Empirical type I error rates of various tests at significance level α = 0.005 for increasing number of neutral RVs with 50,000 simulation replications (B = 10,000 for resampling-based tests).

Annotation-based tests were based on six random annotations. aSPU: adaptive sum of powered score test; aSPU_minP: combining multiple p-values of aSPU tests by minimum p approach; aSPU_Fisher: to combining multiple p-values of aSPU tests by Fisher’s meta-analysis approach; FunSPU: multiple functional annotation-based SPU test; wtFunSPU: global weighted FunSPU; T1: burden test of variants with MAF smaller than 1%; SKAT: the sequence kernel association test; (w): inverse-variance weighted score function in the SPU framework.