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Table 2 Type I error rates of ZMTT(0), ZMTT(0.5), ZMTT(1), ZSGMS, ZSGME, ZMAX3 and Z χ 2 with 2 df based on 10,000 replicates in the presence of confounding factors with the significance level α using R cases and S controls.

From: Robust tests for matched case-control genetic association studies

Scenario

α

ZMTT(0)

ZMTT(0.5)

ZMTT(1)

Z SGMS

Z SGME

Z MAX3

Z χ 2

A

0.05

0.0527

0.0498

0.0518

0.0501

0.0490

0.0527

0.0531

B

 

0.0487

0.0503

0.0493

0.0494

0.0502

0.0515

0.0481

C

 

0.0510

0.0512

0.0509

0.0506

0.0510

0.0513

0.0490

D

 

0.0526

0.0524

0.0537

0.0529

0.0528

0.0516

0.0484

E

 

0.0519

0.0512

0.0534

0.0536

0.0526

0.0501

0.0507

F

 

0.0485

0.0486

0.0479

0.0488

0.0467

0.0501

0.0481

G

 

0.0493

0.0497

0.0490

0.0492

0.0498

0.0457

0.0491

H

 

0.0522

0.0493

0.0480

0.0522

0.0521

0.0525

0.0522

A

0.01

0.0092

0.0081

0.0100

0.0083

0.0081

0.0075

0.0084

B

 

0.0096

0.0091

0.0106

0.0106

0.0103

0.0096

0.0101

C

 

0.0093

0.0101

0.0109

0.0108

0.0104

0.0101

0.0109

D

 

0.0121

0.0101

0.0098

0.0093

0.0093

0.0095

0.0105

E

 

0.0098

0.0094

0.0101

0.0093

0.0092

0.0083

0.0114

F

 

0.0109

0.0095

0.0106

0.0109

0.0102

0.0102

0.0109

G

 

0.0100

0.0094

0.0105

0.0114

0.0103

0.0111

0.0093

H

 

0.0087

0.0111

0.0104

0.0099

0.0103

0.0117

0.0107

  1. A : R = (150, 150, 200), S = (300, 300, 400), P = (0.1, 0.3, 0.5), K = (0.01, 0.05, 0.02)
  2. B : R = (100, 300, 100), S = (200, 600, 200), P = (0.1, 0.3, 0.5), K = (0.01, 0.05, 0.02)
  3. C : R = (300, 300, 400), S = (300, 300, 400), P = (0.1, 0.3, 0.5), K = (0.01, 0.05, 0.02)
  4. D : R = (200, 600, 200), S = (200, 600, 200), P = (0.1, 0.3, 0.5), K = (0.01, 0.05, 0.02)
  5. E : R = (250, 250), S = (500, 500), P = (0.2, 0.4), K = (0.01, 0.02)
  6. F : R = (150, 350), S = (300, 700), P = (0.2, 0.4), K = (0.01, 0.02)
  7. G : R = (500, 500), S = (500, 500), P = (0.2, 0.4), K = (0.01, 0.02)
  8. H : R = (300, 700), S = (300, 700), P = (0.2, 0.4), K = (0.01, 0.02)