive ability than a threshold of 200,000 cells/mL. A model using a single threshold of 200,000 cells/mL regardless of parity was the best to predict BMSCC. The sensitivity and specificity of this final model to correctly predict a BMSCC > 200, 000 cells/mL in the validation dataset were 86.5% and 86.8%, respectively. Important SCC patterns that influenced BMSCC were cows and heifers staying above 200,000 cells/mL for two consecutive recordings during lactation, cows moving from below to above 200,000 cells/mL across the dry period, cows remaining above 200,000 cells/mL across the dry period and heifers calving with an SCC above 200,000 cells/mL in the first month of lactation. The variation between herds in SCC transitions was evaluated and it was concluded that the performance of the top 10% of herds would be useful to provide benchmarks to evaluate dairy herd mastitis.
Sensitivity analysis for unmeasured confounding should be reported more often, especially in observational studies. In the standard Cox proportional hazards model, this requires substantial assumptions and can be computationally difficult. The marginal structural Cox proportional hazards model (Cox proportional hazards MSM) with inverse probability weighting has several advantages compared to the standard Cox model, including situations with only one assessment of exposure (point exposure) and time-independent confounders. We describe how simple computations provide sensitivity for unmeasured confounding in a Cox proportional hazards MSM with point exposure. This is achieved by translating the general framework for sensitivity analysis for MSMs by Robins and colleagues to survival time data. Instead of bias-corrected observations, we correct the hazard rate to adjust for a specified amount of unmeasured confounding. As an additional bonus, the Cox proportional hazards MSM is robust against bias from differential loss to follow-up. As an illustration, the Cox proportional hazards MSM was applied in a reanalysis of the association between smoking and depression in a population-based cohort of Norwegian adults. The association was moderately sensitive for unmeasured confounding.
The method of inverse probability weighting (henceforth, weighting) can be used to adjust for measured confounding and selection bias under the four assumptions of consistency, exchangeability, positivity, and no misspecification of the model used to estimate weights. In recent years, several published estimates of the effect of time-varying exposures have been based on weighted estimation of the parameters of marginal structural models because, unlike standard statistical methods, weighting can appropriately adjust for measured time-varying confounders affected by prior exposure. As an example, the authors describe the last three assumptions using the change in viral load due to initiation of antiretroviral therapy among 918 human immunodeficiency virus-infected US men and women followed for a median of 5.8 years between 1996 and 2005. The authors describe possible tradeoffs that an epidemiologist may encounter when attempting to make inferences. For instance, a tradeoff between bias and precision is illustrated as a function of the extent to which confounding is controlled. Weight truncation is presented as an informal and easily implemented method to deal with these tradeoffs. Inverse probability weighting provides a powerful methodological tool that may uncover causal effects of exposures that are otherwise obscured. However, as with all methods, diagnostics and sensitivity analyses are essential for proper use.
AIDS Clinical Trial Group Randomized Trial 002 compared the effect of high-dose with low-dose 3-azido-3-deoxythymidine (AZT) on the survival of AIDS patients. Embedded within the trial was an essentially uncontrolled observational study of the effect of prophylaxis therapy for pneumocystis carinii pneumonia on survival. In this paper, we estimate the causal effect of prophylaxis therapy on survival by using the method of G-estimation to estimate the parameters of a structural nested failure time model (SNFTM). Our SNFTM relates a subject's observed time of death and observed prophylaxis history to the time the subject would have died if, possibly contrary to fact, prophylaxis therapy had been withheld. We find that, under our assumptions, the data are consistent with prophylaxis therapy increasing survival by 16% or decreasing survival by 18% at the alpha = 0.05 level. The analytic approach proposed in this paper will be necessary to control bias in any epidemiologic study in which there exists a time-dependent risk factor for death, such as pneumocystis carinii pneumonia history, that (A1) influences subsequent exposure to the agent under study, for example, prophylaxis therapy, and (A2) is itself influenced by past exposure to the study agent. Conditions A1 and A2 will be true whenever there exists a time-dependent risk factor that is simultaneously a confounder and an intermediate variable.
To evaluate the effect of natural udder infection with minor pathogens on subsequent natural infection with major pathogens.
7 dairy herds with low bulk milk somatic cell count.
During a 20-month prospective study, milk samples were collected from diary cows at regular intervals and from quarters with clinical signs of mastitis. Incidence of intramammary infection was calculated in uninfected quarters and in quarters infected with minor pathogens. A within-cow, matched case-control analysis was used to evaluate the effect of minor pathogens on subsequent infection with major pathogens.
Quarters infected with minor pathogens had higher somatic cell count than did uninfected quarters. In quarters infected with Corynebacterium bovis, the rate of infection with major pathogens was lower, whereas in quarters infected with coagulase-negative Micrococcaceae, the rate of infection with major pathogens was higher than that in uninfected quarters. From the within-cow comparison, it appeared that, in quarters infected with minor pathogens, infection with major pathogens was significantly lower than that in comparable control quarters not infected with minor pathogens.
Minor pathogens have a protective effect against infection with major pathogens. The protective effect of C bovis against subsequent infection with major pathogens appears to be greater than the effect of coagulase-negative Micrococcaceae.
This study demonstrated five different approaches, with and without time-dependent covariates, to determine the effect of disease on culling. It was also of interest to determine whether the time of the disease had an effect on subsequent culling (i.e., whether disease should be treated as time-dependent covariate). To this purpose, five separate models were studied: Models 1 through 4 were Cox proportional hazards models, and Model 5 was a Weibull model. Model 1 treated disease as a binary, time-independent covariate. Model 2 treated disease as a time-dependent covariate, and one change of status was assumed to occur at the time of disease. Model 3 also assumed that one change in status occurred at the time of disease, but the effect of that change was assumed to be different depending on when the disease occurred. Models 4 (Cox) and 5 (Weibull) assumed an interaction between the occurrence of disease (time of disease) and the occurrence of culling (time of culling). As an illustration, the effect of mastitis on culling was studied for 2998 Holstein dairy cows in 10 herds. Parity and previous 305-d milk yield were also included as covariates; the data were stratified by herd. For all models, mastitis was a significant factor for culling. The significance tests for the estimates from Models 4 and 5 demonstrated that the hazard of culling differed for different stages of lactation, depending on when mastitis had occurred and when its effect on culling occurred; that is, time dependence exists between time of mastitis and time of culling.
A nested case-control study was conducted to identify risk factors for clinical mastitis in heifers. Cases and controls originated from dairy herds that were enrolled in the Production Recording Scheme. Heifers that had been treated for clinical mastitis prepartum or on the day of parturition were eligible for inclusion as cases. The controls were heifers that had not been treated for clinical mastitis before parturition, during their first lactation, or during the dry period. In the final analysis, 4256 heifers with mastitis and 67,072 control heifers were included. An increase in the incidence of clinical mastitis in the herd, a decrease in the bulk milk somatic cell count, and an increase in the mean milk yield of the herd were associated with an increased risk for clinical mastitis. The risk varied among regions, and, depending on region, significant influences of both herd size and composition of the diet were observed. Heifers kept on pasture in summer were at a decreased risk for clinical mastitis. Calving in late spring or summer was associated with greater risk than was calving at other times of the year. An increase in age at first calving was associated with increased risk of mastitis. Mastitis was also more likely to occur in heifers leaking milk or in heifers that had a low milk flow rate in the subsequent lactation. For purchased heifers, risk factors were identified in both their previous and current herds.
The relationship between somatic cell counts (SCCs) up to 400,000 cells/ml in individual cows and clinical mastitis was studied by collecting monthly records for a year from 101 Holstein herds in the west of France. Monthly records obtained after any case of clinical mastitis occurring within the lactation were excluded. The resulting dataset consisted of 29,700 records from 4677 cows. The data were analysed by the logistic regression method. Herd, lactation number, calendar month, milk production, stage of lactation on the day of test, and SCC on previous test days were assumed to affect the likelihood of clinical mastitis. There was no significant relationship between SCC and the subsequent occurrence of clinical mastitis for an SCC up to 100,000 cells/ml, but the risk of clinical mastitis increased as the SCC increased up to 400,000 cells/ml. These results suggest that in individual cows, a low SCC recorded after five days in milk does not lead to an increased risk of clinical mastitis.
The effect of clinical mastitis on milk yield was studied in 24,276 Finnish Ayrshire cows that calved in 1993 and were followed for one lactation (i.e., until culling or the next calving). Cows that had only mastitis, but no other diseases, and cows that had no diseases (healthy cows) during the lactation were included in the study. Monthly test day milk yields were treated as repeated measurements within an animal in a mixed model analysis. Mastitis index categories were created to relate the timing of mastitis to the test day milk measures. Statistical models (a separate model for each parity) included fixed effects of calving season, stage of lactation, and mastitis index. An autoregressive correlation structure was used to model the association among the repeated measurements. The effect of mastitis occurring at different periods during the lactation was studied. The daily loss during the first 2 wk after the occurrence of mastitis varied from 1.0 to 2.5 kg, and the total loss over the entire lactation varied from 110 to 552 kg and depended on parity and the time of mastitis occurrence. Regardless of the time of occurrence during the lactation, mastitis had a long-lasting effect on milk yield; cows with mastitis did not reach their premastitis milk yields during the remainder of the lactation after onset of the disease.
The effects of 15 diseases on time until culling were studied in 39,727 Finnish Ayrshire cows that calved during 1993 and were followed until the next calving or culling. The diseases studied were: dystocia, milk fever, retained placenta, displacement of the abomasum, metritis, non-parturient paresis, ketosis, rumen disorders, acute mastitis, hypomagnesemia, lameness, traumatic reticuloperitonitis, anestrus, ovarian cysts, and teat injuries. Survival analysis, using the Cox proportional hazards model, was performed and diseases were modeled as time-dependent covariates. Different stages of lactation when culling can occur were also considered. Parity, calving season and herd were included as covariates in every model. Parity had a significant effect on culling, the risk of culling being four times higher for a cow in her sixth or higher parity than for a first parity cow. The effects of diseases varied according to when the diseases occurred and when culling occurred. Mastitis, teat injuries and lameness had a significant effect on culling throughout the whole lactation. Anestrus and ovarian cysts had a protective effect against culling at the time when they were diagnosed. In general, diseases affected culling decisions mostly at the time of their occurrence. The effect seemed to decrease with time from the diagnosis of the disease. However, milk fever, dystocia and metritis also had a significant effect on culling at the end of the lactation.
The effects of 15 diseases, pregnancy status and milk yield on culling were studied in 39727 Finnish Ayrshire cows that calved in 1993 and were followed until culling or next calving. Survival analysis, using the Cox proportional hazards model, was performed with diseases, pregnancy status and milk yield as time-dependent covariates. Effects of parity, calving season and herd were also accounted for. Pregnancy status was the single most influential factor affecting culling decisions, followed by milk yield. Several diseases also had a significant effect on culling, the most influential ones being mastitis, lameness, teat injuries, and milk fever. The effects of all of these factors varied according to the stage of lactation. Milk yield had a significant effect on culling decisions, depending on the stage of lactation. At the beginning of lactation, milk production did not have any effect on culling decisions, but later on, the highest producers were at the lowest risk of being culled and the lowest producers had the highest risk. Adjusting for milk yield modified the effects of parity, most diseases and also pregnancy status on culling. Effects of parity increased after including milk yield in the model, indicating that milk yield and parity are interrelated in their effects on culling. The effects of pregnancy status also increased towards the end of lactation when milk yield was accounted for in the model. The effects of mastitis, teat injuries and lameness decreased after adjusting for milk production. These diseases lower milk yield and thus, part of their effect on culling was mediated through milk production. The effects of anestrus and ovarian cysts were mainly modified by pregnancy status, but not by milk yield. The effects of milk fever on culling increased at the beginning of lactation after including milk yield in the model. This suggests that even though cows with milk fever tend to be higher producers, it is the disease as such that triggers the culling decision early in the lactation. The changes in the effects of other diseases after adjusting for milk yield varied, depending on the disease and the stage of lactation.
The effects of 15 diseases and reproductive performance on culling were studied in 39727 Finnish Ayrshire cows that calved in 1993 and were followed until culling or next calving. Survival analysis, using the Cox proportional hazards model, was performed with diseases and pregnancy status as time-dependent covariates. Parity, calving season and herd were included as covariates in every model. The effect of the number of inseminations was also studied. The farmer's knowledge of the cow's pregnancy status had a significant effect on culling. It varied according to the stage of lactation a cow was in; the earlier the farmer knew a cow was pregnant, the smaller was the risk of culling. If a cow had not been inseminated at all, her risk of culling was 10 times higher than if she was inseminated once. If a cow was inseminated more than once, she had a slightly lower risk of being culled than a cow inseminated only once. The effect of parity decreased when pregnancy status and number of inseminations were added to the model, indicating that part of the parity effect was accounted for by reproductive performance. Including diseases in the model with pregnancy status and the number of inseminations did not change the effects of reproductive performance on culling. Mastitis, teat injuries and lameness had the greatest effect on culling (whether adjusted for reproductive performance or not), increasing the risk of culling, followed by anestrus, ovarian cysts and milk fever. In general, the effects of diseases decreased when reproductive performance was also accounted for in the model. When pregnancy status was included in the model, the effects of anestrus and ovarian cysts became slightly more protective, but when the number of inseminations was also considered, they became non-significant at the beginning of lactation and they increased the risk of culling at the end of lactation. Sensitivity analysis, which was run to evaluate the effects of our censoring mechanism on the results, indicated that the censoring times (i.e., the time of next calving) were not fully independent of the event (culling) times; the effects of the diseases and pregnancy status at the very end of the lactation changed slightly from the original model.
Standard methods for survival analysis, such as the time-dependent Cox model, may produce biased effect estimates when there exist time-dependent confounders that are themselves affected by previous treatment or exposure. Marginal structural models are a new class of causal models the parameters of which are estimated through inverse-probability-of-treatment weighting; these models allow for appropriate adjustment for confounding. We describe the marginal structural Cox proportional hazards model and use it to estimate the causal effect of zidovudine on the survival of human immunodeficiency virus-positive men participating in the Multicenter AIDS Cohort Study. In this study, CD4 lymphocyte count is both a time-dependent confounder of the causal effect of zidovudine on survival and is affected by past zidovudine treatment. The crude mortality rate ratio (95% confidence interval) for zidovudine was 3.6 (3.0-4.3), which reflects the presence of confounding. After controlling for baseline CD4 count and other baseline covariates using standard methods, the mortality rate ratio decreased to 2.3 (1.9-2.8). Using a marginal structural Cox model to control further for time-dependent confounding due to CD4 count and other time-dependent covariates, the mortality rate ratio was 0.7 (95% conservative confidence interval = 0.6-1.0). We compare marginal structural models with previously proposed causal methods.
It has long been known that stratifying on variables affected by the study exposure can create selection bias. More recently it has been shown that stratifying on a variable that precedes exposure and disease can induce confounding, even if there is no confounding in the unstratified (crude) estimate. This paper examines the relative magnitudes of these biases under some simple causal models in which the stratification variable is graphically depicted as a collider (a variable directly affected by two or more other variables in the graph). The results suggest that bias from stratifying on variables affected by exposure and disease may often be comparable in size with bias from classical confounding (bias from failing to stratify on a common cause of exposure and disease), whereas other biases from collider stratification may tend to be much smaller.
In randomized clinical trials, subjects are recruited at multiple study centres. Factors that vary across centres may exert a powerful independent influence on study outcomes. A common problem is how to incorporate these centre effects into the analysis of censored time-to-event data. We survey various methods and find substantial advantages in the gamma frailty model. This approach compares favourably with competing methods and appears minimally affected by violation of the assumption of a gamma-distributed frailty. Recent computational advances make use of the gamma frailty model a practical and appealing tool for addressing centre effects in the analysis of multicentre trials.
Robins introduced marginal structural models (MSMs) and inverse probability of treatment weighted (IPTW) estimators for the causal effect of a time-varying treatment on the mean of repeated measures. We investigate the sensitivity of IPTW estimators to unmeasured confounding. We examine a new framework for sensitivity analyses based on a nonidentifiable model that quantifies unmeasured confounding in terms of a sensitivity parameter and a user-specified function. We present augmented IPTW estimators of MSM parameters and prove their consistency for the causal effect of an MSM, assuming a correct confounding bias function for unmeasured confounding. We apply the methods to assess sensitivity of the analysis of Hernán et al., who used an MSM to estimate the causal effect of zidovudine therapy on repeated CD4 counts among HIV-infected men in the Multicenter AIDS Cohort Study. Under the assumption of no unmeasured confounders, a 95 per cent confidence interval for the treatment effect includes zero. We show that under the assumption of a moderate amount of unmeasured confounding, a 95 per cent confidence interval for the treatment effect no longer includes zero. Thus, the analysis of Hernán et al. is somewhat sensitive to unmeasured confounding. We hope that our research will encourage and facilitate analyses of sensitivity to unmeasured confounding in other applications.
The term "selection bias" encompasses various biases in epidemiology. We describe examples of selection bias in case-control studies (eg, inappropriate selection of controls) and cohort studies (eg, informative censoring). We argue that the causal structure underlying the bias in each example is essentially the same: conditioning on a common effect of 2 variables, one of which is either exposure or a cause of exposure and the other is either the outcome or a cause of the outcome. This structure is shared by other biases (eg, adjustment for variables affected by prior exposure). A structural classification of bias distinguishes between biases resulting from conditioning on common effects ("selection bias") and those resulting from the existence of common causes of exposure and outcome ("confounding"). This classification also leads to a unified approach to adjust for selection bias.
Two analytical approaches were used to investigate the relationship between somatic cell concentrations in monthly quarter milk samples and subsequent, naturally occurring clinical mastitis in three dairy herds. Firstly, cows with clinical mastitis were selected and a conventional matched analysis was used to compare affected and unaffected quarters of the same cow. The second analysis included all cows, and in order to overcome potential bias associated with the correlation structure, a hierarchical Bayesian generalised linear mixed model was specified. A Markov chain Monte Carlo (MCMC) approach, that is Gibbs sampling, was used to estimate parameters. The results of both the matched analysis and the hierarchical modelling suggested that quarters with a somatic cell count (SCC) in the range 41,000-100,000 cells/ml had a lower risk of clinical mastitis during the next month than quarters <41,000 cell/ml. Quarters with an SCC >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 1 and 2 months later in quarters with an SCC of 81,000-150,000 cells/ml compared with quarters below this level. The hierarchical modelling analysis identified a further reduced risk of clinical mastitis between 2 and 3 months later in quarters with an SCC 61,000-150,000 cells/ml, compared to other quarters. We conclude that low concentrations of somatic cells in milk are associated with increased risk of clinical mastitis, and that high concentrations are indicative of pre-existing immunological mobilisation against infection. The variation in risk 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. MCMC proved a useful tool for estimating parameters in a hierarchical Bernoulli model. Model construction and an approach to assessing goodness of model fit are described.
A sample of dairy farms in Great Britain with a monthly bulk milk somatic cell count of less than 150,000 cells/ml was enrolled into a 12-month prospective study. At the end of the study, a questionnaire on milking practice and other farm management practices was sent to the 482 farmers who had collected data on the occurrence of mastitis throughout the 12 months. The response rate was 93 per cent. The reported mean incidence of clinical mastitis was 36.9 cases per 100 cow-years. Factors associated with an increase in the incidence of clinical mastitis were cleaning out the straw yard less frequently than every six weeks, more than 5 per cent of cows leaking milk outside the parlour, checking the foremilk, wearing gloves during milking, an average annual milk yield of more than 7000 litres per cow, dipping or spraying teats before milking and keeping milk with a high somatic cell count out of the bulk tank. Factors associated with a decrease in the incidence of clinical mastitis were using a cloth to dry the teats after washing them as part of premilking preparation, using calving boxes for less than 40 per cent of calvings, and using both cubicles and straw yards to house dry cows, as opposed to other housing.
Culling patterns in the Upper Midwest and Northeast regions were examined from Dairy Herd Improvement records from 1993 through 1999. There were 7,087,699 individual cow lactation observations of which 1,458,936 were complete. A probit regression model was used to determine how individual cow and herd characteristics affected the likelihood of a cow being culled. The model predicted whether individual cows were culled each month. With a combination of observable cow and herd characteristics, as well as variables to capture state, year, and farm effects, the model was able to explain, with a 79.5 and 79.9% accuracy rate, individual cow cull decisions in the Upper Midwest and Northeast regions, respectively. Summer (- 11.5% in the Upper Midwest; - 6.4% in the Northeast) and fall (- 18.7% in the Upper Midwest; - 7.9% in the Northeast) calving vs. spring calving, higher than average milk production (- 1.7% per hundredweight in the Upper Midwest; - 0.5% in the Northeast), higher than average protein content (- 0.2% per additional percentage milk protein in the Upper Midwest; - 0.1% in the Northeast), higher milk production persistency (- 2.1% per additional percent persistent in the Upper Midwest; - 1.8% in the Northeast), and expansion (during the early years following the expansion) were associated with a reduced likelihood of a cow being culled. Lower than average fat content (0.04% per additional percentage butterfat in the Upper Midwest; 0.02% in the Northeast), and higher than average somatic cell count (8.8% for each unit increase in somatic cell count score in the Upper Midwest; 7.8% in the Northeast) were associated with an increased likelihood of a cow being culled. The study results are useful in describing patterns of culling and relating them to cow, herd, geographic, and time variables and can act as a benchmark for producers.
In ideal randomised experiments, association is causation: association measures can be interpreted as effect measures because randomisation ensures that the exposed and the unexposed are exchangeable. On the other hand, in observational studies, association is not generally causation: association measures cannot be interpreted as effect measures because the exposed and the unexposed are not generally exchangeable. However, observational research is often the only alternative for causal inference. This article reviews a condition that permits the estimation of causal effects from observational data, and two methods -- standardisation and inverse probability weighting -- to estimate population causal effects under that condition. For simplicity, the main description is restricted to dichotomous variables and assumes that no random error attributable to sampling variability exists. The appendix provides a generalisation of inverse probability weighting.
The aim of this study was to assess the level of somatic cell count (SCC) and to explore the impact of somatic cell score (SCS) on the functional longevity of Canadian dairy cattle by using a Weibull proportional hazards model. Data consisted of 1,911,428 cows from 15,970 herds sired by 7,826 sires for Holsteins, 80,977 cows in 2,036 herds from 1,153 sires for Ayrshires, and 53,114 cows in 1,372 herds from 1,758 sires for Jerseys. Functional longevity was defined as the number of days from the first calving to culling, death, or censoring. The test-day SCC was transformed to a linear score, and the resulting SCS were averaged within each lactation. The average SCS were grouped into 10 classes. The statistical model included the effects of stage of lactation; season of production; annual change in herd size; type of milk recording supervision; age at first calving; effects of milk, fat, and protein yields, calculated as within-herd-year-parity deviations; herd-year-season of calving; SCS class; and sire. The relative culling rate was calculated for animals in each SCS class after accounting for the aforementioned effects. The overall average SCC for Holsteins was 167,000 cells/mL, for Ayrshires was 155,000 cells/mL, and for the Jerseys was 212,000 cells/mL. In all breeds there were no appreciable differences in the relative risk of culling among classes of SCS breed averages (i.e., up to a SCS of 5). However, as the SCS increased beyond the breed average, the relative risk of cows being culled increased considerably. For instance, Holstein, Ayrshire, and Jersey cows with the highest classes of SCS had, respectively, a 4.95, 6.73, and 6.62 times greater risk of being culled than cows with average SCS.
The interaction of the effects of pregnancy status and veterinary-treated clinical mastitis on culling in Swedish dairy cattle was analyzed with survival analysis. The data were from 978,780 cows with first calvings between 1988 and 1996. Four breeds (Swedish Red and White (SRB), Swedish Friesian (SLB), Swedish Polled Breed and Jersey) were included in the analysis, together with the SRB x SLB crossbreds. Length of productive life was defined as the number of days between first calving and culling or censoring (end of data collection). The model (Weibull proportional hazard) included the interaction of parity by pregnancy status by veterinary-treated clinical mastitis, peak test-day milk-yield deviation within herd-year-parity, age at first calving, year by season, region, breed, herd production level, and the random effect of herd. The effects of pregnancy status and veterinary-treated clinical mastitis were modeled as time-dependent covariates. The lactation was divided into five stages during which a veterinary-treated clinical mastitis and culling might occur and in which the pregnancy status was assumed to be known and culling could occur. Open cows had a pronounced effect on culling: they had a very high risk of being culled in all lactations, and it was even higher if they were treated for mastitis in early lactation. For pregnant cows, the later they got pregnant during the lactation, the greater their risk to be culled. The risk associated with cases of veterinary-treated clinical mastitis remained important throughout the lactation.
Many cow-specific risk factors for clinical mastitis (CM) are known. Other studies have analyzed these risk factors separately or only analyzed a limited number of risk factors simultaneously. The goal of this study was to determine the influence of cow factors on the incidence rate of CM (IRCM) with all cow factors in one multivariate model. Also, using a similar approach, the probability of whether a CM case is caused by gram-positive or gram-negative pathogens was calculated. Data were used from 274 Dutch dairy herds that recorded CM over an 18-mo period. The final dataset contained information on 28,137 lactations of 22,860 cows of different parities. In total 5,363 CM cases were recorded, but only 2,525 CM cases could be classified as gram-positive or gram-negative. The cow factors parity, lactation stage, season of the year, information on SCC from monthly test-day records, and CM history were included in the logistic regression analysis. Separate analyses were performed for heifers and multiparous cows in both the first month of lactation and from the second month of lactation onward. For investigating whether CM was caused by gram-positive or gram-negative pathogens, quarter position was included in the logistic regression analysis as well. The IRCM differed considerably among cows, ranging between 0.0002 and 0.0074 per cow-day at risk for specific cows depending on cow factors. In particular, previous CM cases, SCC in the previous month, and mean SCC in the previous lactation increased the IRCM in the current month of lactation. Results indicate that it is difficult to distinguish between gram-positive and gram-negative CM cases based on cow factors alone.