# 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%

Youden index Concordance probability Point closest-to-(0,1) corner
J(copt) CZ(copt) copt 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
1. XZ ≤ τ ~ N(μZ ≤ τ, 1), XZ >τ ~ N(0, 1). The levels of J and CZ are achieved by μZ ≤ τ = 0.51, 1.05, 1.68, 2.56, respectively.