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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(copt) CZ(copt) cJ cCZ cER 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
  1. XZ ≤ τ ~ G(2.5, βZ ≤ τ), XZ >τ ~ G(1.5, 1). The levels of J and CZ are achieved by βZ ≤ τ = 0.79, 1.22, 1.97, 3.82, respectively.