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

A. I. Vazquez^*,1, K. A. Weigel^*, D. Gianola^*,,, D. M. Bates, M. A. Perez-Cabal^#, G. J. M. Rosa^* and Y. M. Chang

^* Department of Dairy Science,
Department of Animal Sciences,
Department of Biostatistics and Medical Informatics, and
Department of Statistics, University of Wisconsin, Madison 53706
^# Departamento de Producción Animal, Universidad Politécnica de Madrid, 28040, Madrid, Spain
Section of Epidemiology and Biostatistics, Leeds Institute of Molecular Medicine, Leeds, United Kingdom

¹ Corresponding author: aivazquez{at}wisc.edu

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.

Key Words: mastitis • Poisson model • ordinal threshold model • probit model