Optimizing the order of hypotheses in serial testing of multiple endpoints in clinical trials

Zhiwei Zhang, Chenguang Wang, James F. Troendle

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Clinical trials usually collect information on a large number of variables or endpoints, including one or more primary endpoints as well as a number of secondary endpoints representing different aspects of treatment effectiveness and safety. In this article, we focus on serial testing procedures that test multiple endpoints in a pre-specified order, and consider how to optimize the order of endpoints subject to any clinical constraints, with respect to the expected number of successes (i.e., endpoints that reach statistical significance) or the expected gain (if endpoints are associated with numerical utilities). We consider some common approaches to this problem and propose two new approaches: a greedy algorithm based on conditional power and a simulated annealing algorithm that attempts to improve a given sequence in a random and iterative fashion. Simulation results indicate that the proposed algorithms are useful for finding a high-performing sequence, and that optimized fixed sequence procedures can be competitive against traditional multiple testing procedures such as Holm's. The methods and findings are illustrated with two examples concerning migraine and asthma.

Original languageEnglish (US)
Pages (from-to)1467-1482
Number of pages16
JournalStatistics in Medicine
Issue number9
StatePublished - Apr 30 2015


  • Chain procedure
  • Fixed sequence
  • Hierarchical testing
  • Multiple comparisons
  • Multiplicity
  • Secondary endpoint

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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