An O'Brien-Fleming sequential trial for comparing three treatments

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We consider a sequential procedure for comparing three treatments with the goal of ultimately selecting the best treatment. This procedure starts with a sequential test to detect an overall treatment difference and eliminates the apparently inferior treatment if this test rejects the equality of the treatments. It then proceeds with a sequential test of the remaining two treatments. We base these sequential tests on the stopping boundaries popularized by O'Brien and Fleming. Our procedure is similar in structure to that used by Siegmund in conjunction with modified repeated significance tests. We compare the performances of the two procedures via a simulation experiment. We derive analytic approximations for an error probability, the power and the expected sample size of our procedure, which we compare to simulated values. Furthermore, we propose a modification of the procedure for the comparison of a standard treatment with experimental treatments.

Original languageEnglish (US)
Pages (from-to)1765-1791
Number of pages27
JournalAnnals of Statistics
Issue number4
StatePublished - Aug 1996


  • Boundary crossing
  • Ranking procedure
  • Repeated significance test

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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