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Test-compatible confidence intervals for adaptive two-stage single-arm designs with binary endpoint.

Kevin Kunzmann1, Meinhard Kieser1

  • 1Institute of Medical Biometry and Informatics, University of Heidelberg, Marsilius Arkaden, Im Neuenheimer Feld 130.3, 69120 Heidelberg, Germany.

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Statistical Inference

Background:

  • Inference in two-stage single-arm designs with binary endpoints presents challenges due to nonunique sample space ordering.
  • Specifying test-compatible confidence intervals for designs with nonconstant second-stage sample sizes is problematic.

Purpose of the Study:

  • To address the challenge of inference in two-stage adaptive designs.
  • To develop and evaluate methods for constructing confidence intervals that are consistent with hypothesis test decisions.

Main Methods:

  • Extended the Clopper-Pearson method to fully adaptive sample size designs by inverting hypothesis tests.
  • Utilized a sample space ordering derived from a test-compatible estimator for test compatibility.
  • Explored a direct optimization approach to minimize mean confidence interval width.

Main Results:

  • The extended Clopper-Pearson approach ensures nominal coverage probability, though intervals may be conservative.
  • The direct optimization approach yielded slightly anti-conservative intervals with negligible improvements in mean width.
  • Both methods aimed to maintain consistency between confidence intervals and test decisions.

Conclusions:

  • Clopper-Pearson-type confidence intervals, using a test-compatible estimator, are recommended for preserving nominal coverage and test-interval compatibility.
  • This approach is preferred when avoiding undershooting the nominal coverage probability is critical.
  • Adaptive designs require careful consideration for valid statistical inference and confidence interval construction.