An application of survival analysis to the genetic evaluation of reproductive life of beef females

Abstract

The primary objective of this study was to develop methodology for animal model survival analysis of reproductive life (RL) in beef females. Other objectives were: 1) to determine whether survival analysis of RL results in improved accuracy of prediction over threshold analysis of stayability (ST), 2) to investigate the effects of right censoring on parameter estimation and genetic prediction of RL, and 3) to determine whether animal model survival analysis is possible for large-scale genetic evaluation of RL using field data from a beef cattle breed association. To meet the primary objective, I first developed a computer simulation program that generated RL data for validating and testing the methodology. Reproductive life was defined as the length of time from entering the herd as a replacement female to being Culled for reproductive failure. The data were simulated from a Weibull model in a factorial arrangement consisting of two levels of true heritability (h2) for underlying RL (0.05 and 0.20) and three levels of the Weibull shape parameter (ρ) (0.6, 0.8, and 1.0) with five replicates per cell. Levels of ρ were based on results of three studies reported in the literature. To estimate h2 for the 30 simulated data sets, I adapted the maximum a posteriori Method R (MAP R) procedure for threshold analysis of categorical traits by substituting a Newton-Raphson algorithm appropriate to a Weibull frailty model. Log-frailties were assumed to be multivariate normal with mean 0 and variance σ2aA, where σ2a was the additive direct genetic variance of RL on the underlying natural logarithmic scale and A was Wright's numerator relationship matrix for all animals. In addition, all data were assumed to be uncensored. Twenty h2 estimates were obtained from each data set, and the results were pooled within each cell. Pooled median h2 estimates for underlying RL were consistently lower than their true values, which may have resulted from natural selection in the simulated data. Despite the low h2 estimates, correlations between estimated breeding values (EBV) computed using estimated and true h2 were very high (greater than 0.98), suggesting that the magnitude of h2 used to evaluate RL does not affect ranking of individual animals. Analyses of ST were conducted using 10 of the data sets simulated previously with true h2 of 0.05 and 0.20 and ρ = 0.8. Twenty heritability estimates were obtained from each data set using the threshold model MAP R procedure, and the h2 estimates were pooled within cell. The pooled median h2 estimates for ST on the underlying liability scale were larger than those for underlying RL (0.0525 vs 0.0378 from data with true h2 of 0.05, and 0.1608 vs 0.1431 from data with true h2 of 0.20). Correlations between animal EBV for underlying ST and RL were strongly negative (-0.7796 and -0.7938 for true h2 of 0.05 and 0.20, respectively), and genetic trends for the two traits were nearly mirror images of one another, suggesting that underlying ST and RL have a high and favorable genetic correlation. However, average accuracies of prediction for RL were approximately 0.10 and 0.15 greater than those for ST among non-foundation animals simulated with true h2 of 0.05 and 0.20, respectively. To determine the effects of censoring on heritability estimation and genetic prediction of RL. I modified the simulation program by randomly censoring females based on an input level of censoring (10, 40, and 70%) and then by randomly truncating their phenotypic RL to obtain censored observations. Three data sets were simulated for each level of censoring, both levels of true h2 and ρ = 0.8. The amount of censoring had no apparent effect on estimates of h: or breeding value. Heritability estimates and genetic predictions were similar among all levels of censoring, including that of no censoring. Average accuracy decreased more rapidly as the level of censoring increased. Average accuracies obtained from uncensored data were about 0.10 higher for non-foundation animals than those from 70% censored data, even though the number of animals increased with the level of censoring. A genetic evaluation of RL was conducted for the Red Angus Association of America (RAAA) using cow disposal information collected through its Total Herd Reporting (THR) program. Reproductive life was defined as the length of time in yr from when a cow produced her first calf as a two-yr-old to when she was culled for infertility or censored, whichever came first. The RAAA provided disposal records on 113,943 dams, which were combined with 670,342 calving records on 176,512 dams from the ST evaluation conducted in January, 2000. The data were edited to retain only those cows who calved annually since age two and who had the opportunity to participate in THR either by calving or by being culled in 1995 and later. The cows were assigned to contemporary groups using the same contemporary group designations from the ST evaluation. Further editing eliminated contemporary groups in which all observations were censored or in which there was no variation among observations. The final data set consisted of records on 8,504 dams in 9 12 contemporary groups, of which 69.76% were censored. The median h2 estimate was 0.0532, in contrast to 0.10 used in the ST evaluation. Genetic trends in EBV for underlying RL and ST were nearly mirror images of one another, as for trends obtained from simulated data. Correlations between EBV for RL and ST were moderately high and favorable (-0.5322 for all animals and -0.4605 for sires). When ST was evaluated for only those animals in the RL analysis, average accuracies of prediction were lower for ST than for RL (0.1340 vs 0.1816). The results of this study show that animal model survival analysis is feasible, even with large data sets and large amounts of censoring, and yields higher accuracy of prediction than threshold analysis of similar traits.