Number of inseminations to conception in Holstein cows using censored records and time-dependent covariates

Three methodologies that accommodate censoring or time-dependent covariates were used to estimate variance components for number of inseminations to conception. Data included 80,071 lactation records and 143,927 artificial inseminations in 47,509 Spanish Holstein cows. Up to 4 inseminations to conception, along with their respective censoring information, were analyzed. An ordinal-censored threshold model (CTM), a sequential threshold model (STM), and a grouped survival analysis via a discrete proportional hazards model (DPH) were implemented. Sire variance estimates on the liability scale were 0.016 and 0.010 for CTM and STM, respectively, and 0.012 for DPH on the logarithmic scale. Heritability estimates on the liability scale were 0.050 and 0.038 with CTM and STM, respectively. All models led to similar rankings of sires, and the strong correlations (0.97 to 0.98) between methodologies suggested robustness in ranking of sires of cows. Service sire variance estimates were 0.021 for both CTM and STM; DPH led to an approximate service sire variance of 0.020. Rankings for service sires between methodologies ranged from 0.76 to 0.90. These lower values are most likely due to differences in the treatment of time-dependent covariates. The STM had greater predictive ability of daughter fertility at first insemination than the other methodologies. However, the CTM predicted daughter fertility more accurately in subsequent inseminations. The DPH and STM had a similar predictive ability of daughter fertility in second and subsequent inseminations.