. 2025 Mar 6;26:222. doi: 10.1186/s12864-025-11318-1

Table 1.

Type I error rates for case-only and case–control designs

Disease prevalence	$α$	1.0%	1.5%	2.0%	2.5%	3.0%	3.5%	4.0%	4.5%	5.0%	10.0%	15.0%	20.0%
(a) Two main effects
case–control	0.001	0.000962	0.000970	0.001041	0.001009	0.000983	0.000958	0.000994	0.000983	0.000970	0.000976	0.000978	0.000997
case-only	0.001	0.001015	0.000942	0.000983	0.001038	0.000990	0.000995	0.001098	0.001067	0.001083	0.001390	0.001667	0.002091
case–control	0.05	0.050330	0.049824	0.049887	0.049905	0.050113	0.050161	0.049653	0.050160	0.049735	0.049845	0.049912	0.050371
case-only	0.05	0.050132	0.050603	0.049854	0.050842	0.050614	0.051195	0.051387	0.052100	0.052221	0.057378	0.063536	0.070049
(b) Only a genetic main effect
case–control	0.001	0.001005	0.000929	0.001021	0.001002	0.000976	0.000999	0.001016	0.001030	0.000981	0.000958	0.000973	0.001068
case-only	0.001	0.001009	0.000969	0.000979	0.000990	0.000995	0.000940	0.001023	0.001030	0.001014	0.000966	0.000986	0.000984
case–control	0.05	0.049911	0.049822	0.050093	0.050012	0.049857	0.049930	0.049642	0.050276	0.050018	0.049894	0.049908	0.050146
case-only	0.05	0.050315	0.049506	0.050062	0.049971	0.049997	0.049994	0.049793	0.050205	0.049727	0.049807	0.049933	0.049700
(c) Only an environment main effect
case–control	0.001	0.000998	0.000981	0.000997	0.000971	0.001026	0.000980	0.000973	0.000951	0.001022	0.001015	0.000960	0.000984
case-only	0.001	0.000952	0.000998	0.000936	0.000968	0.000975	0.001012	0.000962	0.001046	0.000995	0.000998	0.000961	0.000940
case–control	0.05	0.050296	0.050185	0.050248	0.049903	0.050320	0.049931	0.049868	0.049853	0.049658	0.049894	0.049753	0.049896
case-only	0.05	0.049769	0.049906	0.049880	0.050149	0.049980	0.050189	0.049935	0.049731	0.049396	0.049929	0.049621	0.050153
(d) No main effects
case–control	0.001	0.001010	0.000981	0.000929	0.001040	0.000940	0.000984	0.000959	0.000999	0.001019	0.001012	0.000977	0.001056
case-only	0.001	0.000997	0.000904	0.000899	0.000930	0.000952	0.000959	0.000953	0.000959	0.001036	0.000958	0.000941	0.001027
case–control	0.05	0.049769	0.050132	0.049922	0.050361	0.050121	0.050052	0.049907	0.050104	0.050338	0.049919	0.049874	0.050470
case-only	0.05	0.049667	0.049608	0.049764	0.049975	0.050096	0.050202	0.049683	0.050152	0.050234	0.050031	0.049877	0.050120

Data were generated under the null with no interaction for four scenarios: (a) two main effects [ $β_{G} = ln (1.2)$ and $β_{E} = ln (2)$ ]; (b) only a genetic main effect [ $β_{G} = ln (1.2)$ and $β_{E} = 0$ ]; (c) only an environmental main effect [ $β_{G} = 0$ and $β_{E} = ln (2)$ ]; and (d) no main effects $[β_{G} = 0 and β_{E} = 0]$ . The MAF for the genetic variant is 0.2 and the frequency of the environmental exposure is 0.1. The sample sizes are N = 10,000 cases for both the case-only and case–control designs and additionally for the case–control design there are N = 10,000 controls. 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