TABLE 3.

Results of association analysis of four lipid traits in five European studies in the regions of APOE, LPL, and LDLR genes and three traits of the Trinity Students Study in the region of an enzyme gene using the F-approximation based on Pillai-Bartlett trace

Study	Gene	Combinations of traits	P-values of the F-approximation based on Pillai–Bartlett trace					P-values of GAMuT
			Basis of both GVF and βℓ(t)		Basis of beta-smooth only		MANOVA Model (1)	Projection matrix	Linear kernel
			B-sp basis	Fourier basis	B-sp basis	Fourier basis
D2d-2007	APOE	LDL,TG	4.33 × 10−23	8.96 × 10−23	4.33 × 10−23	8.96 × 10−23				4.92 × 10−22	2.01 × 10−4	2.01 × 10−4
		LDL,CHOL	1.21 × 10−20	2.08 × 10−19	1.21 × 10−20	2.08 × 10−19	7.91 × 10−19	4.62 × 10−4	4.62 × 10−4
		TG,CHOL	2.98 × 10−18	2.69 × 10−18	2.98 × 10−18	2.69 × 10−18	1.20 × 10−17	1.61 × 10−3	1.61 × 10−3
		LDL,TG,CHOL	9.10 × 10−20	3.45 × 10−19	9.10 × 10−20	3.45 × 10−19	1.84 × 10−18	7.31 × 10−5	3.51 × 10−4
	LPL	LDL,TG	5.15 × 10−2	2.85 × 10−2	5.15 × 10−2	2.85 × 10−2	4.32 × 10−1	4.36 × 10−5	4.36 × 10−5
FUSION	APOE	LDL,TG	3.05 × 10−7	2.02 × 10−8	3.05 × 10−7	2.02 × 10−8	3.83 × 10−8	1.90 × 10−1	1.90 × 10−1
		LDL,CHOL	1.20 × 10−7	1.29 × 10−8	1.20 × 10−7	1.29 × 10−8	1.75 × 10−8	4.88 × 10−2	4.88 × 10−2
		TG,CHOL	4.25 × 10−4	1.06 × 10−5	4.25 × 10−4	1.06 × 10−5	1.93 × 10−5	4.95 × 10−1	4.95 × 10−1
		LDL,TG,CHOL	8.02 × 10−6	6.44 × 10−7	8.02 × 10−6	6.44 × 10−7	1.11 × 10−6	1.33 × 10−1	9.41 × 10−2
	LPL	LDL,TG	7.11 × 10−5	2.82 × 10−3	7.11 × 10−5	2.82 × 10−3	2.73 × 10−2	2.71 × 10−5	2.71 × 10−5
		LDL,TG,CHOL	8.51 × 10−4	1.79 × 10−2	8.51 × 10−4	1.79 × 10−2	6.32 × 10−2	2.29 × 10−6	8.61 × 10−4
Norway	APOE	LDL,TG	1.42 × 10−25	8.16 × 10−25	1.42 × 10−25	8.16 × 10−25	4.72 × 10−24	2.43 × 10−4	2.43 × 10−4
		LDL,CHOL	8.12 × 10−29	1.64 × 10−27	8.12 × 10−29	1.64 × 10−27	6.70 × 10−27	1.13 × 10−4	1.13 × 10−4
		TG,CHOL	5.32 × 10−20	1.46 × 10−19	5.32 × 10−20	1.46 × 10−19	6.08 × 10−19	1.66 × 10−3	1.66 × 10−3
		LDL,TG,CHOL	1.18 × 10−24	3.06 × 10−23	1.18 × 10−24	3.06 × 10−23	1.68 × 10−22	8.33 × 10−5	2.20 × 10−4
DIAGEN	APOE	LDL,TG	1.78 × 10−8	1.76 × 10−7	1.78 × 10−8	1.76 × 10−7	4.47 × 10−7	3.73 × 10−3	3.73 × 10−3
		LDL,CHOL	1.24 × 10−9	1.44 × 10−8	1.24 × 10−9	1.44 × 10−8	3.24 × 10−8	1.60 × 10−1	1.60 × 10−1
		TG,CHOL	2.99 × 10−6	2.49 × 10−5	2.99 × 10−6	2.49 × 10−5	4.51 × 10−5	1.71 × 10−1	1.71 × 10−1
		LDL,TG,CHOL	1.81 × 10−10	4.43 × 10−9	1.81 × 10−10	4.43 × 10−9	1.19 × 10−8	1.25 × 10−3	1.83 × 10−2
METSIM	APOE	LDL,TG	2.70 × 10−7	3.45 × 10−7	2.70 × 10−7	3.45 × 10−7	7.77 × 10−7	6.29 × 10−4	6.29 × 10−4
		LDL,CHOL	3.87 × 10−5	5.63 × 10−5	3.87 × 10−5	5.63 × 10−5	9.45 × 10−5	3.08 × 10−3	3.08 × 10−3
		LDL,TG,CHOL	1.09 × 10−6	2.08 × 10−6	1.09 × 10−6	2.08 × 10−7	3.91 × 10−6	9.51 × 10−4	1.06 × 10−3
	LDLR	LDL,TG	1.20 × 10−4	2.59 × 10−5	1.20 × 10−4	2.59 × 10−5	2.51 × 10−5	2.85 × 10−4	2.85 × 10−4
		LDL,CHOL	3.24 × 10−5	2.99 × 10−7	3.24 × 10−5	2.99 × 10−7	7.83 × 10−7	1.12 × 10−5	1.12 × 10−5
		TG,CHOL	5.49 × 10−4	2.03 × 10−5	5.49 × 10−4	2.03 × 10−5	2.09 × 10−5	1.76 × 10−5	1.76 × 10−5
		LDL,TG,CHOL	4.26 × 10−5	1.19 × 10−6	4.26 × 10−5	1.19 × 10−6	1.72 × 10−6	6.16 × 10−5	3.24 × 10−5
Trinity	An	A,B	2.14 × 10−20	3.14 × 10−18	2.14 × 10−20	3.14 × 10−18	7.67 × 10−17	4.21 × 10−3	2.44 × 10−3
Students	enzyme	A,C	1.08 × 10−17	9.53 × 10−16	1.08 × 10−17	9.53 × 10−16	4.46 × 10−15	2.36 × 10−3	2.53 × 10−3
Study	gene	B,C	6.54 × 10−15	9.51 × 10−12	6.54 × 10−15	9.51 × 10−12	1.05 × 10−10	8.96 × 10−2	5.83 × 10−2
		A,B,C	2.30 × 10−21	5.87 × 10−18	2.30 × 10−21	5.87 × 10−18	1.56 × 10−16	7.42 × 10−3	3.91 × 10−3

The associations that attain a threshold significance of P < 3.1 × 10⁻⁶ are highlighted in red (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 (5), and the results of “Basis of β-smooth only” were based on smoothing β_ℓ(t) only approach of model (7). GVF, genetic variant function.