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Table 4 Results using the Braun and Gumbel copulas for data simulation under Scenario 3

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 Braun 0.195 0.001 0.004 0.045 0.755
     3.426 3.636 5.358 27.504
   Gumbel 0.174 0.001 0.005 0.042 0.778
     3.459 3.744 5.418 27.855
   Indep 0.149 0.001 0.003 0.035 0.812
     3.384 3.69 4.938 29.169
  0.4 Braun 0.162 0.001 0.005 0.025 0.807
     3.297 3.762 4.884 28.719
   Gumbel 0.139 0 0.003 0.042 0.816
     3.417 3.693 5.487 29.025
   Indep 0.13 0 0.003 0.049 0.818
     3.423 3.705 5.547 28.857
  0.8 Braun 0.143 0 0.002 0.033 0.822
     3.351 3.552 5.502 29.19
   Gumbel 0.101 0 0.002 0.037 0.86
     3.387 3.636 5.568 29.775
   Indep 0.093 0 0.002 0.04 0.865
     3.381 3.804 5.628 29.592
Gumbel 0 Braun 0.189 0.001 0.004 0.047 0.759
     3.327 3.585 5.31 27.942
   Gumbel 0.173 0 0.004 0.044 0.779
     3.336 3.675 5.313 28.224
   Indep 0.16 0.001 0 0.034 0.805
     3.435 3.789 5.172 28.434
  0.4 Braun 0.16 0 0.001 0.048 0.791
     3.45 3.63 5.61 28.101
   Gumbel 0.163 0 0.004 0.049 0.784
     3.363 3.666 5.49 28.164
   Indep 0.156 0 0.001 0.034 0.809
     3.405 3.591 4.977 28.875
  0.8 Braun 0.171 0.001 0.001 0.029 0.798
     3.342 3.645 5.25 28.116
   Gumbel 0.156 0.001 0.004 0.029 0.81
     3.384 3.702 5.262 28.776
   Indep 0.144 0 0.002 0.042 0.812
     3.342 3.804 5.484 28.824
  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.