Associating Multivariate Traits with Genetic Variants Using Collapsing and Kernel Methods with Pedigree- or Population-Based Studies

Table 1

Empirical type I errors of the seven competing methods with continuous traits.

Marker-specific weight	Nominal level	Working correlation	Method
			HoK^3	HoO	HeK	HeO	BT	mPK^4	mPB
Unweighted marker-specific weight^1	0.05	U/U^2	0.04876	0.04960	0.05036	0.05228	0.04914	0.04352	0.04692
		E/E	0.04866	0.04994	0.05016	0.05216	0.04914
	0.01	U/U	0.00918	0.01012	0.01016	0.01030	0.01034	0.00854	0.01036
		E/E	0.00924	0.00994	0.01008	0.01022	0.01028
	0.001	U/U	0.00078	0.00082	0.00086	0.00070	0.00084	0.00084	0.00088
		E/E	0.00080	0.00078	0.00084	0.00070	0.00082
	0.0001	U/U	0.00008	0.00002	0.00006	0.00008	0.00008	0.00006	0.00014
		E/E	0.00006	0.00002	0.00006	0.00008	0.00008
Weighted marker-specific weight	0.05	U/U	0.05030	0.04998	0.05158	0.05134	0.04696	0.04604	0.04536
		E/E	0.05054	0.05010	0.05176	0.05122	0.04714
	0.01	U/U	0.00992	0.00942	0.01080	0.00972	0.00888	0.00978	0.01008
		E/E	0.00992	0.00944	0.01088	0.00978	0.00886
	0.001	U/U	0.00078	0.00086	0.00126	0.00098	0.00082	0.00124	0.00134
		E/E	0.00076	0.00088	0.00122	0.00102	0.00080
	0.0001	U/U	0.00006	0.00008	0.00006	0.00006	0.00010	0.00002	0.00010
		E/E	0.00006	0.00008	0.00008	0.00006	0.00010

¹The unweighted marker-specific weight is given by ; the weighted marker-specific weight is given by . ²U/U represents the structures of the working within-cluster and multivariate-response correlation matrices considered by the unstructured structures; E/E represents the structures of the working within-cluster and multivariate-response correlation matrices considered by the exchangeable structures. ³HoK, HoO, HeK, HeO, and BT are our proposed methods. ⁴mPK and mPB are executed by the R package Multi-SKAT [39].