Computational and Mathematical Methods in Medicine / 2017 / Article / Tab 7

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 sizesMinimum valueYouden indexConcordance probabilityPoint closest-to-(0-1)
corner
Index of Union
Relative biasMSERelative biasMSERelative biasMSERelative biasMSERelative biasMSE

0.801.121.351.381.42500.42900.54910.08620.20950.01740.07130.01000.05210.02430.0133
1000.27350.30010.05650.13210.01260.04640.00160.03140.01950.0078
2000.19340.18130.03950.08850.01160.03050.00240.02110.01560.0065

1.731.791.811.821.78500.07350.47270.02690.22600.01680.11080.01600.06480.03650.0401
1000.04540.33470.02290.13280.00990.06550.01260.03850.02720.0303
2000.03610.22760.02480.09320.00340.04390.00840.02480.02490.0282

2.542.452.412.362.41500.00990.4109−0.02620.24200.00640.16070.00990.0919−0.00870.0840
100−0.00730.2771−0.02450.1554−0.01080.1103−0.00060.0553−0.01000.0699
2000.00420.1955−0.01700.1107−0.00940.0695−0.00370.03430.00260.0600

3.513.423.383.243.3050−0.02060.4773−0.01480.3108−0.00610.25910.01710.1828−0.00910.1859
100−0.01570.3061−0.00660.22210.00040.19570.01270.11120.00640.1561
200−0.02140.2101−0.00280.14630.00040.12910.00950.05990.01480.1107

~,   ~, 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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