Abstract
With the advent of modern genomic methods to adjust for population stratification, the use of external or publicly available controls has become an attractive option for reducing the cost of large-scale case-control genetic association studies. In this article, we study the estimation of joint effects of genetic and environmental exposures from a case-control study where data on genome-wide markers are available on the cases and a set of external controls while data on environmental exposures are available on the cases and a set of internal controls. We show that under such a design, one can exploit an assumption of gene-environment independence in the underlying population to estimate the gene-environment joint effects, after adjustment for population stratification. We develop a semiparametric profile likelihood method and related pseudolikelihood and working likelihood methods that are easy to implement in practice. We propose variance estimators for the methods based on asymptotic theory. Simulation is used to study the performance of the methods, and data from a multi-centre genome-wide association study of bladder cancer is further used to illustrate their application.