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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(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.