We compared different Bayesian models to handle censored data for genetic parameters estimation of age at first calving (AFC) in Brazilian Brahman cattle. Data from females with AFC above 1825 days of age were assumed to have failed to calve and were considered as censored records. Data including information of 53,703 cows were analyzed through the following methods: conventional linear model method (LM), which consider only uncensored records; simulation method (SM), in which the data were augmented by drawing random samples from positive truncated normal distributions; penalty method (PM), in which a constant of 21 days was added to censored records; and the bivariate threshold-linear method (TLcens). The LM was the most suited for genetic evaluation of AFC in Brazilian Brahman cattle based on the predictive ability evaluation through cross-validation analysis. The similar results for LM and PM regarding Spearman correlations, and the higher percentages of selected animals in common, indicated that there was not relevant reranking of animals when censored records were used. In summary, the heritability estimates for AFC ranged from 0.09 (TLcens) to 0.20 (LM). Given its poor predictive performance, the SM is not recommended for handling censored records for genetic evaluation of AFC.
Age at first calving (AFC) is characterized as a censored trait due to missing values provided by recording mistakes and nonoccurrence or delay in calving communication. In this context, we aimed to compare several statistical methods for genetic evaluation of AFC in Guzerá beef cattle under a Bayesian approach. Seven different methods were used for this purpose. The traditional linear mixed model (LM), which considers only uncensored records; the LM with simulated records (SM), which is based on data augmentation framework; the penalty method, in which a constant of 21 d was added to censored records; the bivariate threshold-linear method considering (TLcens) or not (TLmiss) censored information; and the piecewise Weibull proportional hazards model considering (PWPHcens) or not (PWPH) censored records. Heritability estimates ranged from 0.19 (TLcens) to 0.28 (SM) in nonsurvival approaches; and 0.40 and 0.46 to PWPH and PWPHcens methods, respectively. In general, breeding values correlations between different methods and the percentage of selected bulls in common indicated reranking, with these correlation ranging from -0.28 (between SM and PWPH) to 0.99 (between TLmiss and LM). The traditional LM, which considers only uncensored records, should be preferred due to its robustness and simplicity. Based on cross-validation analyses, we conclude that the TLmiss could be also a suitable alternative for breeding value prediction, and censored methods did not improve the analysis.
This technical note presents the program PaGELL v.1.5 (Parametric Genetic Evaluation of Lifespan in Livestock), a flexible software program to analyze (right-censored) longevity data in livestock populations, with a special emphasis on the genetic evaluation of the breeding stock. This software relies on a parametric generalization of the proportional hazard model; more specifically, the baseline hazard function follows a Weibull process and flexibility is gained by including an additional time-dependent effect with the number of change points defined by the user. The program can accommodate 3 different sources of variation (i.e., systematic, permanent environmental, and additive genetic effects) and both fixed and time-dependent patterns (only for systematic and permanent environmental effects). Analyses are performed within a Bayesian context by sampling from the joint posterior distribution of the model, and model fit can be easily determined by the calculation of the deviance information criterion. Although this software has already been used on field data sets, its performance has been double-checked on simulated data set, and results are presented in this technical note. PaGELL v.1.5 was written in Fortran 95 language and, after compiling with the GNU Fortran Compiler v.4.7 and later, it has been tested in Windows, Linux, and MacOS operating systems (both 32- and 64-bit platforms). This program is available at http://www.casellas.info/files/pageII.zip.
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