1. 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 University of Wisconsin-Madison *Email: shuangge@biostat.wisc.edu 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.  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:  Non-symmetric (soft) decision rules: 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. Software Development http://www.stat.wisc.edu/~shuangge/software/main.html 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. Design the Copernicus (Sample Software Interface): 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 Design of Group Sequential Clinical Trials with Multiple Endpoints Case 1: Two endpoints: 1 st survival and 2 nd 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 …… Design of Group Sequential Clinical Trials with Multiple Endpoints Case 1: Two endpoints: 1 st survival and 2 nd 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 Sample size: 1221 Critical Boundaries: End 1 End 2 Look Lower Upper Lower Upper 1 0.0395 2.7010 0.0259 2.7010 2 0.0891 2.7000 0.0486 2.6998 3 0.2529 2.6800 0.1783 2.6930 ………………. Interim Analysis of Copernicus:  2289 patients (1156 treatment & 1133 placebo)  Interim analysis (day): 379, 496, 671, 875.  Information spending: Endpoint 1: 0.060, 0.107, 0.215, 0.390. Endpoint 2: 0.120, 0.220, 0.413, 0.720.  The trial was terminated early with significantly beneficial effects on both endpoints. Interim Analysis (Sample Interface): Discussions:  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. 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 Data Analysis of Group Sequential Clinical Trial Case 1: Two Endpoints: 1 st survival & 2 nd 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: 1 st survival & 2 nd 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 of Group Sequential Clinical Trials with Multiple Endpoints Decision rule: hard Sample size: 1221 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: 1 2 3 4 6 7