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. Author manuscript; available in PMC: 2020 Aug 27.
Published in final edited form as: J Am Stat Assoc. 2017 Jul 13;112(518):508–520. doi: 10.1080/01621459.2016.1228534

Table 2:

Selection percentage for each dose and the percentage of correct selection (PCS) for two representative biomarker patterns under each scenario. The numbers in boldface are target doses.

Dose level
 Percentage of correct selection
1 2 3 4 5
Scenario 1
X = (+ + + + +)
P(YT = 3) 0.100 0.229 0.419 0.631 0.809
P(YE = 2) 0.197 0.117 0.052 0.017 0.004
P(YE = 3) 0.773 0.875 0.946 0.982 0.996
True utility 54.39 49.50 42.49 34.48 27.57
Sel % Proposed 0.720 0.139 0.069 0.031 0.037 0.859
     Direct approach 0.524 0.144 0.124 0.076 0.132 0.668
     Dose-only 0.198 0.196 0.196 0.228 0.182 0.394
X = (− − − − +)
P(YT = 3) 0.051 0.071 0.096 0.126 0.164
P(YE = 2) 0.407 0.393 0.331 0.236 0.142
P(YE = 3) 0.183 0.099 0.043 0.015 0.004
True utility 25.75 18.72 13.20 9.38 6.93
Sel % Proposed 0.923 0.000 0.001 0.001 0.062 0.923
     Direct approach 0.572 0.008 0.008 0.013 0.399 0.572
     Dose-only 0.198 0.196 0.196 0.228 0.182 0.198
Scenario 2
X = (+ + + + +)
P(YT = 3) 0.003 0.005 0.009 0.015 0.023
P(YE = 2) 0.069 0.173 0.210 0.177 0.128
P(YE = 3) 0.002 0.032 0.131 0.257 0.357
True utility 11.78 17.48 26.16 34.11 38.98
Sel % Proposed 0.046 0.010 0.035 0.143 0.762 0.762
    Direct approach 0.024 0.003 0.020 0.058  0.893 0.893
    Dose-only 0.176 0.182 0.208 0.258 0.176 0.176
X = (− − − − +)
P(YT = 3) 0.005 0.019 0.059 0.149 0.301
P(YE = 2) 0.467 0.333 0.238 0.170 0.120
P(YE = 3) 0.421 0.533 0.585 0.600 0.596
True utility 60.63 59.49 53.11 44.22 34.96
Sel % Proposed 0.421 0.139 0.125 0.106 0.208 0.560
     Direct approach 0.424 0.224 0.222 0.089 0.041 0.648
     Dose-only 0.176 0.182 0.208 0.258 0.176 0.358
Scenario 3
X = (+ + + + −)
P(YT = 3) 0.000 0.000 0.001 0.009 0.056
P(YE = 2) 0.148 0.243 0.239 0.184 0.129
P(YE = 3) 0.005 0.056 0.168 0.286 0.373
True utility 16.38 24.57 33.56 38.57 37.11
Sel % Proposed 0.083 0.032 0.164 0.332 0.387 0.719
     Direct approach 0.078 0.005 0.091 0.453 0.371 0.824
     Dose-only 0.224 0.226 0.160 0.196 0.194 0.390
X = (+ + − + +)
P(YT = 3) 0.000 0.002 0.014 0.075 0.250
P(YE = 2) 0.517 0.401 0.259 0.170 0.116
P(YE = 3) 0.115 0.359 0.529 0.604 0.627
True utility 40.67 55.91 59.59 52.29 39.77
Sel % Proposed 0.303 0.319 0.275 0.087 0.016 0.594
     Direct approach 0.204 0.378 0.370 0.046 0.002 0.748
     Dose-only 0.224 0.226 0.160 0.196 0.194 0.386
Scenario 4
X = (+ + + + −)
P(YT = 3) 0.027 0.031 0.035 0.040 0.045
P(YE = 2) 0.416 0.507 0.391 0.187 0.056
P(YE = 3) 0.148 0.296 0.554  0.803  0.943
True utility 27.31 40.12 55.81 68.18 74.18
Sel % Proposed 0.001 0.003 0.009 0.107 0.880 0.987
     Direct approach 0.000 0.002 0.012 0.122 0.864 0.986
     Dose-only 0.118 0.186 0.216 0.242 0.238 0.480
X = (+ + − + +)
P(YT = 3) 0.040 0.091 0.177 0.300 0.458
P(YE = 2) 0.444 0.295 0.078 0.009 0.000
P(YE = 3) 0.350 0.672 0.920 0.991  1.000
True utility 40.89 53.29 57.07 51.68 43.60
Sel % Proposed 0.025 0.100 0.378 0.308 0.189 0.786
     Direct approach 0.001 0.000 0.037 0.184 0.778 0.221
     Dose-only 0.118 0.186 0.216 0.242 0.238 0.644
Scenario 5
X = (− − − − −)
P(YT = 3) 0.025 0.017 0.011 0.007 0.004
P(YE = 2) 0.407 0.393 0.331 0.236 0.142
P(YE = 3) 0.183 0.099 0.043 0.015 0.004
True utility  28.86 23.83 19.10 15.20 12.37
Sel % Proposed 0.824 0.003 0.000 0.000 0.159 0.824
     Direct approach 0.324 0.004 0.008 0.009 0.655 0.324
     Dose-only 0.200 0.210 0.208 0.166 0.216 0.200
X = (− − − + −)
P(YT = 3) 0.026 0.018 0.012 0.008 0.006
P(YE = 2) 0.427 0.464 0.485 0.485 0.465
P(YE = 3) 0.319 0.341 0.374 0.417 0.471
True utility 39.00 43.36 48.36 53.77 59.36
Sel % Proposed 0.067 0.009 0.003 0.002 0.919 0.921
     Direct approach 0.324 0.004 0.008 0.009 0.655 0.664
     Dose-only 0.200 0.210 0.208 0.166 0.216 0.382
Scenario 6
X = (− − − − −)
P(YT = 3) 0.022 0.025 0.028 0.032 0.036
P(YE = 2) 0.394 0.484 0.534 0.535 0.492
P(YE = 3) 0.122 0.143 0.203 0.293 0.402
True utility 25.73 29.01 34.31 40.43 46.73
Sel % Proposed 0.156 0.002 0.003 0.003 0.836 0.836
     Direct approach 0.152 0.003 0.006 0.015 0.824 0.824
     Dose-only 0.176 0.184 0.218 0.209 0.213 0.213
X = (− − − + −)
P(YT = 3) 0.035 0.040 0.045 0.050 0.057
P(YE = 2) 0.394 0.484 0.534 0.535 0.492
P(YE = 3) 0.122 0.143 0.203 0.293 0.402
True utility 23.74 26.64 31.52 37.28  43.26
Sel % Proposed 0.212 0.001 0.003 0.003 0.781 0.781
    Direct approach 0.152 0.003 0.006 0.015 0.824 0.824
    Dose-only 0.176 0.184 0.218 0.209 0.213 0.213
X = (+ + + + +)
P(YT = 3) 0.000 0.000 0.001 0.009 0.054
P(YE = 2) 0.419 0.295 0.178 0.116 0.081
P(YE = 3) 0.399 0.229 0.187 0.195 0.226
True utility  62.59 42.16 32.89 28.78 25.36
Sel % Proposed 0.701 0.020 0.034 0.028 0.154 0.701
     Direct approach 0.748 0.040 0.0586 0.0438 0.0913 0.748
     Dose-only 0.286 0.104 0.058 0.091 0.176 0.286
X = (+ − − + −)
P(YT = 3) 0.000 0.002 0.014 0.073 0.247
P(YE = 2) 0.000 0.000 0.000 0.001 0.008
P(YE = 3) 0.000 0.000 0.000 0.000 0.010
True utility 9.93 9.60 8.64 6.92 5.34
Sel % Proposed 0.010 0.000 0.000 0.008 0.038 0.944
     Direct approach 0.283 0.020 0.023 0.043 0.114 0.519
     Dose-only 0.286 0.104 0.058 0.091 0.176 0.285
Scenario 8
X = (+ + − − −)
P(YT = 3) 0.081 0.056 0.037 0.024 0.016
P(YE = 2) 0.287 0.333 0.368 0.386 0.385
P(YE = 3) 0.094 0.140 0.199 0.271 0.355
True utility 22.09 28.64 36.23 44.55 53.16
Sel % Proposed 0.066 0.008 0.008 0.002 0.830 0.830
     Direct approach 0.065 0.000 0.000 0.005 0.733 0.733
     Dose-only 0.153 0.063 0.075 0.175 0.353 0.353
 X = (+ + − + −)
P(YT = 3) 0.081 0.056 0.037 0.024 0.016
P(YE = 2) 0.002 0.004 0.009 0.016 0.027
P(YE = 3) 0.000 0.000 0.000 0.001 0.002
True utility 7.88 8.44 9.00 9.61 10.38
Sel % Proposed 0.012 0.004 0.000 0.002 0.076 0.906
     Direct approach 0.065 0.000 0.000 0.005 0.733 0.198
     Dose-only 0.153 0.063 0.075 0.175 0.353 0.181