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Table 1 Simulation results for n=500, prevalence at 20%.

From: One statistical test is sufficient for assessing new predictive markers

μ*

μ

Test

ρ=0.0

ρ=0.1

ρ=0.3

ρ=0.5

0.0

0.0

LRT

0.050

0.048

0.053

0.055

  

Wald

0.048

0.045

0.052

0.053

  

AUC

0.004

0.004

0.006

0.003

 

0.1

LRT

0.059

0.057

0.053

0.052

  

Wald

0.057

0.055

0.052

0.051

  

AUC

0.003

0.004

0.002

0.005

 

0.2

LRT

0.048

0.054

0.055

0.049

  

Wald

0.045

0.051

0.054

0.047

  

AUC

0.002

0.004

0.001

0.000

 

0.3

LRT

0.043

0.059

0.052

0.054

  

Wald

0.043

0.056

0.051

0.051

  

AUC

0.002

0.001

0.000

0.002

0.1

0.0

LRT

0.217

0.196

0.215

0.259

  

Wald

0.211

0.191

0.213

0.253

  

AUC

0.027

0.025

0.040

0.043

 

0.1

LRT

0.191

0.218

0.232

0.239

  

Wald

0.187

0.212

0.226

0.237

  

AUC

0.027

0.024

0.029

0.035

 

0.2

LRT

0.199

0.203

0.198

0.253

  

Wald

0.196

0.196

0.195

0.249

  

AUC

0.021

0.015

0.019

0.022

 

0.3

LRT

0.179

0.205

0.200

0.259

  

Wald

0.178

0.205

0.199

0.253

  

AUC

0.011

0.013

0.012

0.018

0.2

0.0

LRT

0.613

0.615

0.646

0.738

  

Wald

0.607

0.613

0.643

0.734

  

AUC

0.196

0.195

0.229

0.294

 

0.1

LRT

0.614

0.621

0.650

0.736

  

Wald

0.611

0.618

0.644

0.729

  

AUC

0.167

0.178

0.203

0.272

 

0.2

LRT

0.604

0.620

0.640

0.740

  

Wald

0.600

0.616

0.637

0.735

  

AUC

0.121

0.121

0.141

0.205

 

0.3

LRT

0.595

0.623

0.641

0.696

  

Wald

0.590

0.620

0.637

0.692

  

AUC

0.096

0.098

0.111

0.153

0.3

0.0

LRT

0.908

0.926

0.942

0.970

  

Wald

0.908

0.925

0.941

0.969

  

AUC

0.581

0.586

0.622

0.745

 

0.1

LRT

0.918

0.915

0.939

0.973

  

Wald

0.916

0.913

0.936

0.972

  

AUC

0.533

0.539

0.592

0.699

 

0.2

LRT

0.910

0.925

0.933

0.971

  

Wald

0.908

0.922

0.931

0.970

  

AUC

0.414

0.432

0.496

0.627

 

0.3

LRT

0.905

0.900

0.937

0.972

  

Wald

0.903

0.898

0.936

0.970

  

AUC

0.359

0.362

0.423

0.520

  1. Entries in the table show the power (for μ* > 0) and the test size (for μ*=0) for the likelihood ratio (LRT) and Wald tests from logistic regression and the Delong et al. test comparing the AUCs. Correlation of the new marker and the existing marker, conditional on the outcome, is represented by ρ.