Variance components analysis for pedigree-based censored survival data using generalized linear mixed models (GLMMs) and Gibbs sampling in BUGS

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Abstract
Complex human diseases are an increasingly important focus of genetic research. Many of the determinants of these diseases are unknown and there is often a strong residual covariance between relatives even when all known genetic and environmental factors have been taken into account. This must be modeled correctly whether scientific interest is focused on fixed effects, as in an association analysis, or on the covariance structure itself. Analysis is straightforward for multivariate normally distributed traits, but difficulties arise with other types of trait. Generalized linear mixed models (GLMMs) offer a potentially unifying approach to analysis for many classes of phenotype including right censored survival times. This includes age‐at‐onset and age‐at‐death data and a variety of other censored traits. Markov chain Monte Carlo (MCMC) methods, including Gibbs sampling, provide a convenient framework within which such GLMMs may be fitted. In this paper, we use BUGS (“Bayesian inference using Gibbs sampling”: a readily available, generic Gibbs sampler) to fit GLMMs for right‐censored survival times in nuclear and extended families. We discuss parameter interpretation and statistical inference, and show how to circumvent a number of important theoretical and practical problems. Using simulated data, we show that model parameters are consistent. We further illustrate our methods using data from an ongoing cohort study. Finally, we propose that the random effects associated with a genetic component of variance (e.g., σ2A) in a GLMM may be regarded as an adjusted “phenotype” and used as input to a conventional model‐based or model‐free linkage analysis. This provides a simple way to conduct a linkage analysis for a trait reflected in a right‐censored survival time while comprehensively adjusting for observed confounders at the level of the individual and latent environmental effects shared across families. Genet. Epidemiol. 19:127–148, 2000.