Journal of Biometrics & Biostatistics

Specification of Generalized Linear Mixed Models for Family Data using Markov Chain Monte Carlo Methods

Abstract

Kris M Jamsen, Sophie G Zaloumis, Katrina J Scurrah and Lyle C Gurrin

Statistical models imposed on family data can be used to partition phenotypic variation into components due to sharing of both genetic and environmental risk factors for disease. Generalized linear mixed models (GLMMs) are useful tools for the analysis of family data, but it is not always clear how to specify individual-level regression equations so that the resulting within-family variance-covariance matrix of the phenotype reflects the correlation implied by the relatedness of individuals within families. This is particularly challenging when families are of varying sizes and compositions. In this paper we propose a general approach to specifying GLMMs for family data that uses a decomposition of the within-family variance-covariance matrix of the phenotype to set up a series of regression equations with fixed and random effects that corresponds to an appropriate genetic model. This “mechanistic” specification is particularly suited to estimation and evaluation of models within a Markov chain Monte Carlo (MCMC) framework. The proposed approach was assessed with simulated data to demonstrate the accuracy of estimation of the variance components. We analyzed data from the Victorian Family Heart Study (families with two generations over-sampled for those with monozygotic and dizygotic twins) and for a binary phenotype (hypertension) that resulted in substantially reduced computation time in the MCMC framework (via WinBUGS) compared with a maximum likelihood approach (via Stata). The proposed approach to model specification in this paper is easily implemented using standard software and can accommodate prior information on the magnitude of fixed or random effects.