Table 4.

Impact of sample size on type I error rates for the case-only design

	Disease prevalence
Number of cases	$\mathbf{\alpha }$	1.0%	1.5%	2.0%	2.5%	3.0%	3.5%	4.0%	4.5%	5.0%	10.0%	15.0%	20.0%
2,500	0.001	0.000983	0.000958	0.000942	0.001019	0.000959	0.000911	0.000962	0.000956	0.001024	0.001057	0.001097	0.001216
	0.05	0.049557	0.049826	0.049762	0.050058	0.050021	0.049818	0.050325	0.050030	0.050102	0.051262	0.053111	0.054364
5,000	0.001	0.000996	0.001050	0.000976	0.000976	0.000972	0.001000	0.000949	0.001010	0.001060	0.001153	0.001275	0.001413
	0.05	0.049919	0.050110	0.049596	0.050317	0.050346	0.050453	0.050565	0.050731	0.050874	0.053727	0.056344	0.059515
10,000	0.001	0.000994	0.001004	0.001058	0.001037	0.001057	0.001106	0.001115	0.001068	0.001097	0.001357	0.001731	0.001966
	0.05	0.050155	0.050387	0.050449	0.050325	0.051138	0.050999	0.051155	0.051520	0.052183	0.057479	0.063428	0.070083
20,000	0.001	0.000980	0.000998	0.001012	0.001052	0.000992	0.001114	0.001162	0.001186	0.001267	0.001838	0.002487	0.003475
	0.05	0.049976	0.050759	0.050546	0.051070	0.051843	0.052863	0.053234	0.053472	0.054632	0.065503	0.078536	0.090791
50,000	0.001	0.001034	0.000988	0.001076	0.001160	0.001208	0.001294	0.001373	0.001544	0.001647	0.003449	0.005998	0.008934
	0.05	0.050299	0.051092	0.051977	0.053040	0.054681	0.055883	0.058031	0.059773	0.061797	0.089890	0.122479	0.154596

Data were generated under the null with no interaction but two main effects [${\beta }_G=ln(1.2)$ and ${\beta }_E=ln(2)$]. The MAF for the genetic variant is 0.2 and the frequency of the environmental exposure is 0.1. Type I error is calculated as the proportion of instances that the null hypothesis is rejected among all 1,000,000 replicates. Type I errors exceeding 5% of the alpha level are highlighted in bold in the table