Table 1 The estimated Type I error rates at different significance levels for the six methods with the phenotypic correlation structure for the 70 phenotypes.

From: A clustering linear combination method for multiple phenotype association studies based on GWAS summary statistics

\({\alpha }\)

\(\boldsymbol{{1\times 10}^{-3}}\)

\(\boldsymbol{1\times {10}^{-4}}\)

\(\boldsymbol{1\times {10}^{-5}}\)

\(\boldsymbol{1\times {10}^{-6}}\)

\(\boldsymbol{1\times {10}^{-7}}\)

SSU

\(1.05\times {10}^{-3}\)

\(\boldsymbol{1.13\times {10}^{-4}}\)

\(\boldsymbol{1.25\times {10}^{-5}}\)

\(\boldsymbol{1.61\times {10}^{-6}}\)

\(\boldsymbol{2.29\times {10}^{-7}}\)

sCLC

\(1.07\times {10}^{-3}\)

\(1.05\times {10}^{-4}\)

\(1.06\times {10}^{-5}\)

\(1.17\times {10}^{-6}\)

\(7.98\times {10}^{-8}\)

Hom

\(1.00\times {10}^{-3}\)

\(9.82\times {10}^{-5}\)

\(1.01\times {10}^{-5}\)

\(9.47\times {10}^{-7}\)

\(9.97\times {10}^{-8}\)

Wald

\(1.01\times {10}^{-3}\)

\(1.00\times {10}^{-4}\)

\(9.98\times {10}^{-6}\)

\(1.17\times {10}^{-6}\)

\(1.7\times {10}^{-7}\)

aMAT

\(9.97\times {10}^{-4}\)

\(1.00\times {10}^{-4}\)

\(1.02\times {10}^{-5}\)

\(1.17\times {10}^{-6}\)

\(1.3\times {10}^{-7}\)

PCFisher

\(1.00\times {10}^{-3}\)

\(9.90\times {10}^{-5}\)

\(1.01\times {10}^{-5}\)

\(1.09\times {10}^{-6}\)

\(1.5\times {10}^{-7}\)

  1. The bold-faced values indicate that the type I error rates cannot be controlled.
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