of controls to protect against false positives while exploiting the power advantage of the case-control design. Murcray et al.99 introduced a two-step analysis of a single-stage GWA study (FIG 1), in which 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 test. The second general approach is the empirical Bayes34 or Bayes model averaging35 methods that combine the case-only and case-control estimators to provide a reasonable trade-off between validity and efficiency. Simulation studies show that these approaches can have better power than the two-step analysis over a range of modest interaction relative risks, while the two-step approach is more powerful for larger relative risks.
