Power for tests of interaction: effect of raising the Type I error rate

Table 1 Effect of Raising the Type I Error Rate on the Statistical Power for the Wald¹ Test of Interaction for Three Study Sizes in a Case-Control Study of Two Binary Exposures²

		Small Study Size (75 Cases & 150 Controls)				Large Study Size (300 cases & 600 controls)				Very Large Study Size (1200 Cases & 2400 Controls)
Type of Interaction		Type I Error Rate				Type I Error Rate				Type I Error Rate
		5%	10%	15%	20%	5%	10%	15%	20%	5%	10%	15%	20%
S1	Sub-additive	43%	55%	63%	69%	95%	97%	98%	99%	>99%	>99%	>99%	>99%
A1	Additive	21%	31%	39%	45%	63%	74%	80%	84%	>99%	>99%	>99%	>99%
A2	Additive	26%	37%	45%	52%	75%	84%	88%	91%	>99%	>99%	>99%	>99%
A3	Additive	24%	35%	43%	49%	71%	81%	86%	89%	>99%	>99%	>99%	>99%
I1	Intermediate	18%	28%	35%	42%	55%	67%	75%	79%	99%	99%	>99%	>99%
I2	Intermediate	11%	18%	24%	30%	28%	40%	48%	54%	79%	87%	91%	93%
M1	Multiplicative	5%	10%	15%	20%	5%	10%	15%	20%	5%	10%	15%	20%
T1	Super-multiplicative	7%	13%	19%	24%	14%	22%	29%	35%	40%	53%	61%	67%
T2	Super-multiplicative	16%	25%	32%	38%	47%	60%	67%	73%	96%	98%	99%	99%
T3	Super-multiplicative	30%	42%	50%	57%	82%	89%	93%	95%	>99%	>99%	>99%	>99%

¹In simulations, almost identical results were obtained for the Likelihood Ratio test and Breslow-Day Test
² Bolded table cells indicate "middle-ground" scenarios in which there is a useful gain in power due to raising the Type I error rate. Italicized table cells indicate "high-ground" scenarios in which power is already high and raising the Type I error rate is unnecessary. Table cells that are neither bolded nor italicized indicate "low-ground" scenarios in which power is so low that raising the Type I error rate does not usefully boost power. A useful gain in power was defined as situations where raising the Type I error rate from 5% to 20% resulted in a 10% or greater gain in power, and power was above 70% when the Type I error rate was 20%.