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Table 6 Results using the Braun and Gumbel copulas for data simulation under Scenario 5

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 0.87 0.001 0.005 0.023 0.101
     4.086 4.59 4.62 11.946
   Gumbel 0.872 0 0.006 0.022 0.1
     4.05 4.44 4.896 11.316
   Indep 0.872 0.002 0.009 0.016 0.101
     4.176 4.656 4.803 11.319
  0.7 Braun 0.928 0 0.004 0.009 0.059
     4.065 4.209 4.56 10.095
   Gumbel 0.887 0.002 0.014 0.014 0.083
     3.936 4.485 4.869 11.748
   Indep 0.895 0.002 0.01 0.016 0.077
     4.254 4.467 4.596 11.256
  0.9 Braun 0.945 0.001 0.004 0.009 0.041
     4.053 4.29 4.566 9.531
   Gumbel 0.904 0.003 0.006 0.016 0.071
     4.248 4.701 5.148 11.091
   Indep 0.905 0 0.006 0.016 0.073
     4.227 4.608 5.196 11.22
Gumbel 0 Braun 0.895 0.001 0.011 0.01 0.083
     4.035 4.41 4.674 11.196
   Gumbel 0.878 0.003 0.008 0.015 0.096
     3.999 4.293 4.692 11.391
   Indep 0.897 0.001 0.007 0.014 0.081
     4.197 4.494 4.659 11.886
  0.4 Braun 0.898 0.002 0.01 0.013 0.077
     3.966 4.254 4.368 11.061
   Gumbel 0.901 0.001 0.004 0.021 0.073
     4.179 4.452 4.89 11.112
   Indep 0.892 0.004 0.006 0.018 0.08
     4.065 4.365 4.644 11.559
  0.8 Braun 0.913 0.003 0.005 0.013 0.066
     4.002 4.536 4.623 10.794
   Gumbel 0.925 0.002 0.005 0.013 0.055
     4.152 4.488 4.632 11.028
   Indep 0.897 0.003 0.006 0.012 0.082
     4.179 4.611 4.452 11.286
  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.