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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.