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Table 6 Simulated data: MWSL estimation comparison between the permutation method and the approximation procedure generating the distribution of the minimum p value as a Beta(1, MeffMWSL)

From: Multiple-testing correction in metabolome-wide association studies

Correlation \(\in\) [0.95-1) Correlation \(\in\) [0.65,0.75) Correlation \(\in\) [0.35,0.45)
  Beta(1,4) Permutation   Beta(1,74) Permutation   Beta(1,282) Permutation
ENT/ANT(%) 0.60% 0.49% ENT/ANT(%) 11.10% 12.48% ENT/ANT(%) 42.30% 49.06%
ENT 4 3 ENT 72 81 ENT 275 319
ENT_CI.low 4 3 ENT_CI.low 72 67 ENT_CI.low 274 293
ENT_CI.up 4 3 ENT_CI.up 72 93 ENT_CI.up 276 343
MWSL 0.012740 0.015879 MWSL 0.000693 0.000620 MWSL 0.000182 0.000155
MWSL_CI.up 0.012797 0.017769 MWSL_CI.up 0.000696 0.000710 MWSL_CI.up 0.000183 0.000170
MWSL_CI.low 0.012684 0.014545 MWSL_CI.low 0.000690 0.000536 MWSL_CI.low 0.000181 0.000138
Correlation \(\in\) [0.85,0.95) Correlation \(\in\) [0.55,0.65) Correlation \(\in\) [0.25,0.35)
  Beta(1,14) Permutation   Beta(1,126) Permutation   Beta(1,416) Permutation
ENT/ANT(%) 2.10% 1.73% ENT/ANT(%) 18.90% 20.68% ENT/ANT(%) 62.37% 66.60%
ENT 14 11 ENT 123 134 ENT 405 433
ENT_CI.low 14 10 ENT_CI.low 122 125 ENT_CI.low 404 440
ENT_CI.up 14 13 ENT_CI.up 123 143 ENT_CI.up 407 433
MWSL 0.003657 0.004482 MWSL 0.000407 0.000373 MWSL 0.000123 0.000108
MWSL_CI.up 0.003673 0.004964 MWSL_CI.up 0.000409 0.000410 MWSL_CI.up 0.000124 0.000117
MWSL_CI.low 0.003641 0.003900 MWSL_CI.low 0.000405 0.000328 MWSL_CI.low 0.000123 0.000097
Correlation \(\in\) [0.75,0.85) Correlation \(\in\) [0.45,0.55) Correlation \(\in\) (0,0.25)
  Beta(1,40) Permutation   Beta(1,195) Permutation   Beta(1,535) Permutation
ENT/ANT(%) 6.00% 5.49% ENT/ANT(%) 29.24% 32.29% ENT/ANT(%) 80.23% 85.26%
ENT 39 36 ENT 190 210 ENT 522 554
ENT_CI.low 39 32 ENT_CI.low 189 192 ENT_CI.low 519 526
ENT_CI.up 39 41 ENT_CI.up 191 228 ENT_CI.up 524 586
MWSL 0.001282 0.001596 MWSL 0.000263 0.000221 MWSL 0.000096 0.000088
MWSL_CI.up 0.001276 0.001796 MWSL_CI.up 0.000264 0.000241 MWSL_CI.up 0.000096 0.000096
MWSL_CI.low 0.001287 0.001386 MWSL_CI.low 0.000262 0.000201 MWSL_CI.low 0.000095 0.000078