On generalized fixed sequence procedures for controlling the FWER

Zhiying Qiu, Wenge Guo, Gavin Lynch

Research output: Contribution to journalArticlepeer-review

Abstract

Testing a sequence of pre-ordered hypotheses to decide which of these can be rejected or accepted while controlling the familywise error rate (FWER) is of importance in many scientific studies such as clinical trials. In this paper, we first introduce a generalized fixed sequence procedure whose critical values are defined by using a function of the numbers of rejections and acceptances, and which allows follow-up hypotheses to be tested even if some earlier hypotheses are not rejected. We then construct the least favorable configuration for this generalized fixed sequence procedure and present a sufficient condition for the FWER control under arbitrary dependence. Based on the condition, we develop three new generalized fixed sequence procedures controlling the FWER under arbitrary dependence. We also prove that each generalized fixed sequence procedure can be described as a specific closed testing procedure. Through simulation studies and a clinical trial example, we compare the power performance of these proposed procedures with those of the existing FWER controlling procedures. Finally, when the pairwise joint distributions of the true null p-values are known, we further improve these procedures by incorporating pairwise correlation information while maintaining the control of the FWER.

Original languageEnglish (US)
Pages (from-to)3968-3983
Number of pages16
JournalStatistics in Medicine
Volume34
Issue number30
DOIs
StatePublished - Dec 30 2015

All Science Journal Classification (ASJC) codes

  • Epidemiology
  • Statistics and Probability

Keywords

  • critical values
  • fallback procedure
  • familywise error rate
  • fixed sequence procedure
  • multiple testing
  • power

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