Table 3.

Results of Association Analysis of Four Lipid Traits in 5 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. 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 ${\beta }_{\ell }\left(t\right)$” were based on smoothing both GVF and genetic effect functions ${\beta }_{\ell }\left(t\right)$ of model (5), and the results of “Basis of β-smooth only” were based on smoothing ${\beta }_{\ell }\left(t\right)$ only approach of model (7).

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 ${\beta }_{\ell }\left(t\right)$		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−b	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 Students Study	An Enzyme Gene	A,B	2.14 × 10−20	3.14 × 10−10	2.14 × 10−20	3.14 × 10−18	7.67 × 10−17	4.21 × 10−3	2.44 × 10−3
		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
		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

Abbreviation: GVF = Genetic Variant Function.