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Biometrics. 2018 Mar;74(1):40-48. doi: 10.1111/biom.12732. Epub 2017 Jun 6.

A gatekeeping procedure to test a primary and a secondary endpoint in a group sequential design with multiple interim looks.

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Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208, U.S.A.
Department of Mathematics and Statistics, Hunter College, New York, New York 10065, U.S.A.
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK.
Cytel Inc., 675 Massachusetts Avenue, Cambridge, Massachusetts 02139, U.S.A.


Glimm et al. (2010) and Tamhane et al. (2010) studied the problem of testing a primary and a secondary endpoint, subject to a gatekeeping constraint, using a group sequential design (GSD) with K=2 looks. In this article, we greatly extend the previous results to multiple (K>2) looks. If the familywise error rate (FWER) is to be controlled at a preassigned α level then it is clear that the primary boundary must be of level α. We show under what conditions one α-level primary boundary is uniformly more powerful than another. Based on this result, we recommend the choice of the O'Brien and Fleming (1979) boundary over the Pocock (1977) boundary for the primary endpoint. For the secondary endpoint the choice of the boundary is more complicated since under certain conditions the secondary boundary can be refined to have a nominal level α'>α, while still controlling the FWER at level α, thus boosting the secondary power. We carry out secondary power comparisons via simulation between different choices of primary-secondary boundary combinations. The methodology is applied to the data from the RALES study (Pitt et al., 1999; Wittes et al., 2001). An R library package gsrsb to implement the proposed methodology is made available on CRAN.


Familywise error rate; Gatekeeping; Lan-DeMets error spending function approach; Multiple comparisons; Multiple endpoints; O'Brien-Fleming boundary; Pocock boundary; Primary power; Secondary power


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