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The effect of ignoring individual heterogeneity in Weibull log-normal sire frailty models¹

L. H. Damgaard^*,,2, I. R. Korsgaard, J. Simonsen, O. Dalsgaard and A. H. Andersen

^* Department of Animal Science and Animal Health, Royal Veterinary and Agricultural University, Grønnegårdsvej 2, 1870 Frederiksberg C, Denmark; and Department of Genetics and Biotechnology, Danish Institute of Agricultural Sciences, P.O. Box 50, 8830 Tjele, Denmark; and Department of Theoretical Statistics, University of Aarhus, 8000 Aarhus C, Denmark

² Corresponding author: lars.damgaard{at}agrsci.dk

The objective of this study was, by means of simulation, to quantify the effect of ignoring individual heterogeneity in Weibull sire frailty models on parameter estimates and to address the consequences for genetic inferences. Three simulation studies were evaluated, which included 3 levels of individual heterogeneity combined with 4 levels of censoring (0, 25, 50, or 75%). Data were simulated according to balanced half-sib designs using Weibull log-normal animal frailty models with a normally distributed residual effect on the log-frailty scale. The 12 data sets were analyzed with 2 models: the sire model, equivalent to the animal model used to generate the data (complete sire model), and a corresponding model in which individual heterogeneity in log-frailty was neglected (incomplete sire model). Parameter estimates were obtained from a Bayesian analysis using Gibbs sampling, and also from the software Survival Kit for the incomplete sire model. For the incomplete sire model, the Monte Carlo and Survival Kit parameter estimates were similar. This study established that when unobserved individual heterogeneity was ignored, the parameter estimates that included sire effects were biased toward zero by an amount that depended in magnitude on the level of censoring and the size of the ignored individual heterogeneity. Despite the biased parameter estimates, the ranking of sires, measured by the rank correlations between true and estimated sire effects, was unaffected. In comparison, parameter estimates obtained using complete sire models were consistent with the true values used to simulate the data. Thus, in this study, several issues of concern were demonstrated for the incomplete sire model.

Key Words: genetics • individual heterogeneity • survival frailty model

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