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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