Adaptive extensions of a two-stage group sequential procedure for testing primary and secondary endpoints (I): Unknown correlation between the endpoints

Ajit C. Tamhane*, Yi Wu, Cyrus R. Mehta

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

In a previous paper we studied a two-stage group sequential procedure (GSP) for testing primary and secondary endpoints where the primary endpoint serves as a gatekeeper for the secondary endpoint. We 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, we used the least favorable value of ρ=1 to compute the critical boundaries of a conservative GSP. Under the latter assumption, we 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, whereas 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. 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 that of O'Brien and Fleming for the primary and of Pocock 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). We give a clinical trial example to illustrate the proposed procedure.

Original languageEnglish (US)
Pages (from-to)2027-2040
Number of pages14
JournalStatistics in Medicine
Volume31
Issue number19
DOIs
StatePublished - Aug 30 2012

Keywords

  • Adaptive designs
  • Familywise error rate
  • Gatekeeping procedures
  • Multiple comparisons
  • O'Brien-Fleming boundary
  • Pocock boundary

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability

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