Table 2.

Simulation results of the overall and interaction score tests, and the alternative methods for interaction detection based on dimension reduction and multiple regression. Nominal p-value threshold was set to 0.05. The first row corresponds to simulating the null hypothesis for both the overall and interaction effects. The second and third rows correspond to the null hypothesis of the interaction effect only. Thus, corresponding detection rates in the first three rows are desired to be below the p-value threshold of 0.05. PCg: first principal component of the genetic data; PCw: first principal component of the cardiovascular disease risk factors; RVT: rare variant test burden variable; WST: weighted sum test burden variable; FHS: the Framingham Heart Study vascular disease risk score.

	Kernel method		Alternative methods
(α_M, α_I)	Overall	Interaction	PCg × FHS	PCg × PCw	RVT × FHS	RVT × PCw	WST × FHS	WST × PCw
(0, 0)	0.048	—	0.051	0.043	0.051	0.040	0.049	0.038
(0.5, 0)	0.908	0.046	0.061	0.046	0.063	0.043	0.062	0.054
(1, 0)	1.000	0.051	0.052	0.052	0.068	0.049	0.061	0.052
(0, 0.5)	0.961	0.918	0.622	0.499	0.578	0.444	0.572	0.455
(0,1)	0.983	0.950	0.681	0.546	0.620	0.508	0.631	0.505
(1, 0.1)	0.999	0.585	0.292	0.242	0.229	0.204	0.226	0.216
(1, 0.25)	0.995	0.865	0.506	0.405	0.432	0.324	0.433	0.325
(1, 0.5)	0.997	0.926	0.591	0.481	0.542	0.413	0.536	0.425
(0.1, 1)	0.984	0.951	0.681	0.529	0.622	0.478	0.610	0.476
(0. 25, 1)	0.986	0.944	0.665	0.521	0.600	0.459	0.601	0.469
(0.5, 1)	0.983	0.951	0.654	0.517	0.612	0.472	0.587	0.446
(0.5, 0. 5)	0.984	0.918	0.625	0.488	0.587	0.423	0.575	0.431
(1, 1)	0.994	0.958	0.660	0.527	0.629	0.488	0.620	0.489