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Constructing multiple test procedures for partially ordered hypothesis sets.

David Edwards1, Jesper Madsen

  • 1Biostatistics Department, Novo Nordisk, Denmark. DEd@novonordisk.com

Statistics in Medicine
|May 4, 2007
PubMed
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This study introduces a generalized hierarchical testing method for clinical trials. It allows partial ordering of hypotheses, enhancing statistical power while controlling the familywise error rate (FWE).

Area of Science:

  • Biostatistics
  • Clinical Trials
  • Statistical Inference

Background:

  • Confirmatory clinical trials require controlling multiplicity to maintain statistical integrity.
  • Hierarchical (fixed sequence) testing procedures are a common method for controlling the familywise error rate (FWE).
  • These procedures necessitate a strict a priori ordering of null hypotheses.

Purpose of the Study:

  • To generalize hierarchical testing procedures to accommodate partially ordered null hypotheses.
  • To develop inference strategies for clinical trials that better align with trial objectives.
  • To ensure strong control of the familywise error rate (FWE) under partial ordering.

Main Methods:

  • Utilizing directed acyclic graphs (DAGs) to represent partial orderings of null hypotheses.

Related Experiment Videos

  • Implementing sequentially rejective procedures where hypotheses are tested only after preceding ones are rejected.
  • Incorporating specific intersection hypotheses to achieve FWE control.

    • Main Results:

    • Demonstrated that generalized procedures based on partial ordering do not inherently control FWE.
    • Showed that adding certain intersection hypotheses enables strong FWE control.
    • Developed a method to construct inference strategies reflecting trial objectives.

    Conclusions:

    • Partially ordered hierarchical testing, augmented with intersection hypotheses, offers a flexible approach to multiplicity control in clinical trials.
    • This method enhances the ability to reflect complex trial objectives within statistical inference strategies.
    • The generalized procedure provides a robust framework for confirmatory trials requiring FWE control.