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Table 5 Results using the Braun and Gumbel copulas for data simulation under Scenario 4

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 0.023 0.003 0.057 0.665 0.252
     3.42 6.39 23.19 11.268
   Gumbel 0.015 0.001 0.055 0.683 0.246
     3.402 7.041 23.358 10.809
   Indep 0.017 0.003 0.078 0.621 0.281
     3.351 7.071 22.74 11.304
  0.7 Braun 0.02 0.001 0.057 0.684 0.238
     3.333 6.849 24.066 10.146
   Gumbel 0.019 0.003 0.069 0.671 0.238
     3.39 7.107 23.286 10.68
   Indep 0.01 0.001 0.085 0.655 0.249
     3.39 7.593 22.854 10.875
  0.9 Braun 0.017 0.001 0.062 0.658 0.262
     3.303 6.996 23.376 10.839
   Gumbel 0.002 0 0.078 0.698 0.222
     3.315 7.476 23.46 10.695
   Indep 0.007 0.001 0.081 0.647 0.264
     3.543 7.743 22.329 11.172
Gumbel 0 Braun 0.027 0.002 0.064 0.664 0.243
     3.282 6.885 23.109 11.034
   Gumbel 0.027 0.001 0.065 0.657 0.25
     3.351 6.711 22.95 11.136
   Indep 0.025 0.002 0.084 0.633 0.256
     3.375 7.374 22.767 10.788
  0.4 Braun 0.025 0.002 0.066 0.631 0.276
     3.504 7.338 22.515 11.013
   Gumbel 0.021 0.002 0.074 0.655 0.248
     3.45 7.296 22.599 11.013
   Indep 0.013 0.001 0.069 0.649 0.268
     3.315 7.032 22.542 11.787
  0.8 Braun 0.012 0.002 0.063 0.65 0.273
     3.318 7.152 22.647 11.502
   Gumbel 0.019 0.001 0.075 0.669 0.236
     3.297 7.038 23.154 10.923
   Indep 0.013 0.004 0.075 0.673 0.235
     3.33 7.389 23.172 10.755
  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.