Efficient designs of gene-environment interaction studies: implications of Hardy-Weinberg equilibrium and gene-environment independence.

It is important to investigate whether genetic susceptibility variants exercise the same effects in populations that are differentially exposed to environmental risk factors. Here, we assess the power of four two-stage case-control design strategies for assessing multiplicative gene-environment (G-E) interactions or for assessing genetic or environmental effects in the presence of G-E interactions. We considered a di-allelic single nucleotide polymorphism G and a binary environmental variable E under the constraints of G-E independence and Hardy-Weinberg equilibrium and used the Wald statistic for all tests. We concluded that (i) for testing G-E interactions or genetic effects in the presence of G-E interactions when data for E are fully available, it is preferable to ascertain data for G in a subsample of cases with similar numbers of exposed and unexposed and a random subsample of controls; and (ii) for testing G-E interactions or environmental effects in the presence of G-E interactions when data for G are fully available, it is preferable to ascertain data for E in a subsample of cases that has similar numbers for each genotype and a random subsample of controls. In addition, supplementing external control data to an existing case-control sample leads to improved power for assessing effects of G or E in the presence of G-E interactions.