Table 3.

The Type I Error and Power for Gene-level Association Tests. We compared the power for simple burden, SKAT, and VT tests for the joint multi-allelic analysis and the analysis that discards multi-allelic sites. The power and type I error were assessed under a threshold of $\alpha =2.5\times {10}^{-6}$ using 1,000,000 replicates.

MAF Cutoff	Pct of Causal Variants	Power
		Burden/SKAT/VT	Burden/SKAT/VT
		Joint Multi-allelic Analysis	Discard Multi-allelic Sites
Type I Error
0.01	0%	2.6 × 10−6/2.1 × 10−6/3.0 × 10−6	2.5 × 10−6/3.1 × 10−6/2.6 ×10−6
0.05	0%	2.5 × 10−6/2.3 × 10−6/2.3 × 10−6	3.0 × 10−6/2.1 × 10−6/2.7 × 10−6
Power—Causal Variants Have Uni-directional Effects
0.01	20%	0.50/0.39/0.68	0.42/0.35/0.61
	50%	0.93/0.79/0.99	0.90/0.77/0.98
0.05	20%	0.42/0.39/0.71	0.37/0.36/0.64
	50%	0.88/0.80/0.99	0.87/0.79/0.99
Power—Causal Variants Have Bi-directional Effects
0.01	20%	0.06/0.16/0.13	0.05/0.13/0.11
	50%	0.14/0.44/0.31	0.14/0.40/0.29
0.05	20%	0.05/0.17/0.14	0.05/0.15/0.12
	50%	0.12/0.42/0.30	0.12/0.40/0.30