Research Article

# Defining an Optimal Cut-Point Value in ROC Analysis: An Alternative Approach

## Table 7

Relative bias and mean square error (MSE) of all methods. The gamma balanced scenario.
 Sample sizes Minimum value Youden index Concordance probability Point closest-to-(0-1) corner Index of Union Relative bias MSE Relative bias MSE Relative bias MSE Relative bias MSE Relative bias MSE 0.80 1.12 1.35 1.38 1.42 50 0.4290 0.5491 0.0862 0.2095 0.0174 0.0713 0.0100 0.0521 0.0243 0.0133 100 0.2735 0.3001 0.0565 0.1321 0.0126 0.0464 0.0016 0.0314 0.0195 0.0078 200 0.1934 0.1813 0.0395 0.0885 0.0116 0.0305 0.0024 0.0211 0.0156 0.0065 1.73 1.79 1.81 1.82 1.78 50 0.0735 0.4727 0.0269 0.2260 0.0168 0.1108 0.0160 0.0648 0.0365 0.0401 100 0.0454 0.3347 0.0229 0.1328 0.0099 0.0655 0.0126 0.0385 0.0272 0.0303 200 0.0361 0.2276 0.0248 0.0932 0.0034 0.0439 0.0084 0.0248 0.0249 0.0282 2.54 2.45 2.41 2.36 2.41 50 0.0099 0.4109 −0.0262 0.2420 0.0064 0.1607 0.0099 0.0919 −0.0087 0.0840 100 −0.0073 0.2771 −0.0245 0.1554 −0.0108 0.1103 −0.0006 0.0553 −0.0100 0.0699 200 0.0042 0.1955 −0.0170 0.1107 −0.0094 0.0695 −0.0037 0.0343 0.0026 0.0600 3.51 3.42 3.38 3.24 3.30 50 −0.0206 0.4773 −0.0148 0.3108 −0.0061 0.2591 0.0171 0.1828 −0.0091 0.1859 100 −0.0157 0.3061 −0.0066 0.2221 0.0004 0.1957 0.0127 0.1112 0.0064 0.1561 200 −0.0214 0.2101 −0.0028 0.1463 0.0004 0.1291 0.0095 0.0599 0.0148 0.1107
~,   ~, and was taken as 0.79, 1.22, 1.97, and 3.82, respectively; for the true cut-points , , and , the results of Rota and Antolini’s were used; for the true cut-point , the objective function is maximized.

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