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

Complex human diseases are an increasingly important focus of genetic resea rch. Many of the determinants of these diseases are unknown and there is of ten a strong residual covariance between relatives even when all known gene tic and environmental factors have been taken into account. This must be mo deled correctly whether scientific interest is focused on fixed effects, as in an association analysis, or on the covariance structure itself. Analysi s is straightforward for multivariate normally distributed traits, but diff iculties arise with other types of trait. Generalized linear mixed models ( GLMMs) offer a potentially unifying approach to analysis for many classes o f phenotype including right censored survival times. This includes age-at-o nset and age-at-death data and a variety of other censored traits. Markov c hain Monte Carlo (MCMC) methods, including Gibbs sampling, provide a conven ient framework within which such GLMMs may be fitted. In this paper, we use BUGS ("Bayesian inference using Gibbs sampling": a readily available, gene ric Gibbs sampler) to fit GLMMs for right-censored survival times in nuclea r and extended families. We discuss parameter interpretation and statistica l inference, and show how to circumvent a number of important theoretical a nd practical problems. Using simulated data, we show that model parameters are consistent. We further illustrate our methods using data from an ongoin g cohort study. Finally, we propose that the random effects associated with a genetic component of variance (e.g., sigma(A)(2)) in a GLMM may be regar ded as an adjusted "phenotype" and used as input to a conventional model-ba sed 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 w hile comprehensively adjusting for observed confounders at the level of the individual and latent environmental effects shared across families. (C) 20 00 Wiley-Liss, Inc.