Prediction of longevity breeding values for US Holstein sires using survival analysis methodology

Breeding values of Holstein sires for daughter longevity in each of 9 geographical regions of the United States were predicted using a Weibull proportional hazards model. Longevity (also commonly referred to as herd life or length of productive life) was defined as the number of days from first calving until culling or censoring. Records from 2,322,389 Holstein cows with first calving from 1990 to 2000 were used. In addition to the sire's additive genetic merit, our failure time model included time-dependent effects of herd-year-season of calving, parity-stage of lactation, and within-herd-year quintiles for mature equivalent fat plus protein yield, as well as the time-independent effect of age at first calving. Sire variances and parameters of the Weibull distribution were estimated separately for each region. The relative risk of culling for daughters of each individual sire was expressed relative to that of daughters of an average sire (within a specific region). Predicted breeding values for functional longevity, expressed as relative risk ratios, ranged from 0.7 to 1.3. Sizable differences were observed between geographical regions in sire rankings, as well as estimated sire variances and gamma parameters (of the distribution of herd-year-season effects), suggesting that a single national ranking may not be appropriate for every region. Two random samples of herds were selected from the full national data set; these contained 375,086 records and 256,751 records, respectively. Predicted transmitting abilities (PTA) of sires for daughter longevity were calculated using the Weibull proportional hazards (sire) model described previously but without the correction for milk production. These were compared with predictions from a linear (animal) model, as currently used for routine genetic evaluation of length of productive life in the United States. Logistic regression of daughters' stayability to 36, 48, 60, 72, or 84 mo of life (among animals that had opportunity to stay that long) on sires' PTA indicated that the proportional hazards model yielded more accurate predictions of daughter longevity than the linear animal model, even though the latter relied on denser pedigree information.