BMC Medical Research Methodology

Table 5 Relative Bias and Mean Square Error (MSE) of the cut-point in the Gamma scenario ^† with diseased and disease-free fraction 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_J	c_CZ	c_ER	N	Relative bias	MSE	Relative bias	MSE	Relative bias	MSE
0.2	0.36	1.12	1.35	1.38	50	0.2038	0.3822	0.0532	0.1584	0.0464	0.1235
					100	0.1605	0.2987	0.0429	0.0975	0.0352	0.0712
					200	0.0840	0.1825	0.0138	0.0638	0.0087	0.0446
					400	0.0668	0.1156	0.0105	0.0348	0.0086	0.0261
0.4	0.49	1.79	1.81	1.82	50	0.0863	0.4446	0.0605	0.2700	0.0473	0.1771
					100	0.0460	0.2585	0.0408	0.1529	0.0311	0.1001
					200	0.0267	0.1740	0.0136	0.0924	0.0059	0.0521
					400	0.0144	0.1183	0.0133	0.0571	0.0062	0.0346
0.6	0.64	2.45	2.41	2.36	50	0.0391	0.5201	0.0411	0.4108	0.0383	0.2741
					100	0.0297	0.3288	0.0293	0.2380	0.0267	0.1536
					200	0.0186	0.2117	0.0170	0.1539	0.0138	0.0815
					400	0.0067	0.1433	0.0077	0.0941	0.0081	0.0445
0.8	0.81	3.42	3.38	3.24	50	0.0610	0.9808	0.0663	0.9103	0.0782	0.7477
					100	0.0526	0.5678	0.0508	0.5156	0.0429	0.3593
					200	0.0210	0.3317	0.0241	0.3039	0.0166	0.1739
					400	0.0090	0.1929	0.0107	0.1693	0.0079	0.0885

^†X_Z ≤ τ ~ G(2.5, β_Z ≤ τ), X_Z >τ ~ G(1.5, 1). ^‡The levels of J and CZ are achieved by β_Z ≤ τ = 0.79, 1.22, 1.97, 3.82, respectively.

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