Table 3.

Power of multivariate tests for four continuous traits with pairwise correlation ρ: Q is the proposed MSKAT statistic incorporating the trait correlation, Q′ is the sum of individual trait SKAT statistics, Pmin is the Bonferroni corrected minimum p-value based on the individual trait SKAT significance p-values, and MKMR is the multivariate kernel machine regression approach. Only the first L = 2 traits are associated with the rare variant set. The causal rare variant proportion is θ and their regression coefficient is set as −d log₁₀(MAF). The highest powered tests in each column are bold-faced.

(d, θ)	(0.25,0.25)			(0.2,0.5)			(0.15,0.75)
ρ	0.2	0.5	0.8	0.2	0.5	0.8	0.2	0.5	0.8
Q	0.147	0.294	0.749	0.223	0.427	0.896	0.156	0.326	0.854
Q ′	0.085	0.029	0.012	0.136	0.048	0.019	0.088	0.030	0.012
Pmin	0.123	0.123	0.123	0.175	0.175	0.174	0.119	0.118	0.118
MKMR	0.117	0.262	0.721	0.177	0.381	0.879	0.120	0.285	0.837