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. Author manuscript; available in PMC: 2015 Jan 27.
Published in final edited form as: J Biopharm Stat. 2014;24(3):608–633. doi: 10.1080/10543406.2014.888437

Table IV.

Relative bias, standard deviation and root mean squared error (RMSE) for the optimality statistics (V3, J3 and D3) associated with each selection approach

Scenario True Optimality
Statistic		 Relative Bias Standard Deviation RMSE
n=m=k=20 n=m=k=40 n=m=k=80 n=50, m=35,
k=25		 n=m=k=20 n=m=k=40 n=m=k=80 n=50, m=35,
k=25		 n=m=k=20 n=m=k=40 n=m=k=80 n=50, m=35,
k=25
1 Youden: 1.766 0.0104 −0.0023 −0.0036 0.0013 0.1357 0.1016 0.0737 0.1081 0.1369 0.1017 0.0740 0.1082
CP: 0.725 0.0121 0.0206 0.0153 0.0159 0.0870 0.0643 0.0465 0.0688 0.0874 0.0661 0.0479 0.0697
Volume: 0.197 0.0029 −0.0260 −0.0229 −0.0137 0.0536 0.0379 0.0274 0.0406 0.0537 0.0383 0.0278 0.0407
2 Youden: 1.395 0.0365 0.0159 0.0064 0.0220 0.1435 0.1033 0.0761 0.1079 0.1523 0.1057 0.0766 0.1121
CP: 0.938 −0.0033 0.0015 0.0040 −0.0009 0.0880 0.0627 0.0461 0.0669 0.0881 0.0627 0.0462 0.0669
Volume: 0.096 0.0460 0.0107 −0.0046 0.0234 0.0347 0.0239 0.0170 0.0256 0.0350 0.0240 0.0170 0.0257
3 Youden: 1.501 0.0199 0.0126 0.0044 0.0106 0.1512 0.1100 0.0818 0.1174 0.1541 0.1116 0.0820 0.1184
CP: 0.876 0.0017 0.0000 0.0033 0.0031 0.0910 0.0657 0.0490 0.0707 0.0910 0.0657 0.0491 0.0707
Volume: 0.121 0.0254 0.0147 −0.0033 0.0076 0.0404 0.0288 0.0215 0.0308 0.0405 0.0289 0.0215 0.0308
4 Youden: 1.966 −0.0015 −0.0055 −0.0075 −0.0039 0.1384 0.0997 0.0732 0.1099 0.1384 0.1003 0.0746 0.1102
CP: 0.615 0.0297 0.0252 0.0220 0.0241 0.0882 0.0636 0.0467 0.0693 0.0901 0.0655 0.0486 0.0709
Volume: 0.271 −0.0182 −0.0262 −0.0288 −0.0215 0.0637 0.0459 0.0344 0.0506 0.0639 0.0464 0.0353 0.0510
5 Youden: 2.039 0.0032 −0.0045 −0.0047 −0.0060 0.1334 0.0975 0.0709 0.0998 0.1336 0.0979 0.0716 0.1005
CP = 0.589 0.0103 0.0174 0.0126 0.0171 0.0871 0.0631 0.0452 0.0622 0.0873 0.0639 0.0458 0.0630
Volume: 0.299 0.0029 −0.0182 −0.0163 −0.0191 0.0682 0.0483 0.0347 0.0481 0.0682 0.0486 0.0351 0.0485
6 Youden: 1.833 0.0037 0.0030 0.0021 0.0041 0.1452 0.0992 0.0710 0.1105 0.1453 0.0994 0.0711 0.1108
CP: 0.789 −0.0229 −0.0221 −0.0199 −0.0247 0.1000 0.0702 0.0504 0.0809 0.1016 0.0723 0.0528 0.0832
Volume: 0.174 0.0761 0.0601 0.0491 0.0693 0.0618 0.0426 0.0305 0.0496 0.0632 0.0439 0.0317 0.0510

The samples sizes for the healthy, transitional and diseased populations are given by n, m, and k respectively.

Youden = generalized Youden index, CP = closest to perfection, and Volume = max volume

The RMSE, relative bias and standard deviation estimates are as described in section 4.1.