On Bayesian Sequential Clinical Trial Designs

TL;DR

This paper reviews Bayesian sequential clinical trial designs, discussing their theoretical foundations, practical considerations for interim analyses, and insights into the likelihood principle, supported by theoretical results and numerical studies.

Contribution

It provides a comprehensive review of Bayesian sequential designs, addressing whether adjustments are needed for interim analyses from multiple statistical perspectives.

Findings

Bayesian designs can be adjusted for interim analyses from different perspectives.

The likelihood principle's role in Bayesian sequential trials is clarified.

Numerical studies demonstrate the practical performance of various Bayesian designs.

Abstract

Clinical trials usually involve sequential patient entry. When designing a clinical trial, it is often desirable to include a provision for interim analyses of accumulating data with the potential for stopping the trial early. We review Bayesian sequential clinical trial designs based on posterior probabilities, posterior predictive probabilities, and decision-theoretic frameworks. A pertinent question is whether Bayesian sequential designs need to be adjusted for the planning of interim analyses. We answer this question from three perspectives: a frequentist-oriented perspective, a calibrated Bayesian perspective, and a subjective Bayesian perspective. We also provide new insights into the likelihood principle, which is commonly tied to statistical inference and decision making in sequential clinical trials. Some theoretical results are derived, and numerical studies are conducted to illustrate and assess these designs.