Flexible, efficient borrowing: A power prior structure for Bayesian interim analysis

Abstract

When making decisions about whether a product can meet required performance standards, it is often of interest to make decisions as soon as enough information has been obtained–even if that is before the conclusion of the planned test or experimental design. Evaluating data with the intent of stopping a test early is referred to as interim analysis, which can be used to address time and cost constraints. In such cases, it is important to execute tests as efficiently and effectively as possible. A Bayesian method for improving efficiency is to use informative priors to incorporate previous information—such as expert opinion or previous data—to create more precise parameter estimates and avoid allocating costly resources in a sub-optimal manner. We consider the class of power priors and variants thereof, proposing a variant that allows for a computationally efficient MCMC sampling method in an interim analysis setting to evaluate a product. A novel power prior that accounts for differences and similarities between current and previous data sets, and its role in analysis, is considered in an interim analysis construct. Simulations demonstrate previous information can be leveraged using this proposed prior to stop testing early and obtain more precise parameter estimates.

KEYWORDS:

• Bayesian adaptive design
• Bayesian mission mean
• normalized power priors
• partial borrowing power priors
• predictive probability

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Victoria R. C. Sieck

Victoria R.C. Sieck earned her Ph.D. in statistics from the from the University of New Mexico in 2021. She is an Assistant Professor of Statistics at the Air Force Institute of Technology (AFIT), Department of Mathematics and Statistics and an Operations Research Analyst in the US Air Force (USAF). Her research interests include design of experiments and developing innovate Bayesian approaches to DoD testing.

Fletcher G. W. Christensen

Fletcher G.W. Christensen earned his Ph.D. in statistics from UC Irvine in 2017. He is an Assistant Professor of Statistics at the University of New Mexico, Department of Mathematics and Statistics. His research interests include Bayesian nonparametrics, model selection methods, and foundations of statistics.