Genetic variance components analysis for binary phenotypes using generalized linear mixed models (GLMMs) and Gibbs sampling

The common complex diseases such as asthma are an important focus of geneti c research, and studies based on large numbers of simple pedigrees ascertai ned from population-based sampling frames are becoming commonplace. Many of the genetic and environmental factors causing these diseases are unknown a nd there is often a strong residual covariance between relatives even after all known determinants are taken into account. This must be modelled corre ctly whether scientific interest is focused on fixed effects, as in an asso ciation analysis, or on the covariances themselves. Analysis is straightfor ward for multivariate Normal phenotypes, 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 mult ivariate Normal traits, binary traits, and censored survival times. Markov Chain Monte Carlo methods, including Gibbs sampling, provide a convenient f ramework within which such models may be fitted. In this paper, Bayesian in ference Using Gibbs Sampling (a generic Gibbs sampler; BUGS) is used to fit GLMMs for multivariate Normal and binary phenotypes in nuclear families. B UGS is easy to use and readily available. We motivate a suitable model stru cture for Normal phenotypes and show how the model extends to binary traits . We discuss parameter interpretation and statistical inference and show ho w to circumvent a number of important theoretical and practical problems th at we encountered. Using simulated data we show that model parameters seem consistent and appear unbiased in smaller data sets. We illustrate our meth ods using data from an ongoing cohort study. (C) 1999 Wiley-Liss, Inc.