Table 1

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

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


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.

Vickers et al. BMC Medical Research Methodology 2011 11:13   doi:10.1186/1471-2288-11-13

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