Table 2.

Simulation results of type I error rates of the proposed F-tests of the fixed effect models based on sequence data generated by COSI, when the genetic variant functions were taken as additive. The results of “Basis of both GVF and β(t)” were based on the model (3), the results of “FPCA” were based on the model (4), and the results of “Basis of beta-smooth only” were based on the model (6), respectively

Nominal level α	Sample size	Basis of both GVF and β(t)		FPCA	Basis of beta-smooth only
		B-sp basis	Fourier basis		B-sp basis	Fourier basis
0.05	250	0.049816	0.049839	0.049850	0.048148	0.046349
	500	0.049955	0.050035	0.049817	0.049779	0.046926
	1000	0.050112	0.050188	0.050266	0.050141	0.049293
	1500	0.050000	0.049933	0.050065	0.049967	0.049800
	2000	0.050211	0.050143	0.050370	0.050191	0.050163
0.01	250	0.009757	0.009925	0.009832	0.009458	0.009205
	500	0.009930	0.010094	0.010031	0.009900	0.009414
	1000	0.010164	0.010005	0.010058	0.010139	0.009794
	1500	0.010012	0.010058	0.010053	0.010003	0.009988
	2000	0.009926	0.010061	0.010129	0.009928	0.010064
0.001	250	0.000987	0.000995	0.001028	0.000968	0.000916
	500	0.001018	0.001007	0.000986	0.001012	0.000946
	1000	0.001037	0.000988	0.001018	0.001044	0.000965
	1500	0.000949	0.000998	0.000997	0.000943	0.000996
	2000	0.000931	0.000967	0.001054	0.000931	0.000961
0.0001	250	0.000102	0.000109	9.70E-05	9.20E-05	1.00E-04
	500	0.000106	9.80E-05	9.60E-05	0.000107	9.90E-05
	1000	0.000108	8.80E-05	9.30E-05	0.000108	8.60E-05
	1500	0.000110	8.60E-05	0.000101	0.000112	8.90E-05
	2000	9.40E-05	0.000106	0.000120	9.40E-05	0.000104