The inability of many of the groups to detect a G×E interaction that reached a genome-wide level of significance is likely to be due to inadequate sample sizes. To explore the power to detect an interaction in a GWAS, we adopt a standard logistic model framework for a disease outcome (D), with form logit[Pr(D=1|G,E)] = β0 + βg G + βe E + βge G×E. This model parameterizes the baseline disease prevalence (β0), the main effects of G (βg) and E (βe), and the G×E interaction (βge). The quantity of interest is the interaction ORge = exp(βge) = ORG | E=1 / ORG | E=0, or, in other words, the odds ratio for a given SNP (G) in exposed (E=1) individuals divided by the odds ratio for G in unexposed (E=0) individuals. The epidemiologist may want to adopt the alternative exposure-based interpretation for ORge, specifically ORE | G=1 / ORE | G=0. Table II shows the required number of case-control pairs required to achieve 80% power for detecting an interaction, for various underlying values of ORge, minor allele frequencies, and
