Schematic representation of the two-step GEWIS test for G×E interaction of Murcray et al. G₁,…G_M denotes the genotypes at each SNP in a GWAS and E denotes a binary exposure variable. G-E association is first tested in the combined case and control sample and only the most significant SNPs are then tested for G×E interaction using the standard case-control (in this example, the second and fourth rows are taken forward to the second step). Despite the dilution of the induced G-E association in the first step by the inclusion of the controls, this approach yields a second-step test that is independent of the first and hence need only be corrected for the number of SNPs actually taken forward to the second. They showed that the resulting procedure has dramatically better power than a conventional single-step case-control comparison. The optimal design depends only weakly on the true model parameters. For rare diseases with a 1:1 ratio, any first-stage significance level of α₁ ~ 0.0001 yields roughly similar power, although a common disease would require a much larger α₁. In an application to the CHS GWA study for asthma, the first-stage test of association between SNPs and in utero tobacco smoke exposure in the combined case-control sample identified 15,006 SNPs that attained the optimized first-step threshold of α₁ = 0.025; of these, the second stage case-control test yielded one nearly significant interaction (the second example in the figure), which would not have been deemed genomewide significant in a traditional 1-step test, nor by its main effect. This SNP shows no effect in the absence of in utero tobacco exposure and exposure shows no effect in non-carriers of the minor allele. The first row illustrates the most significant SNP × E interaction in a conventional single-stage test that fails the first-step procedure and hence is declared non-significant in the two-step procedure. The fourth row illustrates the most significant SNP–E association in the first step, which shows no sign of SNP×E interaction in the second step. (The marginal totals differ slightly from row to row because of missing genotypes.)