Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham's-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable differences between the two approaches are found. In particular, we prove a theorem that characterizes a surprising aymptotic discrepancy between fully Bayes and empirical Bayes. This discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical-Bayes estimate. Indeed, even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true variable-inclusion probability, the potential for a serious difference remains.Comment: Published in at http://dx.doi.org/10.1214/10-AOS792 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stability selection for mixed effect models with large numbers of predictor variables: A simulation study

Covariate selection when the number of available variables is large relative to the number of observations is problematic in epidemiology and remains the focus of continued research. Whilst a variety of statistical methods have been developed to attempt to overcome this issue, at present very few methods are available for wide data that include a clustered outcome. The purpose of this research was to make an empirical evaluation of a new method for covariate selection in wide data settings when the dependent variable is clustered. We used 3300 simulated datasets with a variety of defined structures and known sets of true predictor variables to conduct an empirical evaluation of a mixed model stability selection procedure. Comparison was made with an alternative method based on regularisation using the least absolute shrinkage and selection operator (Lasso) penalty. Model performance was assessed using several metrics including the true positive rate (proportion of true covariates selected in a final model) and false discovery rate (proportion of variables selected in a final model that were non-true (false) variables). For stability selection, the false discovery rate was consistently low, generally remaining ≤ 0.02 indicating that on average fewer than 1 in 50 of the variables selected in a final model were false variables. This was in contrast to the Lasso-based method in which the false discovery rate was between 0.59 and 0.72, indicating that generally more than 60% of variables selected in a final model were false variables. In contrast however, the Lasso method attained higher true positive rates than stability selection, although both methods achieved good results. For the Lasso method, true positive rates remained ≥ 0.93 whereas for stability selection the true positive rate was 0.73–0.97. Our results suggest both methods may be of value for covariate selection with high dimensional data with a clustered outcome. When high specificity is needed for identification of true covariates, stability selection appeared to offer the better solution, although with a slight loss of sensitivity. Conversely when high sensitivity is needed, the Lasso approach may be useful, even if accompanied by a substantial loss of specificity. Overall, the results indicated the loss of sensitivity when employing stability selection is relatively small compared to the loss of specificity when using the Lasso and therefore stability selection may provide the better option for the analyst when evaluating data of this type

Cow- and herd-level risk factors for lameness in partly housed pasture-based dairy cows

Lameness in dairy cows is a major animal welfare concern and has substantial economic impact through reduced production and fertility. Previous risk factor analyses have focused on housed systems, rather than those where cows were grazed for the majority of the year and housed only for the winter period. Therefore, the aim of this observational study was to identify a robust set of cow-level and herd-level risk factors for lameness in a pasture-based system, based on predictors from the housing and grazing periods. Ninety-nine farms were visited during the grazing period (April 2019–September 2019), and 85 farms were revisited during the housing period (October 2019–February 2020). At each visit, all lactating cows were scored for lameness (0 = good mobility, 1 = imperfect mobility, 2 = impaired mobility, 3 = severely impaired mobility), and potential herd-level risk factors were recorded through questionnaires and infrastructure measurements. Routine cow-level management data were also collected. Important risk factors for lameness were derived though triangulation of results from elastic net regression, and from logistic regression model selection using modified Bayesian information criterion. Both selection methods were implemented using bootstrapping. This novel approach has not previously been used in a cow-level or herd-level risk factor analysis in dairy cows, to the authors' knowledge. The binary outcome variable was lameness status, whereby cows with a lameness score of 0 or 1 were classed as non-lame and cows with a score of 2 or 3 were classed as lame. Cow-level risk factors for increased lameness prevalence were age and genetic predicted transmitting ability for lameness. Herd-level risk factors included farm and herd size, stones in paddock gateways, slats on cow tracks near the collecting yard, a sharper turn at the parlor exit, presence of digital dermatitis on the farm, and the farmers' perception of whether lameness was a problem on the farm. This large-scale study identified the most important associations between risk factors and lameness, based on the entire year (grazing and housing periods), providing a focus for future randomized clinical trials

Lameness and pain management on Irish dairy farms

Lameness is a major concern for animal welfare due to the associated pain, and has significant negative economic and environmental consequences. Irish dairying differs from most other systems, whereby cows are out to grass for the majority of the year and housed over the winter months; therefore, research from other system types can be hard to apply to Irish dairy farms. Reducing lameness on Irish dairy farms is vitally important, as the welfare-friendly credentials of Irish dairy products are key to positioning Ireland as a leading supplier of dairy products internationally. In order to reduce lameness, further work is required on the prevalence, causes and risk factors for lameness in Irish dairy cows. The Irish dairy industry would also benefit from knowing what lameness management practices are currently in place on Irish dairy farms. The aim of this thesis was to gain knowledge on lameness and pain management in an Irish pasture-based dairy system. The first study (Papers 1-3) involved lameness scoring cows from 99 pasture-based dairy herds in Ireland during the grazing period, and from 85 of these herds during the housing period. At each visit, infrastructure measurements were taken (housing facilities, milking facilities and cow tracks) and a questionnaire was undertaken with the farmer to identify background information and farm management practices. Cow-level data was also collected (e.g. breed, parity and milk yield). For 98 of the farms visited during the grazing period and for 74 of the farms visited during the housing period, the hind hooves of up to a maximum of 20 lame cows were examined and hoof lesions were recorded. The second study (Paper 4) involved sending a questionnaire on attitudes to pain and the use of non-steroidal anti-inflammatory drugs (NSAIDs) on Irish dairy farms, to both dairy farmers and veterinarians that work with dairy cows in Ireland. Over 1000 questionnaires were returned by dairy farmers and 116 by veterinarians. Paper 1 determined the most important cow-level and herd-level risk factors for lameness in Irish pasture-based dairy herds, based on both the grazing and housing period. Triangulation of elastic net regression and logistic regression using modified Bayesian information criterion, with bootstrapping, were used to obtain a robust set of risk factors. Cow-level risk factors included age and genetic predicted transmitting ability for lameness, and herd-level risk factors included herd and farm size, the distance cows had to turn at the milking parlour exit, stones in paddock gateways, and slats on the cow track near the collecting yard; farmer’s perception of lameness and digital dermatitis in their herd was also associated with lameness outcomes. Paper 2 reported the lameness prevalence during both the grazing and housing periods, and identified lameness management practices that are currently in place on Irish dairy farms. This paper also described current infrastructure and general farm management that may relate to lameness. The median herd lameness prevalence was 7.9% during grazing and 9.1% during housing. This study identified many potential areas of lameness management that could be improved upon on Irish farms; for example, only one farmer carried out lameness scoring, 6% routine trimming and 31% regular footbathing. The majority of farms also had rough (uneven, larger stones, bumps and holes are common, signs of wear or erosion) cow tracks present, and had less than 1.1 cubicles per cow in all pens. Paper 3 identified the prevalence of hoof lesions in lame dairy cows, correlations between lesions, the lesions that were associated with more severe lameness, and risk factors for digital dermatitis. The most prevalent lesions were white line separation, sole haemorrhage and overgrown claws. Digit amputation, foul of the foot, sole ulcer, white line abscess and toe necrosis were associated with more severe lameness. Overgrown claws and penetration of a foreign body were more common during grazing than housing. The strongest correlation at herd-level was between toe necrosis and digital dermatitis, and between overgrown claws and corkscrew claws at cow-level. Cow track characteristics, as well as the farmer’s perception of lameness and digital dermatitis in the herd were associated with digital dermatitis risk. Paper 4 reported attitudes to pain and pain relief by dairy farmers and veterinarians in Ireland, and the use of NSAIDs for various dairy cow and calf conditions and procedures, including those related to lameness. This study showed that veterinarians and farmers are potentially becoming habituated to pain; they scored the conditions and procedures they saw most regularly as less painful than those less commonly seen. Higher pain scores were also associated with higher NSAID use; however, for some conditions and procedures NSAID use was low despite the pain score given. The cost of NSAIDs was also considered less of an issue to farmers than veterinarians thought. This thesis provides valuable insights into dairy cow health and welfare, with a particular focus on lameness. Compared to other countries, a relatively low lameness prevalence was reported during both the grazing and housing period; however, approximately one in ten lame cows is still arguably too high. Farmers should strive for the lowest lameness prevalence possible for welfare and economic reasons. This thesis also showed that there are many areas of lameness management that could be improved upon. Knowledge gained from this thesis will provide guidance for future research and allow information to be disseminated to farmers and veterinarians, thus further decreasing lameness and improving pain management on Irish dairy farms

Lameness and pain management on Irish dairy farms

Lameness is a major concern for animal welfare due to the associated pain, and has significant negative economic and environmental consequences. Irish dairying differs from most other systems, whereby cows are out to grass for the majority of the year and housed over the winter months; therefore, research from other system types can be hard to apply to Irish dairy farms. Reducing lameness on Irish dairy farms is vitally important, as the welfare-friendly credentials of Irish dairy products are key to positioning Ireland as a leading supplier of dairy products internationally. In order to reduce lameness, further work is required on the prevalence, causes and risk factors for lameness in Irish dairy cows. The Irish dairy industry would also benefit from knowing what lameness management practices are currently in place on Irish dairy farms. The aim of this thesis was to gain knowledge on lameness and pain management in an Irish pasture-based dairy system. The first study (Papers 1-3) involved lameness scoring cows from 99 pasture-based dairy herds in Ireland during the grazing period, and from 85 of these herds during the housing period. At each visit, infrastructure measurements were taken (housing facilities, milking facilities and cow tracks) and a questionnaire was undertaken with the farmer to identify background information and farm management practices. Cow-level data was also collected (e.g. breed, parity and milk yield). For 98 of the farms visited during the grazing period and for 74 of the farms visited during the housing period, the hind hooves of up to a maximum of 20 lame cows were examined and hoof lesions were recorded. The second study (Paper 4) involved sending a questionnaire on attitudes to pain and the use of non-steroidal anti-inflammatory drugs (NSAIDs) on Irish dairy farms, to both dairy farmers and veterinarians that work with dairy cows in Ireland. Over 1000 questionnaires were returned by dairy farmers and 116 by veterinarians. Paper 1 determined the most important cow-level and herd-level risk factors for lameness in Irish pasture-based dairy herds, based on both the grazing and housing period. Triangulation of elastic net regression and logistic regression using modified Bayesian information criterion, with bootstrapping, were used to obtain a robust set of risk factors. Cow-level risk factors included age and genetic predicted transmitting ability for lameness, and herd-level risk factors included herd and farm size, the distance cows had to turn at the milking parlour exit, stones in paddock gateways, and slats on the cow track near the collecting yard; farmer’s perception of lameness and digital dermatitis in their herd was also associated with lameness outcomes. Paper 2 reported the lameness prevalence during both the grazing and housing periods, and identified lameness management practices that are currently in place on Irish dairy farms. This paper also described current infrastructure and general farm management that may relate to lameness. The median herd lameness prevalence was 7.9% during grazing and 9.1% during housing. This study identified many potential areas of lameness management that could be improved upon on Irish farms; for example, only one farmer carried out lameness scoring, 6% routine trimming and 31% regular footbathing. The majority of farms also had rough (uneven, larger stones, bumps and holes are common, signs of wear or erosion) cow tracks present, and had less than 1.1 cubicles per cow in all pens. Paper 3 identified the prevalence of hoof lesions in lame dairy cows, correlations between lesions, the lesions that were associated with more severe lameness, and risk factors for digital dermatitis. The most prevalent lesions were white line separation, sole haemorrhage and overgrown claws. Digit amputation, foul of the foot, sole ulcer, white line abscess and toe necrosis were associated with more severe lameness. Overgrown claws and penetration of a foreign body were more common during grazing than housing. The strongest correlation at herd-level was between toe necrosis and digital dermatitis, and between overgrown claws and corkscrew claws at cow-level. Cow track characteristics, as well as the farmer’s perception of lameness and digital dermatitis in the herd were associated with digital dermatitis risk. Paper 4 reported attitudes to pain and pain relief by dairy farmers and veterinarians in Ireland, and the use of NSAIDs for various dairy cow and calf conditions and procedures, including those related to lameness. This study showed that veterinarians and farmers are potentially becoming habituated to pain; they scored the conditions and procedures they saw most regularly as less painful than those less commonly seen. Higher pain scores were also associated with higher NSAID use; however, for some conditions and procedures NSAID use was low despite the pain score given. The cost of NSAIDs was also considered less of an issue to farmers than veterinarians thought. This thesis provides valuable insights into dairy cow health and welfare, with a particular focus on lameness. Compared to other countries, a relatively low lameness prevalence was reported during both the grazing and housing period; however, approximately one in ten lame cows is still arguably too high. Farmers should strive for the lowest lameness prevalence possible for welfare and economic reasons. This thesis also showed that there are many areas of lameness management that could be improved upon. Knowledge gained from this thesis will provide guidance for future research and allow information to be disseminated to farmers and veterinarians, thus further decreasing lameness and improving pain management on Irish dairy farms