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Exact tests using binary data in adaptive two or multi-stage designs.

Huan Yin1, Weizhen Wang2, Zhongzhan Zhang1

  • 1College of Applied Sciences, Beijing University of Technology, Beijing, P. R. China.

Statistical Methods in Medical Research
|December 10, 2019
PubMed
Summary

This study proves that Type I error rates in adaptive two-stage and multi-stage designs are maximized at the null hypothesis boundary. This finding helps in deriving optimal designs for clinical trials with binary data.

Keywords:
Binomial distributionType I error ratephase II clinical trialpowersample size

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Statistical Inference

Background:

  • Adaptive two-stage designs are commonly used for treatments with binary data.
  • One-sided tests for proportions are standard, with designs optimized at the null hypothesis boundary.
  • Uncertainty exists regarding maximum Type I error rates when stage 2 sample sizes vary.

Purpose of the Study:

  • To rigorously prove that Type I error rates are maximized at the null boundary in adaptive two-stage designs.
  • To derive optimal designs based on this proven principle.
  • To extend these findings to multi-stage designs (m > 2).

Main Methods:

  • Demonstrating that tests within a specific family exhibit non-decreasing power with respect to the proportion 'p'.
  • Utilizing this property to establish the condition for maximum Type I error rate.
  • Deriving optimal design parameters for two-stage and m-stage sequential trials.

Main Results:

  • Confirmed that the maximum Type I error rate in adaptive two-stage designs occurs at the boundary of the null hypothesis space.
  • Established a method for deriving optimal designs for these adaptive trials.
  • Extended the findings to demonstrate similar properties for m-stage designs (m > 2).

Conclusions:

  • The study provides theoretical justification for optimizing adaptive clinical trial designs at the null hypothesis boundary.
  • The derived methods are applicable to a broad range of tests used in sequential designs.
  • These results enhance the reliability and efficiency of multi-stage clinical trial planning.