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

Table 3

Relative bias and mean square error (MSE) of all methods. The normal homoscedastic 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. 25	50	0.0080	0.5622	0.3088	0.2358	0.0432	0.0696	0.0357	0.0513	0.0306	0.0191
	100	0.1303	0.4604	0.3129	0.1675	0.0588	0.0428	0.0526	0.0315	0.0505	0.0116
	200	−0.0174	0.3652	0.1510	0.1158	0.0145	0.0259	0.0221	0.0195	0.0262	0.0074
0.52	50	0.0068	0.2307	0.1161	0.1266	0.0066	0.0676	0.0112	0.0427	0.0172	0.0265
	100	−0.0314	0.1752	0.0732	0.0783	0.0072	0.0392	0.0084	0.0258	0.0035	0.0201
	200	−0.0073	0.1190	0.0438	0.0490	0.0078	0.0242	0.0119	0.0145	0.0109	0.0153
0.84	50	0.0040	0.1263	0.0563	0.0822	−0.0026	0.0557	−0.0038	0.0369	−0.0016	0.0341
	100	0.0140	0.0839	0.0476	0.0538	0.0023	0.0372	0.0024	0.0219	0.0020	0.0268
	200	−0.0036	0.0631	0.0282	0.0362	0.0039	0.0237	0.0029	0.0128	0.0042	0.0214
1.28	50	0.0011	0.0872	0.0292	0.0676	0.0015	0.0563	0.0032	0.0410	0.0033	0.0467
	100	0.0018	0.0558	0.0269	0.0444	0.0025	0.0368	0.0029	0.0245	0.0030	0.0336
	200	−0.0028	0.0343	0.0170	0.0248	0.0017	0.0205	0.0013	0.0119	0.0021	0.0200

,  , and was taken as 0.51, 1.05, 1.68, and 2.56, respectively.