Simulation-based Type I error for the seven stratified GWAMA approaches to detect GxS.

Shown is the type I error at a 5% significance level derived from simulated data as the proportion of variants with nominally significant difference test (PDiffbalanced strata design (n1 = 100,000, n2 = 100,000; split in half for two-stage approaches), variants with MAF = 0.05 or 0.30, and phenotypes simulated under the null hypothesis of no GxS, i.e. no difference between stratum-specific effects (H0: β1 = β2 = β). We present the results for β = 0 and β ≠ 0. For the second setting, we set β as the minimum effect size detectable at 80% power for the given MAF and the given sample size for the difference test (n = 200 000 for one-stage approaches, β = 0.029, 0.014 for MAF = 0.05, MAF = 0.30, respectively; nStage = 100,000 for the two-stage approaches, β = 0.041, 0.019 for MAF = 0.05, MAF = 0.30, respectively). Marked in bold are violated type 1 error rates.