BMC Medical Research Methodology

Table 2 Relative bias and Mean Square Error (MSE) of the cut-point in the normal homoscedastic scenario ^† with diseased and disease-free fractions of 50% and a censoring level of 25%

From: Optimal cut-point definition in biomarkers: the case of censored failure time outcome

				Youden index		Concordance probability		Point closest-to-(0,1) corner
J(c_opt)^‡	CZ(c_opt)^‡	c_opt	N	Relative bias	MSE	Relative bias	MSE	Relative bias	MSE
0.2	0.36	0.25	50	0.1327	0.3204	0.1582	0.1366	0.1498	0.0983
			100	0.1172	0.2448	0.1078	0.0798	0.1016	0.0565
			200	0.0777	0.1951	0.0796	0.0525	0.0561	0.0388
			400	0.1123	0.1196	0.0541	0.0304	0.0408	0.0214
0.4	0.49	0.52	50	0.0728	0.2029	0.0740	0.1202	0.0739	0.0793
			100	0.0490	0.1332	0.0327	0.0771	0.0339	0.0489
			200	0.0200	0.0946	0.0101	0.0522	0.0031	0.0294
			400	0.0042	0.0573	0.0037	0.0274	0.0075	0.0157
0.6	0.64	0.84	50	0.0651	0.1446	0.0589	0.1182	0.0477	0.0817
			100	0.0491	0.0947	0.0428	0.0428	0.0355	0.0355
			200	0.0185	0.0605	0.0237	0.0447	0.0192	0.0237
			400	0.0058	0.0367	0.0055	0.0255	0.0004	0.0148
0.8	0.81	1.28	50	0.0514	0.1236	0.0523	0.1158	0.0473	0.0990
			100	0.0384	0.0786	0.0373	0.0722	0.0299	0.0505
			200	0.0149	0.0464	0.0140	0.0401	0.0081	0.0259
			400	0.0053	0.0314	0.0064	0.0271	0.0024	0.0158

^†X_Z ≤ τ ~ N(μ_Z ≤ τ, 1), X_Z >τ ~ N(0, 1). ^‡The levels of J and CZ are achieved by μ_Z ≤ τ = 0.51, 1.05, 1.68, 2.56, respectively.

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