Table 2.

Simulation study evaluating the main effect adjustment of G (775 subjects). A linear main effect of E was fitted. Each cell presents the type I error rate/power based on 1000 replicates. MinP: single SNP analysis using GEE adjusted by the effective number of independent tests (Gao et al., 2008). iSKAT: region based test proposed by Lin et al. (2013). rareGE: rareGE test proposed by Chen et al. (2014) assuming a random main effect of G. GE-none: the proposed test adjusting for none of the SNPs. $\text{GE-wPCA}/\text{wPCAM-}\sqrt{m}$: the proposed test adjusting for the leading $\sqrt{m}$ components using the weighted PCA and robust(wPCA)/model-based(wPCAM) inference. GE-true: the proposed test with the correct model, which correctly correctly includes all SNPs with non-zero main effects. Type I error rate and power were both evaluated at α = 0.05. Power is empirically calibrated to α = 0.05 and marked as “*” when a method has type I error rate > 0.07.

Cross-sectional data
q	Type I error rate				Power
	C1 holds		C1 does not hold		C1 holds		C1 does not hold
	400	700	400	700	400	700	400	700
MinP	0.052	0.047	0.116	0.129	0.426	0.355	0.676*	0.636*
iSKAT	0.050	0.066	0.055	0.060	0.557	0.505	0.780	0.747
rareGE	0.054	0.055	0.072	0.059	0.634	0.561	0.821*	0.810
GE-none	0.025	0.038	0.189	0.181	0.446	0.402	0.769	0.778
$\text{GE-wPCA-}\sqrt{m}$	0.030	0.038	0.040	0.030	0.540	0.514	0.771	0.741
$\text{GE-wPCAM-}\sqrt{m}$	0.041	0.038	0.048	0.048	0.591	0.561	0.805	0.785
GE-true	0.036	0.038	0.045	0.041	0.584	0.509	0.797	0.759

Longitudinal data
q	Type I error rate				Power
	C1 holds		C1 does not hold		C1 holds		C1 does not hold
	400	700	400	700	400	700	400	700
MinP	0.028	0.033	0.088	0.108	0.472	0.462	0.568*	0.575*
GE-none	0.045	0.039	0.187	0.173	0.560	0.564	0.477*	0.435*
$\text{GE-wPCA-}\sqrt{m}$	0.033	0.034	0.031	0.034	0.588	0.569	0.687	0.682
$\text{GE-wPCAM-}\sqrt{m}$	0.034	0.037	0.032	0.040	0.626	0.589	0.736	0.708
GE-true	0.040	0.034	0.038	0.039	0.615	0.589	0.724	0.707