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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.