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 (PDiff<0.05) relative to the number of variants tested for difference (1,000,000 in the difference test without filtering, number of filtered variants in the approaches with filtering). The simulation results are based on a balanced 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.