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.