Table 2.

Type I errors of ΔAUC test, LRT, and RERI test. The sample sizes are 500 and 200 affected individuals and an equal number of unaffected individuals. The correlations between the genetic factor and treatment are ρ = 0 and ρ = 0.50. The estimated type I errors are shown under various true values of the main effects β and δ (note: γ = 0). In our simulations, the genetic factor had 3 levels and treatment had 2 levels. Hence, we report two RERIs: RERI₁₁ and RERI₂₁.

Number affected	β	δ	ρ = 0				ρ = 0.50
			ΔAUC	LRT	RERI11	RERI21	ΔAUC	LRT	RERI11	RERI21
500	0.15	0.1	0.03	0.05	0.07	0.06	0.07	0.07	0.04	0.03
	0.35	0.1	0.07	0.07	0.06	0.07	0.04	0.04	0.06	0.06
	0.55	0.1	0.08	0.06	0.03	0.03	0.07	0.06	0.05	0.07
	0.75	0.1	0.02	0.03	0.05	0.03	0.04	0.09	0.06	0.08
	0.95	0.1	0.02	0.05	0.03	0.03	0.02	0.03	0.04	0.03
	0.75	0.6	0.01	0.04	0.01	0.7	0.02	0.09	0.03	0.35
200	0.15	0.1	0.03	0.04	0.04	0.03	0.06	0.08	0.01	0.02
	0.35	0.1	0.03	0.02	0.05	0.03	0.05	0.10	0.03	0.03
	0.55	0.1	0.04	0.08	0.02	0.04	0.05	0.08	0.04	0.04
	0.75	0.1	0.03	0.02	0.04	0.02	0.03	0.02	0.00	0.01
	0.95	0.1	0.05	0.07	0.01	0.01	0.05	0.05	0.01	0.02
	0.75	0.6	0.01	0.05	0.01	0.13	0.02	0.02	0.00	0.04