Table 1.

Results of association analysis of lipid traits in five European studies in the regions of APOE and LDLR genes using the F-approximation based on Pillai– Bartlett trace

			P -values of the F-approximation based on Pillai-Bartlett Trace
			Basis of both GVF and βℓ(t)			Basis of beta-smooth only		Multivariate Model (1)	P-values of SKAT-O
Study	Gene	Traits	B-sp basis	Fourier basis	FPCA	B-sp basis	Fourier Basis
D2d-2007	APOE	LDL	1.89 × 10−25	9.02 × 10−25	3.47 × 10−23	1.89 × 10−25	9.02 × 10−25	2.85 × 10−24	5.87 × 10−13
		CHOL	9.09 × 10−18	3.01 × 10−17	1.27 × 10−16	9.09 × 10− 18	3.01 × 10− 17	7.97 × 10− 17	1.72 × 10− 9
		LDL, CHOL	1.21 × 10−20	2.08 × 10−19	1.90 × 10−19	1.21 × 10−20	2.08 × 10−19	7.91 × 10−19	X
FUSION	APOE	LDL	4.34 × 10−10	2.24 × 10−11	3.15 × 10−10	4.34 × 10−10	2.24 × 10−11	3.42 × 10−11	8.61 × 10−14
Stage 2		CHOL	1.34 × 10−12	4.92 × 10−13	3.18 × 10−12	1.34 × 10−12	4.92 × 10−13	8.70 × 10−13	1.64 × 10−12
		LDL,CHOL	1.20 × 10−7	1.29 × 10−8	4.65 × 10−8	1.20 × 10−7	1.29 × 10−8	1.75 × 10−8	X
Norway	APOE	LDL	3.79 × 10−28	1.90 × 10−27	7.15 × 10−26	3.79 × 10−28	1.90 × 10−27	6.05 × 10−27	6.21 × 10−6
		TG	5.69 × 10−4	3.94 × 10−4	6.80 × 10−5	5.69 × 10−4	3.95 × 10−4	6.55 × 10−4	5.55 × 10−2
		CHOL	2.12 × 10−14	6.15 × 10−14	2.46 × 10−13	2.12 × 10−14	6.15 × 10−14	1.35 × 10−13	3.00 × 10−3
		LDL,TG	1.42 × 10−25	8.16 × 10−25	9.55 × 10−25	1.42 × 10−25	8.16 × 10−25	4.72 × 10−24	X
		LDL,CHOL	8.12 × 10−29	1.64 × 10−27	6.88 × 10−28	8.12 × 10−29	1.64 × 10−27	6.70 × 10−27	X
		TG,CHOL	5.32 × 10−20	1.46 × 10−19	1.46 × 10−20	5.32 × 10−20	1.46 × 10−19	6.08 × 10−19	X
		LDL,TG,CHOL	1.18 × 10−24	3.06 × 10−23	1.13 × 10−24	1.18 × 10−24	3.06 × 10−23	1.68 × 10−22	X
DIAGEN	APOE	LDL	7.84 × 10−7	3.31 × 10−6	5.82 × 10−6	7.84 × 10−7	3.31 × 10−6	5.76 × 10−6	2.37 × 10−1
		TG	3.51 × 10−3	8.53 × 10−3	1.09 × 10−3	3.51 × 10−3	8.53 × 10−3	1.23 × 10−2	7.59 × 10−2
		CHOL	1.91 × 10−3	5.61 × 10−3	1.77 × 10−2	1.91 × 10−3	5.61 × 10−3	7.38 × 10−3	4.73 × 10−1
		LDL,TG	1.78 × 10−8	1.76 × 10−7	2.76 × 10−8	1.78 × 10−8	1.76 × 10−7	4.47 × 10−7	X
		LDL,CHOL	1.24 × 10−9	1.44 × 10−8	5.06 × 10−8	1.24 × 10−9	1.44 × 10−8	3.24 × 10−8	X
		TG,CHOL	2.99 × 10−6	2.49 × 10−5	6.76 × 10−6	2.99 × 10−6	2.49 × 10−5	4.51 × 10−5	X
		LDL,TG,CHOL	1.81 × 10−10	4.43 × 10−9	1.83 × 10−9	1.81 × 10−10	4.43 × 10−9	1.19 × 10−8	X
METSIM	APOE	LDL	1.85 × 10−5	1.98 × 10−5	9.71 × 10−7	1.85 × 10−5	1.98 × 10−5	3.45 × 10−5	1.25 × 10−4
		TG	2.80 × 10−2	3.43 × 10−2	7.66 × 10−2	2.80 × 10−2	3.43 × 10−2	3.96 × 10−2	4.04 × 10−1
		CHOL	1.87 × 10−2	1.84 × 10−2	4.33 × 10−3	1.87 × 10−2	1.84 × 10−2	2.73 × 10−2	5.43 × 10−2
		LDL,TG	2.70 × 10−7	3.45 × 10−7	1.47 × 10−7	2.70 × 10−7	3.45 × 10−7	7.77 × 10−7	X
		LDL,CHOL	3.87 × 10−5	5.63 × 10−5	2.84 × 10−6	3.87 × 10−5	5.63 × 10−5	9.45 × 10−5	X
		LDL,TG,CHOL	1.09 × 10−6	2.08 × 10−6	8.30 × 10−7	1.09 × 10−6	2.08 × 10−7	3.91 × 10−6	X
	LDLR	LDL	1.72 × 10−4	2.20 × 10−5	9.42 × 10−6	1.72 × 10−4	2.20 × 10−5	4.01 × 10−5	1.50 × 10−2
		CHOL	3.47 × 10−4	2.97 × 10−6	1.31 × 10−5	3.47 × 10−4	2.97 × 10−6	5.67 × 10−6	5.79 × 10−3
		LDL,CHOL	3.24 × 10−5	2.99 × 10−7	2.02 × 10−6	3.24 × 10−5	2.99 × 10−7	7.83 × 10−7	X

Notes: The associations that attain a threshold significance of P < 3.1 × 10⁻⁶ are highlighted in bold [Liu et al. 2014]. The results of “Basis of both GVF and β_ℓ(t)” were based on smoothing both GVF and genetic effect functions β_ℓ(t) of model (7), the results of “FPCA Approach” were based on FPCA approach of model (8), the results of “Basis of beta-Smooth Only” were based on smoothing β_ℓ(t) only approach of model (3), and the P-values of SKAT-O were based of R Package SKAT. GVF, genetic variant function.