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Table 2 Results using the Braun and Gumbel copulas for data simulation under Scenario 1

From: Evaluating the performance of copula models in phase I-II clinical trials under model misspecification

Data ψ k Model    Dose   
    Futility 1 2 3 4
Braun 0.5 Braun 0.039 0.045 0.212 0.475 0.229
     5.91 12.792 17.13 8.298
   Gumbel 0.038 0.039 0.225 0.482 0.216
     6.075 12.738 16.596 8.775
   Indep 0.037 0.046 0.223 0.504 0.19
     6 13.146 16.923 8.115
  0.7 Braun 0.037 0.034 0.197 0.514 0.218
     5.667 12.966 17.496 7.86
   Gumbel 0.023 0.032 0.235 0.524 0.186
     5.613 13.32 17.562 7.941
   Indep 0.033 0.035 0.219 0.528 0.185
     5.796 13.356 17.334 7.77
  0.9 Braun 0.024 0.018 0.208 0.514 0.236
     5.19 12.888 17.58 8.814
   Gumbel 0.011 0.037 0.225 0.538 0.189
     5.901 13.428 17.895 7.542
   Indep 0.006 0.041 0.226 0.526 0.201
     5.994 13.605 17.349 7.95
Gumbel 0 Braun 0.042 0.033 0.217 0.503 0.205
     6.054 12.786 17.007 8.373
   Gumbel 0.042 0.041 0.21 0.499 0.208
     6.033 12.651 17.094 8.28
   Indep 0.034 0.054 0.208 0.478 0.226
     6.591 12.447 16.671 8.622
  0.4 Braun 0.036 0.034 0.216 0.506 0.208
     5.871 12.828 17.157 8.322
   Gumbel 0.029 0.039 0.222 0.461 0.249
     5.775 13.287 16.029 9.081
   Indep 0.018 0.044 0.213 0.501 0.224
     5.946 12.81 17.205 8.67
  0.8 Braun 0.036 0.028 0.237 0.475 0.224
     5.886 13.875 16.119 8.307
   Gumbel 0.016 0.036 0.231 0.506 0.211
     5.877 13.182 17.34 8.22
   Indep 0.032 0.032 0.216 0.524 0.196
     5.388 13.242 17.616 8.079
  1. The first row is the selection probability for dose z; and the second is the average number of patients treated at dose z. Y T and Y S are simulated with association, ψ k ; k=1,2 when appropriate. The operating characteristics for the target dose are in bold.