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A variational approach to optimal two-stage designs.

Maximilian Pilz1, Kevin Kunzmann1, Carolin Herrmann2,3

  • 1Institute of Medical Biometry and Informatics, University Medical Center Ruprecht-Karls University Heidelberg, Heidelberg, Germany.

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Summary

Adaptive clinical trial designs allow flexibility by recalculating sample size. This study presents a globally optimal adaptive design, demonstrating that combination tests are unnecessary for type one error control, leading to more efficient trials.

Keywords:
adaptive designclinical trialinverse normal combination testoptimal designsample size calculation

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Area of Science:

  • Clinical Trials Methodology
  • Biostatistics
  • Adaptive Trial Design

Background:

  • Adaptive two-stage designs enhance clinical trial flexibility through sample size recalculation.
  • Existing methods, like Jennison and Turnbull's (2015) inverse normal combination test, aim to optimize designs based on expected sample size and conditional power.
  • Controlling type one error rate is crucial in adaptive designs.

Purpose of the Study:

  • To develop a general adaptive two-stage design that is globally optimal.
  • To demonstrate that combination tests are not essential for maintaining the type one error rate.
  • To investigate the efficiency of the inverse normal method and the relationship between local and global optimality in adaptive designs.

Main Methods:

  • Utilized variational techniques to derive a generally optimal adaptive design.
  • Focused on predefined global optimality criteria.
  • Analyzed the necessity of combination tests for type one error rate control.

Main Results:

  • A novel general adaptive design was developed using variational techniques.
  • Demonstrated that combination tests are not required for controlling the type one error rate.
  • The proposed design offers improved efficiency compared to existing methods.

Conclusions:

  • A new, globally optimal adaptive two-stage design can be achieved without relying on combination tests.
  • This approach provides greater efficiency and flexibility in clinical trial sample size recalculation.
  • The findings offer insights into the relationship between interim-based rules and overall design optimality.