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Table 3 Results using the Braun and Gumbel copulas for data simulation under Scenario 2

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 0.147 0.748 0.094 0.011 0
     33.159 5.922 0.798 0.042
   Gumbel 0.13 0.732 0.121 0.016 0.001
     32.652 6.984 1.161 0.084
   Indep 0.129 0.770 0.093 0.008 0
     34.542 5.826 0.825 0.063
  0.7 Braun 0.16 0.744 0.091 0.005 0
     32.919 6.315 0.645 0.039
   Gumbel 0.106 0.761 0.117 0.016 0
     34.059 6.762 0.81 0.09
   Indep 0.098 0.781 0.109 0.012 0
     34.671 6.516 0.705 0.09
  0.9 Braun 0.204 0.707 0.086 0.003 0
     31.878 6.18 0.396 0.018
   Gumbel 0.071 0.799 0.114 0.015 0.001
     34.977 7.2 0.63 0.063
   Indep 0.095 0.773 0.122 0.009 0.001
     34.329 6.789 0.795 0.078
Gumbel 0 Braun 0.14 0.722 0.126 0.012 0
     32.889 6.69 0.756 0.051
   Gumbel 0.124 0.745 0.122 0.008 0.001
     33.714 6.564 0.786 0.069
   Indep 0.13 0.751 0.111 0.007 0.001
     33.585 6.465 0.738 0.099
  0.4 Braun 0.159 0.741 0.09 0.009 0.001
     33.39 5.886 0.96 0.066
   Gumbel 0.127 0.755 0.1 0.016 0.002
     33.882 6.234 1.02 0.09
   Indep 0.118 0.758 0.113 0.011 0
     33.36 7.059 0.927 0.036
  0.8 Braun 0.16 0.742 0.094 0.004 0
     32.991 6.048 0.534 0.06
   Gumbel 0.081 0.799 0.104 0.014 0.002
     35.247 6.657 0.84 0.048
   Indep 0.113 0.76 0.118 0.009 0
     34.068 6.528 0.801 0.081
  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.