TABLE 2.

Average of Binormal AUC and Empirical Standard Errors for Both Binormal and Empirical AUCs Based on 10,000 Datasets Generated for Each Scenario

Sample Size	Number of Categories	True AUC	κ = 0.1 (Highly Non-binormal)			κ= 0.33			κ = 3 (Binormal-like)
			Monte Carlo Estimates for AUC for the Fitted Binormal ROC		STD of Empirical AUC* for Continuous Data	Monte Carlo Estimates for AUC for the Fitted Binormal ROC		STD of Empirical AUC* for Continuous Data	Monte Carlo Estimates for AUC for the Fitted Binormal ROC		STD of Empirical AUC* for Continuous Data
			AUC	STD		AUC	STD		AUC	STD
100:100	10	0.6	0.61	0.040	0.040	0.61	0.042	0.040	0.61	0.044	0.040
		0.7	0.71	0.036	0.037	0.70	0.036	0.037	0.70	0.038	0.037
		0.8	0.81	0.032	0.032	0.80	0.032	0.032	0.80	0.032	0.031
		0.9	0.89	0.029	0.025	0.89	0.028	0.024	0.90	0.024	0.022
50:50	10	0.6	0.61	0.055	0.056	0.61	0.058	0.057	0.61	0.060	0.056
		0.7	0.71	0.051	0.053	0.71	0.052	0.052	0.70	0.053	0.052
		0.8	0.81	0.045	0.046	0.80	0.046	0.045	0.80	0.045	0.044
		0.9	0.89	0.041	0.035	0.89	0.039	0.033	0.90	0.034	0.031
100:100	5	0.6	0.60	0.041	0.040	0.60	0.041	0.040	0.60	0.041	0.040
		0.7	0.70	0.039	0.037	0.70	0.039	0.037	0.70	0.039	0.037
		0.8	0.79	0.038	0.032	0.79	0.037	0.032	0.80	0.035	0.031
		0.9	0.87	0.040	0.025	0.85	0.039	0.024	0.89	0.033	0.022
50:50	5	0.6	0.60	0.058	0.056	0.60	0.059	0.057	0.60	0.058	0.056
		0.7	0.70	0.055	0.053	0.70	0.056	0.052	0.70	0.056	0.052
		0.8	0.79	0.055	0.046	0.79	0.053	0.045	0.80	0.050	0.044
		0.9	0.89	0.058	0.035	0.85	0.056	0.033	0.88	0.050	0.031

AUC, area under the ROC curve; ROC, receiver operating characteristic.

^*The empirical AUC was computed for continuous data and therefore is theoretically unbiased; the negligibly small empirical bias was not shown for brevity.