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Table 3 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 38%

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 0.1345 0.3419 0.1918 0.1514 0.1812 0.1099
    100 0.1347 0.2592 0.1042 0.0894 0.1225 0.0627
    200 0.0547 0.2084 0.0638 0.0572 0.0652 0.0413
    400 0.0932 0.1395 0.0177 0.0350 0.0200 0.0245
0.4 0.49 0.52 50 0.0912 0.2147 0.0829 0.1303 0.0624 0.0891
    100 0.0595 0.1418 0.0460 0.0841 0.0438 0.0518
    200 0.0106 0.1039 0.0082 0.0541 0.0024 0.0339
    400 0.0085 0.0641 −0.0021 0.0314 0.0009 0.0173
0.6 0.64 0.84 50 0.0446 0.1596 0.0560 0.1262 0.0507 0.0890
    100 0.0628 0.1094 0.0599 0.0794 0.0492 0.0494
    200 0.0258 0.0653 0.0256 0.0492 0.0212 0.0260
    400 0.0042 0.0408 0.0052 0.0287 0.0012 0.0160
0.8 0.81 1.28 50 0.0461 0.1404 0.0435 0.1340 0.0310 0.1186
    100 0.0449 0.0883 0.0411 0.0792 0.0282 0.0587
    200 0.0132 0.0503 0.0108 0.0462 0.0073 0.0297
    400 0.0039 0.0367 0.0041 0.0323 0.0030 0.0185
  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.