Comparison of linear, skewed-linear, and proportional hazard models for the analysis of lambing interval in Ripollesa ewes

Genetic evaluation of age at first calving for Guzerá beef cattle using linear, threshold, and survival Bayesian models

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.

Technical note: PaGELL v.1.5: A flexible parametric program for the Bayesian analysis of longevity data within the context of animal breeding

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.

Comparison between linear and proportional hazard models for the analysis of age at first lambing in the Ripollesa breed

Age at first lambing (AFL) plays a key role on the reproductive performance of sheep flocks, although there are no genetic selection programs accounting for this trait in the sheep industry. This could be due to the non-Gaussian distribution pattern of AFL data, which must be properly accounted for by the analytical model. In this manuscript, two different parameterizations were implemented to analyze AFL in the Ripollesa sheep breed, that is, the skew-Gaussian mixed linear model (sGML) and the piecewise Weibull proportional hazards model (PWPH). Data were available from 10 235 ewes born between 1972 and 2013 in 14 purebred Ripollesa flocks located in the north-east region of Spain. On average, ewes gave their first lambing short after their first year and a half of life (590.9 days), and within-flock averages ranged between 523.4 days and 696.6 days. Model fit was compared using the deviance information criterion (DIC; the smaller the DIC statistic, the better the model fit). Model sGML was clearly penalized (DIC=200 059), whereas model PWPH provided smaller estimates and reached the minimum DIC when one cut point was added to the initial Weibull model (DIC=132 545). The pure Weibull baseline and parameterizations with two or more cut points were discarded due to larger DIC estimates (>134 200). The only systematic effect influencing AFL was the season of birth, where summer- and fall-born ewes showed a remarkable shortening of their AFL, whereas neither birth type nor birth weight had a relevant impact on this reproductive trait. On the other hand, heritability on the original scale derived from model PWPH was high, with a model estimate place at 0.114 and its highest posterior density region ranging from 0.079 and 0.143. As conclusion, Gaussian-related mixed linear models should be avoided when analyzing AFL, whereas model PWPH must be viewed as better alternative with superior goodness of fit; moreover, the additive genetic background underlying this reproductive trait supports its inclusion into current genetic selection programs given its economic importance.