Table 1. Association analysis of lipid traits in eight European cohorts by homogeneous likelihood-ratio tests (Hom-LRT), Hom-MetaSKAT-O, and Hom-MetaSKAT.

		P-values of Hom-LRT
		Basis of both GVF and ${\beta }_{\ell }\left(t\right)$		Basis of β-smooth only			P-values of Hom-Meta-
Traits	Gene	B-spline basis	Fourier basis	B-spline basis	Fourier basis	Additive model (7)	SKAT	SKAT-O
HDL	LPL	$\mathbf{3.06}\times {\mathbf{10}}^{-\mathbf{6}}$	$\mathbf{6.13}\times {\mathbf{10}}^{-\mathbf{9}}$	$3.64\times {10}^{-6}$	$\mathbf{6.75}\times {\mathbf{10}}^{-\mathbf{7}}$	$8.32\times {10}^{-4}$	$1.08\times {10}^{-3}$	$1.21\times {10}^{-3}$
LDL	APOB	$\mathbf{3.35}\times {\mathbf{10}}^{-\mathbf{9}}$	$7.50\times {10}^{-4}$	$\mathbf{5.76}\times {\mathbf{10}}^{-\mathbf{8}}$	$1.87\times {10}^{-4}$	$3.84\times {10}^{-5}$	$1.63\times {10}^{-2}$	$2.51\times {10}^{-2}$
	APOE	$\mathbf{1.27}\times {\mathbf{10}}^{-\mathbf{87}}$	$\mathbf{3.42}\times {\mathbf{10}}^{-\mathbf{91}}$	$\mathbf{4.07}\times {\mathbf{10}}^{-\mathbf{83}}$	$\mathbf{4.42}\times {\mathbf{10}}^{-\mathbf{90}}$	$\mathbf{4.23}\times {\mathbf{10}}^{-\mathbf{89}}$	$\mathbf{1.18}\times {\mathbf{10}}^{-\mathbf{43}}$	$\mathbf{6.67}\times {\mathbf{10}}^{-\mathbf{44}}$
	LDLR	$\mathbf{8.25}\times {\mathbf{10}}^{-\mathbf{15}}$	$\mathbf{1.67}\times {\mathbf{10}}^{-\mathbf{14}}$	$\mathbf{5.09}\times {\mathbf{10}}^{-\mathbf{15}}$	$\mathbf{9.24}\times {\mathbf{10}}^{-\mathbf{14}}$	$\mathbf{7.14}\times {\mathbf{10}}^{-\mathbf{17}}$	$\mathbf{1.03}\times {\mathbf{10}}^{-\mathbf{10}}$	$\mathbf{2.94}\times {\mathbf{10}}^{-\mathbf{10}}$
	PCSK9	$\mathbf{2.29}\times {\mathbf{10}}^{-\mathbf{6}}$	$\mathbf{5.36}\times {\mathbf{10}}^{-\mathbf{10}}$	$\mathbf{1.65}\times {\mathbf{10}}^{-\mathbf{6}}$	$\mathbf{1.27}\times {\mathbf{10}}^{-\mathbf{7}}$	$\mathbf{2.35}\times {\mathbf{10}}^{-\mathbf{17}}$	$\mathbf{6.18}\times {\mathbf{10}}^{-\mathbf{7}}$	$\mathbf{2.00}\times {\mathbf{10}}^{-\mathbf{6}}$
TG	APOE	$4.95\times {10}^{-6}$	$6.61\times {10}^{-6}$	$\mathbf{5.13}\times {\mathbf{10}}^{-\mathbf{7}}$	$\mathbf{1.90}\times {\mathbf{10}}^{-\mathbf{6}}$	$\mathbf{1.37}\times {\mathbf{10}}^{-\mathbf{6}}$	$1.34\times {10}^{-3}$	$2.59\times {10}^{-3}$
	LPL	$\mathbf{2.03}\times {\mathbf{10}}^{-\mathbf{11}}$	$\mathbf{7.48}\times {\mathbf{10}}^{-\mathbf{13}}$	$\mathbf{2.60}\times {\mathbf{10}}^{-\mathbf{11}}$	$\mathbf{4.23}\times {\mathbf{10}}^{-\mathbf{14}}$	$\mathbf{5.52}\times {\mathbf{10}}^{-\mathbf{7}}$	$1.78\times {10}^{-5}$	$1.77\times {10}^{-5}$
CHOL	APOB	$\mathbf{1.98}\times {\mathbf{10}}^{-\mathbf{8}}$	$7.88\times {10}^{-3}$	$\mathbf{2.19}\times {\mathbf{10}}^{-\mathbf{7}}$	$1.16\times {10}^{-4}$	$\mathbf{6.60}\times {\mathbf{10}}^{-\mathbf{8}}$	$6.17\times {10}^{-2}$	$1.00\times {10}^{-1}$
	APOE	$\mathbf{2.48}\times {\mathbf{10}}^{-\mathbf{53}}$	$\mathbf{3.12}\times {\mathbf{10}}^{-\mathbf{53}}$	$\mathbf{1.52}\times {\mathbf{10}}^{-\mathbf{48}}$	$\mathbf{1.36}\times {\mathbf{10}}^{-\mathbf{51}}$	$\mathbf{1.98}\times {\mathbf{10}}^{-\mathbf{51}}$	$\mathbf{9.08}\times {\mathbf{10}}^{-\mathbf{23}}$	$\mathbf{2.15}\times {\mathbf{10}}^{-\mathbf{22}}$
	HNF1A	$1.08\times {10}^{-1}$	$1.84\times {10}^{-2}$	$8.94\times {10}^{-3}$	$\mathbf{2.84}\times {\mathbf{10}}^{-\mathbf{6}}$	$1.74\times {10}^{-1}$	$1.89\times {10}^{-1}$	$2.77\times {10}^{-1}$
	LDLR	$\mathbf{8.10}\times {\mathbf{10}}^{-\mathbf{11}}$	$\mathbf{8.49}\times {\mathbf{10}}^{-\mathbf{10}}$	$\mathbf{8.59}\times {\mathbf{10}}^{-\mathbf{10}}$	$\mathbf{6.68}\times {\mathbf{10}}^{-\mathbf{9}}$	$\mathbf{2.07}\times {\mathbf{10}}^{-\mathbf{12}}$	$\mathbf{3.43}\times {\mathbf{10}}^{-\mathbf{7}}$	$\mathbf{1.15}\times {\mathbf{10}}^{-\mathbf{6}}$

The associations that attain a threshold significance of $P<3.1\times {10}^{-6}$ are boldface (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 (3), the results of “Basis of β-smooth only” were based on the smoothing ${\beta }_{\ell }\left(t\right)$ only approach of model (5), the results of “Additive model (7)” were based on the additive effect model (7), and the P-values of Hom-MetaSKAT and Hom-MetaSKAT-O were based on the R package MetaSKAT. GVF, genetic variant function.