Table 2.

Results of association analysis of three traits of the Trinity Students Study in the region of an enzyme gene 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 Linear Model (1)	P-values of SKAT-O
Traits	B-spline basis	Fourier basis	FPCA	B-spline basis	Fourier basis
A	1.73 × 10−13	7.89 × 10−13	1.54 × 10−15	1.73 × 10−13	7.89 × 10−13	2.84 × 10−12	2.16 × 10−10
B	3.44 × 10−13	1.80 × 10−11	1.58 × 10−13	3.44 × 10−13	1.80 × 10−11	1.23 × 10−10	2.72 × 10−5
C	1.11 × 10−11	9.91 × 10−10	8.67 × 10−11	1.11 × 10−11	9.91 × 10−10	3.78 × 10−9	1.25 × 10−5
(A, B)	2.14 × 10−20	3.14 × 10−18	3.00 × 10−21	2.14 × 10−20	3.14 × 10−18	7.67 × 10−17	X
(A, C)	1.08 × 10−17	9.53 × 10−16	9.29 × 10−18	1.08 × 10−17	9.53 × 10−16	4.46 × 10−15	X
(B, C)	6.54 × 10−15	9.51 × 10−12	1.19 × 10−14	6.54 × 10−15	9.51 × 10−12	1.05 × 10−10	X
(A, B, C)	2.30 × 10−21	5.87 × 10−18	3.74 × 10−21	2.30 × 10−21	5.87 × 10−18	1.56 × 10−16	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