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. Author manuscript; available in PMC: 2019 Mar 1.
Published in final edited form as: Genet Epidemiol. 2017 Dec 10;42(2):134–145. doi: 10.1002/gepi.22105

Table 1.

Simulation 1: Type I error estimates at various levels α. This table lists the type I error estimates divided by the significance level α and the corresponding 100(1 − α)% confidence intervals in brackets. The ideal point estimate for any cell is 1. Estimates are based on 108 null datasets, each with K traits, 1 SNP and sample size 1, 000.

Level α Method K = 5 K = 10
ρ= 0.2 ρ = 0.4 ρ = 0.6 ρ = 0.2 ρ = 0.4 ρ = 0.6
10−2 SHom 0.95 [0.95, 0.95] 1.00 [1.00, 1.00] 1.03 [1.03, 1.03] 1.00 [1.00, 1.00] 1.07 [1.07, 1.07] 1.01 [1.01, 1.01]
SHet 1.05 [1.05, 1.05] 1.05 [1.04, 1.05] 0.98 [0.98, 0.98] 1.01 [1.01, 1.01] 1.06 [1.06, 1.06] 1.02 [1.01, 1.02]
minP 1.03 [1.03, 1.03] 1.03 [1.03, 1.03] 1.02 [1.02, 1.02] 1.04 [1.04, 1.04] 1.03 [1.03, 1.03] 1.03 [1.03, 1.03]
metaMANOVA 1.05 [1.05, 1.05] 1.05 [1.04, 1.05] 0.98 [0.98, 0.98] 1.04 [1.04, 1.04] 0.97 [0.97, 0.97] 1.06 [1.06, 1.06]
metaUSAT 0.82 [0.82, 0.82] 0.92 [0.92, 0.92] 0.93 [0.93, 0.93] 0.93 [0.93, 0.93] 1.01 [1.01, 1.01] 1.06 [1.06, 1.06]
10−3 SHom 0.93 [0.93, 0.93] 1.00 [1.00, 1.00] 1.03 [1.03, 1.03] 1.00 [1.00, 1.00] 1.11 [1.11, 1.12] 1.02 [1.02, 1.03]
SHet 1.11 [1.10, 1.11] 1.12 [1.11, 1.12] 1.02 [1.02, 1.02] 1.01 [1.01, 1.02] 1.10 [1.09, 1.10] 1.02 [1.02, 1.03]
minP 1.05 [1.05, 1.06] 1.05 [1.05, 1.06] 1.05 [1.05, 1.06] 1.07 [1.07, 1.08] 1.06 [1.06, 1.06] 1.07 [1.07, 1.07]
metaMANOVA 1.09 [1.09, 1.10] 1.08 [1.08, 1.08] 0.99 [0.99, 1.00] 1.08 [1.07, 1.08] 0.98 [0.98, 0.98] 1.11 [1.11, 1.12]
metaUSAT 0.90 [0.90, 0.90] 1.00 [1.00, 1.00] 1.02 [1.01, 1.02] 1.05 [1.05, 1.05] 1.13 [1.12, 1.13] 1.19 [1.18, 1.19]
10−4 SHom 0.90 [0.89, 0.91] 1.00 [1.00, 1.00] 1.09 [1.08, 1.10] 1.01 [1.00, 1.02] 1.17 [1.16, 1.18] 1.04 [1.03, 1.05]
SHet 1.18 [1.17, 1.19] 1.22 [1.21, 1.23] 1.09 [1.08, 1.10] 1.04 [1.03, 1.05] 1.14 [1.13, 1.15] 1.05 [1.04, 1.06]
minP 1.10 [1.09, 1.11] 1.10 [1.09, 1.11] 1.13 [1.12, 1.14] 1.13 [1.12, 1.14] 1.11 [1.10, 1.12] 1.13 [1.12, 1.14]
metaMANOVA 1.14 [1.13, 1.15] 1.13 [1.12, 1.14] 1.03 [1.02, 1.04] 1.11 [1.10, 1.12] 0.99 [0.98, 1.00] 1.17 [1.16, 1.18]
metaUSAT 1.21 [1.20, 1.22] 1.29 [1.28, 1.30] 1.18 [1.17, 1.19] 1.59 [1.58, 1.61] 1.49 [1.48, 1.51] 1.39 [1.38, 1.40]
10−5 SHom 0.88 [0.85, 0.91] 1.00 [0.97, 1.03] 1.12 [1.09, 1.15] 1.07 [1.03, 1.10] 1.28 [1.25, 1.32] 1.11 [1.08, 1.14]
SHet 1.31 [1.27, 1.34] 1.36 [1.32, 1.40] 1.17 [1.14, 1.21] 1.12 [1.09, 1.16] 1.27 [1.23, 1.31] 1.12 [1.09, 1.16]
minP 1.14 [1.10, 1.17] 1.16 [1.12, 1.19] 1.30 [1.27, 1.34] 1.23 [1.20, 1.27] 1.13 [1.09, 1.16] 1.25 [1.21, 1.28]
metaMANOVA 1.17 [1.14, 1.20] 1.16 [1.12, 1.19] 1.03 [1.00, 1.06] 1.19 [1.16, 1.23] 1.03 [1.00, 1.06] 1.31 [1.27, 1.34]
metaUSAT 1.38 [1.35, 1.42] 1.45 [1.41, 1.49] 1.28 [1.25, 1.45] 1.92 [1.88, 1.97] 1.74 [1.70, 1.79] 1.58 [1.54, 1.62]
10−6 SHom 0.80 [0.71, 0.89] 0.92 [0.82, 1.02] 1.11 [1.00, 1.22] 1.12 [1.01, 1.23] 1.49 [1.37, 1.61] 1.26 [1.15, 1.38]
SHet 1.44 [1.32, 1.56] 1.43 [1.31, 1.55] 1.26 [1.15, 1.37] 1.21 [1.10, 1.32] 1.47 [1.35, 1.59] 1.26 [1.15, 1.38]
minP 1.31 [1.20, 1.42] 1.27 [1.16, 1.38] 1.64 [1.51, 1.77] 1.30 [1.19, 1.41] 1.16 [1.05, 1.27] 1.45 [1.33, 1.57]
metaMANOVA 1.19 [1.08, 1.30] 1.10 [0.99, 1.21] 1.00 [0.90, 1.10] 1.32 [1.21, 1.43] 1.23 [1.12, 1.34] 1.54 [1.42, 1.66]
metaUSAT 1.46 [1.34, 1.58] 1.48 [1.36, 1.60] 1.33 [1.22, 1.45] 2.38 [2.23, 2.53] 2.21 [2.06, 2.36] 2.08 [1.94, 2.22]
5 × 10−7 SHom 0.72 [0.60, 0.84] 0.82 [0.69, 0.95] 1.00 [0.86, 1.14] 1.20 [1.05, 1.35] 1.50 [1.33, 1.67] 1.25 [1.09, 1.41]
SHet 1.30 [1.14, 1.46] 1.42 [1.25, 1.59] 1.32 [1.16, 1.48] 1.30 [1.14, 1.46] 1.38 [1.21, 1.55] 1.17 [1.02, 1.32]
minP 1.46 [1.29, 1.63] 1.30 [1.14, 1.46] 1.90 [1.71, 2.10] 1.42 [1.25, 1.59] 1.08 [0.93, 1.23] 1.64 [1.46, 1.82]
metaMANOVA 1.20 [1.05, 1.36] 1.25 [1.09, 1.41] 1.15 [1.00, 1.30] 1.32 [1.16, 1.48] 1.20 [1.05, 1.35] 1.62 [1.44, 1.80]
metaUSAT 1.54 [1.36, 1.72] 1.74 [1.55, 1.92] 1.54 [1.36, 1.71] 2.52 [2.30, 2.74] 2.42 [2.20, 2.64] 2.18 [1.97, 2.39]