Analysis of Failure Times Measured on Dairy Cows: Theoretical Considerations in Animal Breeding

Abstract

Failure time analysis is described and proposed for use in survival studies of dairy cows. The Cox regression model is emphasized. Inclusion of random effects in Cox models or other nonlinear models is recommended if such models are to be used in genetic evaluations. Maximum a posteriori estimation is proposed for prediction of random effects. This procedure requires knowledge of variances of random effects. “Quadratic type” estimates for variance components in nonlinear models are described. Genetic evaluations usually entail solving a large system of equations. For cases in this paper, equations are nonlinear. To solve large systems of equations corresponding to certain Cox regression models, a procedure analogous to Gauss-Seidel iteration is proposed.