Table 3. Estimated type I error probability for test of deviation from HWP of SNP₂, a causal SNP to primary disease but unassociated with secondary phenotype (MAF = 40%), at 0.05 and 0.0001 significance levels in simulation studies^* using different approaches for HWP testing.

Approaches		α = 0.05				α = 0.0001
		0.1	0.3	0.5	0.7	0.1	0.3	0.5	0.7
LRT_t	0.1	0.627260	0.573700	0.550220	0.559390	0.053796	0.040312	0.034674	0.037743
	0.3	0.210050	0.198150	0.200780	0.196990	0.003259	0.002515	0.002577	0.002789
	0.5	0.050007	0.049852	0.049675	0.051325	0.000071	0.000113	0.000062	0.000160
	0.7	0.216220	0.219080	0.217210	0.215410	0.003184	0.003390	0.003172	0.002850
mHWP_t	0.1	0.631460	0.584970	0.536990	0.488360	0.053770	0.026639	0.010651	0.007235
	0.3	0.210800	0.208130	0.200800	0.168160	0.003330	0.001737	0.000933	0.000374
	0.5	0.050602	0.054912	0.054477	0.048824	0.000073	0.000057	0.000016	0.000005
	0.7	0.218030	0.229660	0.232740	0.228650	0.003316	0.003497	0.002618	0.001366
LRT_d	0.1	0.050558	0.050690	0.050830	0.051459	0.000092	0.000117	0.000148	0.000103
	0.3	0.051329	0.055468	0.056119	0.052864	0.000089	0.000129	0.000150	0.000111
	0.5	0.050079	0.054422	0.055539	0.053985	0.000067	0.000120	0.000057	0.000145
	0.7	0.050483	0.051177	0.051220	0.050447	0.000094	0.000136	0.000103	0.000107
mHWP_d	0.1	0.054121	0.054870	0.054884	0.055146	0.000067	0.000117	0.000097	0.000100
	0.3	0.056680	0.061018	0.061881	0.057905	0.000077	0.000068	0.000089	0.000040
	0.5	0.048408	0.052943	0.053900	0.052227	0.000067	0.000145	0.000057	0.000132
	0.7	0.055468	0.056702	0.056614	0.056278	0.000024	0.000100	0.000055	0.000081
eLRT	0.1	0.050108	0.049843	0.049292	0.050494	0.000096	0.000125	0.000095	0.000046
	0.3	0.050273	0.050039	0.049661	0.050889	0.000065	0.000133	0.000101	0.000102
	0.5	0.049889	0.050504	0.049880	0.050395	0.000076	0.000065	0.000070	0.000105
	0.7	0.049888	0.049224	0.051004	0.050025	0.000068	0.000139	0.000087	0.000115
emHWP	0.1	0.055240	0.050562	0.038818	0.025086	0.000070	0.000032	0.000012	0.000012
	0.3	0.053956	0.046384	0.034750	0.022099	0.000047	0.000008	0.000012	0.000008
	0.5	0.052390	0.055258	0.046097	0.032279	0.000076	0.000041	0.000020	<0.000001
	0.7	0.055004	0.054376	0.055794	0.054795	0.000002	0.000085	0.000046	0.000102

*Simulation studies were based on 1,000,000 replicates, each replicate with 2,000 cases in terms of primary disease and 2,000 controls frequency-matched on secondary phenotype.

MAF: minor allele frequency.

LRT_t: LRT approach, using presence and absence of secondary phenotype as cases and controls.

mHWP_t: mHWP exact test, using presence and absence of secondary phenotype as cases and controls.

LRT_d: LRT approach, using presence and absence of primary disease as cases and controls.

mHWP_d: mHWP exact test, using presence and absence of primary disease as cases and controls.

eLRT: extended LRT approach.

emHWP: extended mHWP exact test.

: prevalence of primary disease in general population.

: prevalence of secondary phenotype in general population.