# Software Development http://www.stat.wisc.edu/~shuangge/software/main.html Motivation: Clinical trial with multiple

Software Development
http://www.stat.wisc.edu/~shuangge/software/main.html

Motivation:
Clinical trial with multiple endpoints:
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:
1. All cause mortality,
2. The earliest time of mortality and hospitalization.

Statistical goal:
Stop early if treatment effect is clear in all endpoints.
Control the many possible error rates.
Develop user-friendly software.
o Two types of response:
normal distributed response: (pooled mean),
time-to-event (survival type) response: (logrank test).
o Two types of decision rule:
hard decision rule (no vague component),
soft decision rule (at least one vague component).

Overall Strategy (Design of Clinical Trail):
Construct marginal critical boundaries with certain alpha/beta
spending functions.

Design and Analysis of Group Sequential Clinical Trials
with Multiple Endpoints and Software Development
Shuangge Ma*, Michael R. Kosorok and Thomas D. Cook
Department of Biostatsitics and Medical Informatics
*Email: [email protected]
Interim Analysis of Copernicus:

Overall Strategy (Interim Analysis):

2289 patients (1156 treatment & 1133 placebo)

At each interim analysis:

Interim analysis (day): 379, 496,

Compute the marginal critical regions based on the marginal alpha/beta spending
functions and then take spatial product.

Information spending:
Endpoint 1: 0.060, 0.107, 0.215, 0.390.
Endpoint 2: 0.120, 0.220, 0.413, 0.720.

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.

Construct an appropriate multivariate decision rule.
Adjust marginal critical boundaries to conform to a global alpha
spending function.

Plot of Bivariate Critical Regions:
Symmetric

(hard) decision
rules:

671, 875.

The trial was terminated early with significantly beneficial effects on both
endpoints.

Interim Analysis (Sample Interface):

Design the Copernicus:
Design features:
Endpoint 1: =0.0009 (Placebo) =0.00072 (treatment)
(t)=0.05*t, (t)=0.1*t.
Endpoint 2: =0.002 (Placebo) =0.0012 (treatment)
(t)=0.05*t, (t)=0.05*t.
Global:
=0.05, =0.05.
Enrollment: 900 days, Follow up: 85 days.

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

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 1
0.003
0.003
0.006
379
Look 2
0.00235
0.00235 0.0047 496
Look 3
0.0054
0.0054 0.0108 671
Look 4
0.00875
0.00875 0.0175 875

Design the Copernicus (Sample Software Interface):
Data Analysis of Group Sequential Clinical Trial
Design of Group Sequential Clinical Trials with Multiple
Endpoints
(Version 1.0)
Section I: Calculations of Sample Size and Critical Boundaries

Design of Group Sequential Clinical Trials with Multiple
Endpoints
Select the hard alternatives you want to control for type II error:
(1) H-0,
(5) H-+,

(2) H+0,
(6) H++,

(3) H0+,
(7) H--,

(4) H0-,
(8) H+-

Please input here: 1 2 3 4 6 7
Copyright Shuangge Ma and Michael R. Kosorok
Department of Biostatistics and Medical Informatics

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

Non-symmetric
(soft) decision
rules:

Data Analysis of Group Sequential Clinical Trial

Critical Boundaries and Test Statistics
End 1
End 2
Lower Upper Test
Lower Upper Test
Look 1 0.008 2.095 0.920 0.075 1.940 1.107
Look 2 0.006 2.842 1.449 0.986 2.561 1.491
Look 3 0.036 2.731 2.429 2.407 2.407 2.829
Look 4 0.353 2.666 3.448 2.478 2.478 2.941

Discussions:
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:
1
The betaSpend for this endpoint is:
1
The lambdaNull for this endpoint is:
0.0002
The lambdaAlter for this endpoint is:
0.00012
The entry for this trial is:
900
The followup for this trial is:
85

Design of Group Sequential Clinical Trials with Multiple
Endpoints
Decision rule: hard
Critical Boundaries:

Sample size: 1221
End 1

Look
1
2
3

Lower
Upper
0.0395
2.7010
0.0891
2.7000
0.2529
2.6800
.

End 2
Lower
Upper
0.0259
2.7010
0.0486
2.6998
0.1783
2.6930

Design of Group Sequential Clinical Trials with Multiple
Endpoints
Decision rule: hard

Sample size: 1221

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.

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