Length of Productive Life of Dairy Cows. 1. Justification of a Weibull Model

Abstract The length of productive life of 39,683 grade Holstein cows milked in 150 large herds in New York state between 1981 and 1986 was analyzed by modeling their hazard, which is a measure of their probability of being culled. Animals still alive when the analysis was performed were assigned a record equal to the current value of their length of productive life. The concept of hazard allows an adequate statistical treatment of these censored records. The proportional hazards models considered involve a baseline hazard function and log-linear time-dependent explanatory variables affecting culling rate. These include a herd×year effect, a stage of lactation×lactation number effect, and a within herd and level of milk production effect (normalized rank based on 305 mature equivalent milk yield). A semiparametric analysis, for which the baseline hazard function is completely unspecified (Cox's regression), showed that the assumption of proportional hazards is appropriate, that all the effects in the model are highly significant, and that the baseline hazard function can be closely approximated by a Weibull hazard function of the form λ(t) = λp(λt) p−1 . Such an approximation greatly simplifies computations and facilitates further genetic and nongenetic studies on longevity of dairy cows.