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The two-phase sampling design is a cost-efficient way of collecting expensivecovariate information on a judiciously selected subsample. It is natural toapply such a strategy for collecting genetic data in a subsample enriched forexposure to environmental factors for gene-environment interaction (G x E)analysis. In this paper, we consider two-phase studies of G x E interactionwhere phase I data are available on exposure, covariates and disease status.Stratified sampling is done to prioritize individuals for genotyping at phaseII conditional on disease and exposure. We consider a Bayesian analysis basedon the joint retrospective likelihood of phases I and II data. We addressseveral important statistical issues: (i) we consider a model with multiplegenes, environmental factors and their pairwise interactions. We employ aBayesian variable selection algorithm to reduce the dimensionality of thispotentially high-dimensional model; (ii) we use the assumption of gene-gene andgene-environment independence to trade off between bias and efficiency forestimating the interaction parameters through use of hierarchical priorsreflecting this assumption; (iii) we posit a flexible model for the jointdistribution of the phase I categorical variables using the nonparametric Bayesconstruction of Dunson and Xing [J. Amer. Statist. Assoc. 104 (2009)1042-1051].

Bayesian semiparametric analysis for two-phase studies of gene-environment interaction