Unknown Correlation Coefficient Between a Primary and a Secondary Endpoint in a Two-stage Group Sequential Design

• Activity Number: 36
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Yi Wu*+ and Ajit C. Tamhane and Cyrus R Mehta
• Companies: and Northwestern University and Cytel Inc.
• Keywords: Group sequential procedure ; Multiple endpoints ; Clinical trials ; Sample size re-estimation ; Familywise error rate

Abstract

We consider a two-stage group sequential procedure (GSP) with a primary and a secondary endpoint where the secondary endpoint is tested only if the primary endpoint shows significance. We assume that the two endpoints follow a bivariate normal distribution with unknown correlation coefficient $\rho$. Setting $\rho = 1$ will provide the most conservative critical boundary (Tamhane, Mehta and Liu 2010). However, replacing $\rho$ with its sample estimate $r$ will cause familywise error rate (FWER) inflation when $r$ is less than $\rho$. We have developed an approach to control the overall FWER with adjusted second stage critical boundary utilizing the upper confidence limit of $\rho$. We show that the power gain for rejecting the secondary hypothesis of the new approach over the conservative method is significant.