BMC Medical Research Methodology

Table 4 Relative bias and Mean Square Error (MSE) of the cut-point in the normal homoscedastic scenario ^† with different disease fractions 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	Disease fraction	Relative bias	MSE	Relative bias	MSE	Relative bias	MSE
0.2	0.36	0.25	100	15%	0.2296	0.3298	0.4150	0.1390	0.4114	0.1060
			150	33%	0.2188	0.2089	0.1921	0.0611	0.1749	0.0440
			200	25%	0.0973	0.2125	0.1758	0.0666	0.1822	0.0482
			250	20%	0.1872	0.1871	0.2246	0.0592	0.2164	0.0421
0.4	0.49	0.52	100	15%	0.1389	0.1944	0.2084	0.1320	0.2450	0.1051
			150	33%	0.0786	0.1048	0.0625	0.0575	0.0741	0.0370
			200	25%	0.0516	0.1147	0.0701	0.0606	0.0674	0.0381
			250	20%	0.0926	0.0990	0.0951	0.0528	0.0940	0.0346
0.6	0.64	0.84	100	15%	0.1457	0.1658	0.1503	0.1366	0.1765	0.1101
			150	33%	0.0522	0.0778	0.0547	0.0590	0.0453	0.0367
			200	25%	0.0500	0.0744	0.0516	0.0512	0.0515	0.0286
			250	20%	0.0543	0.0742	0.0585	0.0569	0.0596	0.0344
0.8	0.81	1.28	100	15%	0.1219	0.1534	0.1283	0.1478	0.1337	0.1274
			150	33%	0.0401	0.0702	0.0439	0.0645	0.0387	0.0432
			200	25%	0.0360	0.0568	0.0375	0.0513	0.0438	0.0364
			250	20%	0.0535	0.0641	0.0558	0.0585	0.0535	0.0390

^†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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