Defining an Optimal Cut-Point Value in ROC Analysis: An Alternative Approach
Table 8
Bootstrap standard deviation, coverage probability, and mean length of the 95% confidence interval estimation of all methods. The gamma balanced scenario.
Sample sizes
Minimum value
Youden index
Concordance probability
Point closest-to-(0-1) corner
Index of Union
Coverage
Mean length
Coverage
Mean length
Coverage
Mean length
Coverage
Mean length
Coverage
Mean length
0.80
1.12
1.35
1.38
1.41
50
0.6613
0.878
2.5752
0.4468
0.934
1.7152
0.2661
0.969
1.0299
0.2284
0.966
0.8804
0.1105
0.971
0.4336
100
0.5048
0.893
1.9022
0.3585
0.943
1.3967
0.2142
0.968
0.8394
0.1771
0.964
0.6805
0.0838
0.970
0.3202
200
0.3997
0.918
1.5638
0.2952
0.946
1.1355
0.1737
0.969
0.6829
0.1450
0.968
0.5751
0.0774
0.960
0.2872
1.73
1.79
1.81
1.82
1.74
50
0.6767
0.934
2.5512
0.4719
0.950
1.8199
0.3317
0.964
1.3298
0.2529
0.966
0.9481
0.1894
0.971
0.7289
100
0.5719
0.942
2.2325
0.3617
0.956
1.4270
0.2551
0.968
0.9812
0.1946
0.965
0.7422
0.1674
0.961
0.6163
200
0.4730
0.958
1.8935
0.3026
0.959
1.1626
0.2096
0.965
0.8076
0.1564
0.958
0.5983
0.1618
0.950
0.5822
2.54
2.45
2.41
2.36
2.48
50
0.6409
0.966
2.4846
0.4866
0.970
1.9271
0.4002
0.959
1.5788
0.3024
0.968
1.1684
0.2891
0.971
1.1234
100
0.5257
0.958
1.9721
0.3901
0.967
1.5215
0.3310
0.964
1.2616
0.2347
0.968
0.8941
0.2631
0.969
0.9996
200
0.4422
0.965
1.6817
0.3296
0.964
1.3089
0.2624
0.967
1.0213
0.1849
0.968
0.7279
0.2452
0.970
0.9433
3.51
3.42
3.38
3.24
3.37
50
0.6881
0.964
2.6282
0.5559
0.963
2.2071
0.5091
0.959
1.9967
0.4241
0.957
1.6429
0.4295
0.964
1.6911
100
0.5491
0.968
2.0911
0.4706
0.962
1.8332
0.4421
0.963
1.7384
0.3315
0.970
1.2972
0.3947
0.969
1.5351
200
0.4511
0.968
1.7641
0.3823
0.957
1.5002
0.3594
0.958
1.4143
0.2427
0.966
0.9504
0.3292
0.965
1.2568
~, ~, 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 empirically estimated objective function is maximized.
