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Table 2 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 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) copt N Relative bias MSE Relative bias MSE Relative bias MSE
0.2 0.36 0.25 50 0.1327 0.3204 0.1582 0.1366 0.1498 0.0983
    100 0.1172 0.2448 0.1078 0.0798 0.1016 0.0565
    200 0.0777 0.1951 0.0796 0.0525 0.0561 0.0388
    400 0.1123 0.1196 0.0541 0.0304 0.0408 0.0214
0.4 0.49 0.52 50 0.0728 0.2029 0.0740 0.1202 0.0739 0.0793
    100 0.0490 0.1332 0.0327 0.0771 0.0339 0.0489
    200 0.0200 0.0946 0.0101 0.0522 0.0031 0.0294
    400 0.0042 0.0573 0.0037 0.0274 0.0075 0.0157
0.6 0.64 0.84 50 0.0651 0.1446 0.0589 0.1182 0.0477 0.0817
    100 0.0491 0.0947 0.0428 0.0428 0.0355 0.0355
    200 0.0185 0.0605 0.0237 0.0447 0.0192 0.0237
    400 0.0058 0.0367 0.0055 0.0255 0.0004 0.0148
0.8 0.81 1.28 50 0.0514 0.1236 0.0523 0.1158 0.0473 0.0990
    100 0.0384 0.0786 0.0373 0.0722 0.0299 0.0505
    200 0.0149 0.0464 0.0140 0.0401 0.0081 0.0259
    400 0.0053 0.0314 0.0064 0.0271 0.0024 0.0158
  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.