The two-phase sampling design is a cost-efficient way of collecting expensive
covariate information on a judiciously selected subsample. It is natural to
apply such a strategy for collecting genetic data in a subsample enriched for
exposure to environmental factors for gene-environment interaction (G x E)
analysis. In this paper, we consider two-phase studies of G x E interaction
where phase I data are available on exposure, covariates and disease status.
Stratified sampling is done to prioritize individuals for genotyping at phase
II conditional on disease and exposure. We consider a Bayesian analysis based
on the joint retrospective likelihood of phases I and II data. We address
several important statistical issues: (i) we consider a model with multiple
genes, environmental factors and their pairwise interactions. We employ a
Bayesian variable selection algorithm to reduce the dimensionality of this
potentially high-dimensional model; (ii) we use the assumption of gene-gene and
gene-environment independence to trade off between bias and efficiency for
estimating the interaction parameters through use of hierarchical priors
reflecting this assumption; (iii) we posit a flexible model for the joint
distribution of the phase I categorical variables using the nonparametric Bayes
construction of Dunson and Xing [J. Amer. Statist. Assoc. 104 (2009)
1042-1051].Comment: Published in at http://dx.doi.org/10.1214/12-AOAS599 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org