BMC Medical Research Methodology

Table 1 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 12%

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	0.1613	0.3046	0.1503	0.1264	0.1854	0.0891
			100	0.1168	0.2226	0.0687	0.0719	0.0769	0.0513
			200	0.0696	0.1750	0.0546	0.0501	0.0589	0.0360
			400	0.0813	0.1137	0.0507	0.0273	0.0404	0.0199
0.4	0.49	0.52	50	0.0793	0.1870	0.0623	0.1158	0.0618	0.0785
			100	0.0584	0.1295	0.0346	0.0724	0.0356	0.0462
			200	0.0038	0.0870	0.0009	0.0462	0.0032	0.0279
			400	0.0073	0.0536	0.0070	0.0270	0.0100	0.0147
0.6	0.64	0.84	50	0.0724	0.1378	0.0599	0.1157	0.0555	0.0763
			100	0.0311	0.0884	0.0350	0.0675	0.0259	0.0421
			200	0.0147	0.0575	0.0201	0.0408	0.0152	0.0227
			400	0.0086	0.0332	0.0015	0.0240	−0.0009	0.0138
0.8	0.81	1.28	50	0.0568	0.1203	0.0531	0.1117	0.0528	0.0880
			100	0.0399	0.0727	0.0379	0.0669	0.0291	0.0465
			200	0.0167	0.0435	0.0149	0.0383	0.0115	0.0241
			400	0.0033	0.0290	0.0021	0.0253	0.0027	0.0148

^†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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