Statistical Analysis of Length of Productive Life for Dairy Cows of the Normande Breed

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Abstract
The length of productive life of 103,214 Normande cows milked from 1979 to 1989 in purebred herds was analyzed using a mixed Weibull model: their probability of being culled, or hazard function, was supposed to be the product of a baseline Weibull hazard function and explanatory variables that were log-linear and time-dependent. Fixed effects that may have an impact on culling rate were successively added to the model. Two random effects, a herd-year and a sire effect, were also included. The dispersion parameter of the log-gamma prior distributions assumed for these effects was estimated maximizing a marginal posterior density obtained after algebraic integration of the corresponding random effect. The other effects and the Weibull parameter could not be integrated out easily. The probability of being culled was not changed by age at first calving but increased with stage of lactation. It also increased for low producing cows and for herds of decreasing size, especially during the 3 mo preceding the end of the period on which yearly milk production is calculated for the European Community quota system. This last phenomenon seems to be crucial for proper statistical and genetic analysis of length of productive life. The estimated variances of the herd-year and sire effects indicated a large influence of these effects on culling rate. Under certain assumptions, the standard deviation of sire effects can be assessed at > .5 expected complete lactations. This value is not reduced by consideration of differences in milk production of the cows.