## Abstract

We generalize a multistage procedure for parallel gatekeeping to what we refer to as k-out-of-n gatekeeping in which at least k out of n hypotheses ( 1 ≤ k ≤ n) in a gatekeeper family must be rejected in order to test the hypotheses in the following family. This gatekeeping restriction arises in certain types of clinical trials; for example, in rheumatoid arthritis trials, it is required that efficacy be shown on at least three of the four primary endpoints. We provide a unified theory of multistage procedures for arbitrary k, with k=1 corresponding to parallel gatekeeping and k=n to serial gatekeeping. The theory provides an insight into the construction of truncated separable multistage procedures using the closure method. Explicit formulae for calculating the adjusted p-values are given. The proposed procedure is simpler to apply for this particular problem using a stepwise algorithm than the mixture procedure and the graphical procedure with memory using entangled graphs.

Original language | English (US) |
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Pages (from-to) | 1321-1335 |

Number of pages | 15 |

Journal | Statistics in Medicine |

Volume | 33 |

Issue number | 8 |

DOIs | |

State | Published - Apr 15 2014 |

## Keywords

- Closed procedure
- Error rate function
- Familywise error rate
- Hochberg procedure
- Holm procedure
- Hommel procedure
- Separable procedures
- Truncated procedures

## ASJC Scopus subject areas

- Epidemiology
- Statistics and Probability