Adaptive Extensions of a Two-Stage Group Sequential Procedure for Testing a Primary and a Secondary Endpoint (I): Unknown Correlation Between the Endpoints

Tamhane, Mehta and Liu [1] studied a two-stage group sequential procedure (GSP) for testing a primary and a secondary endpoint where the primary endpoint serves as a gatekeeper for the secondary endpoint. They assumed a simple setup of a bivariate normal distribution for the two endpoints with the correlation coefficient ρ between them being either an unknown nuisance parameter or a known constant. Under the former assumption they used the least favorable value of ρ = 1 to compute the critical boundaries of a conservative GSP. Under the latter assumption they computed the critical boundaries of an exact GSP. However, neither assumption is very practical. The ρ = 1 assumption is too conservative resulting in loss of power, while the known ρ assumption is never true in practice. In this Part I of a two-part paper on adaptive extensions of this two-stage procedure (Part II deals with sample size re-estimation), we propose an intermediate approach that uses the sample correlation coefficient r from the first stage data to adaptively adjust the secondary boundary after accounting for the sampling error in r via an upper confidence limit on ρ by using a method due to Berger and Boos [2]. We show via simulation that this approach achieves 5%-11% absolute secondary power gain for ρ ≤ 0.5. The preferred boundary combination in terms of high primary as well as secondary power is O’Brien and Fleming [3] for the primary and Pocock [4] for the secondary. The proposed approach using this boundary combination achieves 72%-84% relative secondary power gain (with respect to the exact GSP that assumes known ρ). A clinical trial example is given to illustrate the proposed procedure. Copyright c ⃝ 0000 John Wiley & Sons, Ltd.