36 – Innovations in Adaptive Design
Unknown Correlation Coefficient Between a Primary and a Secondary Endpoint in a Two-Stage Group Sequential Design
Cyrus R. Mehta
Cytel Inc.
Ajit C. Tamhane
Northwestern University
Yi Wu
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 �. Setting � = 1 will provide the most conservative critical boundary (Tamhane, Mehta and Liu 2010). However, replacing � with its sample estimate r will cause familywise error rate (FWER) inflation when r is less than �. We have developed an approach to control the overall FWER with adjusted second stage critical boundary utilizing the upper confidence limit of �. We show that the power gain for rejecting the secondary hypothesis of the new approach over the conservative method is significant.
