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. 2014 Apr 14;14:51. doi: 10.1186/1471-2288-14-51

Table 5.

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

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

The first row is the selection probability for dose z; and the second is the average number of patients treated at dose z. YT and YS are simulated with association, ψk; k=1,2 when appropriate. The operating characteristics for the target dose are in bold.