Poisson versus threshold models for genetic analysis of clinical mastitis in US Holsteins

Abstract

Typically, clinical mastitis is coded as the presence or absence of disease in a given lactation, and records are analyzed with either linear models or binary threshold models. Because the presence of mastitis may include cows with multiple episodes, there is a loss of information when counts are treated as binary responses. Poisson models are appropriated for random variables measured as the number of events, and although these models are used extensively in studying the epidemiology of mastitis, they have rarely been used for studying the genetic aspects of mastitis. Ordinal threshold models are pertinent for ordered categorical responses; although one can hypothesize that the number of clinical mastitis episodes per animal reflects a continuous underlying increase in mastitis susceptibility, these models have rarely been used in genetic analysis of mastitis. The objective of this study was to compare probit, Poisson, and ordinal threshold models for the genetic evaluation of US Holstein sires for clinical mastitis. Mastitis was measured as a binary trait or as the number of mastitis cases. Data from 44,908 first-parity cows recorded in on-farm herd management software were gathered, edited, and processed for the present study. The cows were daughters of 1,861 sires, distributed over 94 herds. Predictive ability was assessed via a 5-fold cross-validation using 2 loss functions: mean squared error of prediction (MSEP) as the end point and a cost difference function. The heritability estimates were 0.061 for mastitis measured as a binary trait in the probit model and 0.085 and 0.132 for the number of mastitis cases in the ordinal threshold and Poisson models, respectively; because of scale differences, only the probit and ordinal threshold models are directly comparable. Among healthy animals, MSEP was smallest for the probit model, and the cost function was smallest for the ordinal threshold model. Among diseased animals, MSEP and the cost function were smallest for the Poisson model, followed by the ordinal threshold model. In general, the models for count variables more accurately identified diseased animals and more accurately predicted mastitis costs. Healthy animals were more accurately identified by the probit model.

Predictive ability of alternative models for genetic analysis of clinical mastitis

“…Models for binary traits, such as probit, logit or linear models, tend to predict healthy cows relatively well. Information from different populations shows that these three models give very similar results; results shown in Tables 4 and 5 as well as in previous studies (Vazquez et al. 2009b and Koeck et al.…”

“…The ordinal censored threshold model had a better predictive ability for diseased cows. Arguably, in a previous study, the Poisson model had a smaller MSEP than the ordinal threshold model, and it was expected that ZIP could have a better performance in both prediction of zeros and prediction of counts of mastitis cases (Vazquez et al. 2009b).…”

“…2006). More details on the likelihood, prior and posterior distributions of the unknowns, can be found in Vazquez et al. (2009a,b) for the linear and threshold liability models, in Chang et al.…”

“…2006), Poisson models (Pérez‐Cabal et al. 2009; Vazquez et al. 2009a,b) or with zero‐inflated Poisson (ZIP) models (Rodrigues‐Motta et al.…”

Weak effects of common genetic variation in oxytocin and vasopressin receptor genes on rhesus macaque social behavior

“…Following (Davies, Scarpino, Pongwarin, Scott, & Matz, 2015; Nakagawa & Schielzeth, 2010; Vazquez et al, 2009), we estimated the narrow-sense heritability of each behavior j using the equation ${\gamma }_j^2/\left({\gamma }_j^2+{\sigma }_j^2+{\pi }^2/3\right)$ where ${\sigma }_j^2$ is the sum of the variance components associated with permanent environmental and maternal effects. Note that heritability as estimated here refers to heritability of the latent continuous variables underlying logistic regression, rather than of the discrete behavioral data itself.…”