1. Design and Analysis of Group Sequential Clinical Trials and Software Development
Shuangge Ma, Michael R. Kosorok, Thomas D. Cook
Department of Biostatistics and Medical Informatics
University of Wisconsin-Madison
Pittsburgh, PA. March 30th, 2004
11/17/2018
Shuangge Ma, UW-Madison

2. Shuangge Ma, UW-Madison
Outline
Clinical trial with multiple endpoints: Copernicus.
Overall strategy:
Design of clinical trials with multiple endpoints.
Interim analysis of clinical trials.
Software development:
Design Copernicus with the software.
Interim analysis of the Copernicus trial.
Discussions and other considerations.
11/17/2018
Shuangge Ma, UW-Madison

3. Multivariate Clinical Trial: the Copernicus
Copernicus: a large-scale, prospective, randomized, double-blind, placebo-controlled trial.
Target: test the effect of the beta-blocker carvedilol on the survival of patients with severe heart failure.
Primary outcomes of interests:
All cause mortality,
The earliest time of mortality and hospitalization.
11/17/2018
Shuangge Ma, UW-Madison

4. Shuangge Ma, UW-Madison
Goal
Statistical goal:
Stop early if treatment effect is clear in all endpoints.
Control the many possible error rates.
Develop user-friendly software.
11/17/2018
Shuangge Ma, UW-Madison

5. Overall Strategy (Design)
Construct marginal critical boundaries with certain alpha/beta spending functions.
Construct an appropriate multivariate decision rule.
Adjust marginal critical boundaries to conform to a global alpha spending function.
11/17/2018
Shuangge Ma, UW-Madison

6. Overall Strategy (Interim Analysis)
At each interim analysis:
Compute the marginal critical regions based on the marginal alpha/beta spending functions and then take spatial product.
Adjust the spatial product to conform to the global alpha spending function.
Estimate the conditional distribution of the bivariate test statistic at the current look.
11/17/2018
Shuangge Ma, UW-Madison

7. Shuangge Ma, UW-Madison
Design the Copernicus
Design features:
Endpoint 1: = (Placebo)
= (treatment)
(t)=0.05*t, (t)=0.1*t.
Endpoint 2: =0.002 (Placebo)
= (treatment)
(t)=0.05*t, (t)=0.05*t.
Global: =0.05, =0.05.
Enrollment: 900 days, Follow up: 85 days.
11/17/2018
Shuangge Ma, UW-Madison

8. Software Development (Design the Copernicus)
Design of Group Sequential Clinical Trials with Multiple Endpoints
(Version 1.0)
Section I: Calculations of Sample Size and Critical Boundaries
Copyright ® Shuangge Ma and Michael R. Kosorok
Department of Biostatistics and Medical Informatics
University of Wisconsin-Madison
11/17/2018
Shuangge Ma, UW-Madison

9. Design the Copernicus (Sample Interface)
Design of Group Sequential Clinical Trials with Multiple Endpoints
Select the hard alternatives you want to control for type II error:
(1) H-0, (2) H+0, (3) H0+, (4) H0-, (5) H-+, (6) H++, (7) H--, (8) H+-
Please input here:
11/17/2018
Shuangge Ma, UW-Madison

10. Design the Copernicus (Sample Interface)
Design of Group Sequential Clinical Trials with Multiple Endpoints
Case 1: Two endpoints: 1st survival and 2nd survival
For the first survival endpoint:
Information Spending:
Relative Information (1): 0.125
Relative Information (2): 0.250
Relative Information (3): 0.375
Relative Information (4): 0.500 ……
11/17/2018
Shuangge Ma, UW-Madison

11. Design the Copernicus (Sample Interface)
Design of Group Sequential Clinical Trials with Multiple Endpoints
Case 1: Two endpoints: 1st survival and 2nd survival
For the first survival endpoint:
The alphaSpend for this endpoint is:
The betaSpend for this endpoint is:
The lambdaNull for this endpoint is:
The lambdaAlter for this endpoint is:
The entry for this trial is:
The followup for this trial is:
11/17/2018
Shuangge Ma, UW-Madison

12. Design the Copernicus (Sample Interface)
Design of Group Sequential Clinical Trials with Multiple Endpoints
Decision rule: hard Sample size:
Critical Boundaries:
End End 2
Look Lower Upper Lower Upper
……………….
11/17/2018
Shuangge Ma, UW-Madison

13. Design the Copernicus (Sample Interface)
Design of Group Sequential Clinical Trials with Multiple Endpoints
Decision rule: hard
Sample size:
11/17/2018
Shuangge Ma, UW-Madison

14. Interim Analysis of Copernicus
2289 patients (1156 treatment & 1133 placebo)
Interim analysis (day): 379, , ,
Information spending:
Endpoint 1: 0.060, 0.107, 0.215,
Endpoint 2: 0.120, 0.220, 0.413,
11/17/2018
Shuangge Ma, UW-Madison

15. Interim Analysis (Sample Interface)
Data Analysis of Group Sequential Clinical Trial
Case 1: Two Endpoints: 1st survival & 2nd Survival
For the first survival endpoint:
Please input the name of the second information file:
survival1a.txt
11/17/2018
Shuangge Ma, UW-Madison

16. Interim Analysis (Sample Interface)
Data Analysis of Group Sequential Clinical Trial
Case 1: Two Endpoints: 1st survival & 2nd Survival
For the first survival endpoint:
Global alpha Alpha Beta Look Time
Look
Look
Look
Look
11/17/2018
Shuangge Ma, UW-Madison

17. Interim Analysis (Sample Interface)
Data Analysis of Group Sequential Clinical Trial
Critical Boundaries and Test Statistics
End End 2
Lower Upper Test Lower Upper Test
Look
Look
Look
Look
11/17/2018
Shuangge Ma, UW-Madison

18. Interim Analysis (Sample Interface)
Data Analysis of Group Sequential Clinical Trial
11/17/2018
Shuangge Ma, UW-Madison

19. Shuangge Ma, UW-Madison
Software Development
11/17/2018
Shuangge Ma, UW-Madison

20. Shuangge Ma, UW-Madison
Discussion
This methodology and the software have been well tested.
The Software can be used to analyze clinical trials with one or two primary endpoints.
Two types of responses are considered:
1. approximately Gaussian response, and
2. time-to-event response.
Source code available for Unix and Windows systems.
11/17/2018
Shuangge Ma, UW-Madison