Defining an Optimal Cut-Point Value in ROC Analysis: An Alternative Approach

Table 7

Relative bias and mean square error (MSE) of all methods. The gamma balanced scenario.

					Sample sizes	Minimum value		Youden index		Concordance probability		Point closest-to-(0-1); corner		Index of Union
						Relative bias	MSE	Relative bias	MSE	Relative bias	MSE	Relative bias	MSE	Relative bias	MSE
0.80	1.12	1.35	1.38	1.42	50	0.4290	0.5491	0.0862	0.2095	0.0174	0.0713	0.0100	0.0521	0.0243	0.0133
					100	0.2735	0.3001	0.0565	0.1321	0.0126	0.0464	0.0016	0.0314	0.0195	0.0078
					200	0.1934	0.1813	0.0395	0.0885	0.0116	0.0305	0.0024	0.0211	0.0156	0.0065
1.73	1.79	1.81	1.82	1.78	50	0.0735	0.4727	0.0269	0.2260	0.0168	0.1108	0.0160	0.0648	0.0365	0.0401
					100	0.0454	0.3347	0.0229	0.1328	0.0099	0.0655	0.0126	0.0385	0.0272	0.0303
					200	0.0361	0.2276	0.0248	0.0932	0.0034	0.0439	0.0084	0.0248	0.0249	0.0282
2.54	2.45	2.41	2.36	2.41	50	0.0099	0.4109	−0.0262	0.2420	0.0064	0.1607	0.0099	0.0919	−0.0087	0.0840
					100	−0.0073	0.2771	−0.0245	0.1554	−0.0108	0.1103	−0.0006	0.0553	−0.0100	0.0699
					200	0.0042	0.1955	−0.0170	0.1107	−0.0094	0.0695	−0.0037	0.0343	0.0026	0.0600
3.51	3.42	3.38	3.24	3.30	50	−0.0206	0.4773	−0.0148	0.3108	−0.0061	0.2591	0.0171	0.1828	−0.0091	0.1859
					100	−0.0157	0.3061	−0.0066	0.2221	0.0004	0.1957	0.0127	0.1112	0.0064	0.1561
					200	−0.0214	0.2101	−0.0028	0.1463	0.0004	0.1291	0.0095	0.0599	0.0148	0.1107

~,   ~, and was taken as 0.79, 1.22, 1.97, and 3.82, respectively; for the true cut-points , , and , the results of Rota and Antolini’s were used; for the true cut-point , the objective function is maximized.