Table 5.

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. All L = 4 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	0.597	0.807	0.988	0.779	0.928	0.999	0.681	0.882	0.997
Q ′	0.453	0.225	0.099	0.646	0.376	0.183	0.523	0.257	0.110
Pmin	0.277	0.275	0.271	0.376	0.372	0.366	0.266	0.262	0.257
MKMR	0.586	0.801	0.987	0.767	0.926	0.998	0.672	0.880	0.996