test that has been shown to be a more robust choice to detect markers involved in disease risk because it jointly tests for main effect and interaction [Kraft et al., 2007]. The case-only analysis has been shown to be a powerful alternative to test for G×E [Khoury and Flanders, 1996; Piegorsch et al., 1994]. However, in a genome-wide setting, the assumption of G×E independence in the population is untenable across the large number of markers. Recently, Murcray et al. [2009] developed a two-step method that uses a case-only style screening step on the combined case-control sample to reduce the number of markers tested formally for interaction. They show that their two-step test is more powerful than a traditional logistic regression model for interaction under a wide range of scenarios, even in the presence of an association between gene and environment in the population. Mukherjee and Chatterjee [2008] developed an empirical Bayes-type shrinkage estimator to model G×E interactions with the efficiency of the case-only design and unbiasedness of a case-control design. By combining case-control and case-only analysis, Li and Conti [2009] developed a Bayes model averaging approach to obtain a single estimate of the interaction effect. Through simulation, their Bayes model
