Evaluation of a contract breeding management program in selected Ohio dairy herds with event-time analysis II. Parametric frailty models.

The effect of a contract breeding program offered by a breeding co-operative was assessed using parametric frailty models with event-time analysis technique in a field study of Ohio dairies. The program featured tail chalking and daily evaluation of cows for insemination by co-operative technicians; dairy employees no longer handled estrus detection activities. Test day records were obtained between early 2002 and mid-2004 for 16,453 lactations representing 11,398 cows in 31 herds identified as well-managed client herds by the breeding co-operative. Various parametric distributions for event times available in a commercial software (Stata 9.1, College Station, TX) were tested to assess which distribution fit the calving-to-conception data best. After identifying the distribution with the best fit, a full model with potential confounders and other significant predictors of time to pregnancy was developed and then frailty terms were included in the model. Generalized gamma and log-normal distributions fit the data best, but since gamma distribution does not allow the use of frailty effects, log-normal distribution was used in further modeling. Separate accelerated failure time models with frailty terms to account for latent effects at the herd, cow, or lactation level were developed, testing both gamma and inverse Gaussian frailty distributions. In these models, potential confounders and statistically significant predictors were also controlled for, and the association between the contract breeding program and the mean time to pregnancy was characterized using time ratios. The log-normal model identified that interval to pregnancy was associated with breed, herd size, use of ovulation synchronization protocols, parity, calving season and somatic cell score (above or below 4.5) and maximum milk yield prior to pregnancy or censoring. While controlling for these factors, there was a reduction in average time to pregnancy among cows managed under the contract breeding program. All frailty terms were highly significant, regardless of whether it was an individual frailty at the lactation level or a shared frailty at the cow or herd level, suggesting that there was considerable heterogeneity within these levels. Inclusion of a frailty term at the herd level changed the estimate for the contract breeding program considerably, while a frailty term on other levels did not, indicating that herd characteristics (e.g., overall management) have a substantial impact on reproductive performance and should be accounted for in the analysis. Interpretation using time ratios with or without a shared herd frailty found that the contract breeding program was associated with a reduction of 6.5% and 14.1% in mean time to pregnancy, respectively.