Genet. Sel. Evol. 35 (2003) 457-468
DOI: 10.1051/gse:2003034

Longitudinal random effects models for genetic analysis of binary data with application to mastitis in dairy cattle

Romdhane Rekaya^a, Daniel Gianola^{b, b} and George Shook<sup>b

a</sup>  Department of Animal and Dairy Science, University of Georgia, Athens, GA 30602, USA
^b  Department of Dairy Science, University of Wisconsin, Madison, WI 53706, USA

(Received 13 June 2002; accepted 13 March 2003)

Abstract
A Bayesian analysis of longitudinal mastitis records obtained in the course of lactation was undertaken. Data were 3341 test-day binary records from 329 first lactation Holstein cows scored for mastitis at 14 and 30 days of lactation and every 30 days thereafter. First, the conditional probability of a sequence for a given cow was the product of the probabilities at each test-day. The probability of infection at time  t for a cow was a normal integral, with its argument being a function of "fixed" and "random" effects and of time. Models for the latent normal variable included effects of: (1) year-month of test + a five-parameter linear regression function ("fixed", within age-season of calving) + genetic value of the cow + environmental effect peculiar to all records of the same cow + residual. (2) As in (1), but with five parameter random genetic regressions for each cow. (3) A hierarchical structure, where each of three parameters of the regression function for each cow followed a mixed effects linear model. Model 1 posterior mean of heritability was 0.05. Model 2 heritabilities were: 0.27, 0.05, 0.03 and 0.07 at days 14, 60, 120 and 305, respectively. Model 3 heritabilities were 0.57, 0.16, 0.06 and 0.18 at days 14, 60, 120 and 305, respectively. Bayes factors were: 0.011 (Model 1/Model 2), 0.017 (Model 1/Model 3) and 1.535 (Model 2/Model 3). The probability of mastitis for an "average" cow, using Model 2, was: 0.06, 0.05, 0.06 and 0.07 at days 14, 60, 120 and 305, respectively. Relaxing the conditional independence assumption via an autoregressive process (Model 2) improved the results slightly.

Key words: mastitis / longitudinal / threshold model

Correspondence and reprints: Romdhane Rekaya
    e-mail: rrekaya@arches.uga.edu

© INRA, EDP Sciences 2003