The Power Prior: Theory and Applications

• Activity Number: 464
• Type: Invited
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Joseph Ibrahim* and Ming-Hui Chen and Fang Chen and Yeongjin Gwon
• Companies: The University of North Carolina and University of Connecticut and SAS Institute and University of Connecticut
• Keywords: Bayesian analysis ; historical data ; prior elicitation ; clinical trials ; Gibbs sampling

Abstract

The power prior, first introduced by Ibrahim and Chen (2000), has been widely used in many applications covering a large number of disciplines. The power prior is intended to be an informative prior constructed from historical data. It has been used in clinical trials, genetics, health care, psychology, environmental health, engineering, economics, and business. It has also been applied for a wide variety of models and settings, both in the experimental design and analysis contexts. In this talk, we discuss the power prior and its applications to date. We review its theoretical properties, variations in its formulation, statistical contexts for which it has been used, applications, and its advantages over other informative priors. We review models for which it has been used, including generalized linear models, survival models, and random effects models. Various optimality properties of the power priors in posterior inference are established and several examples involving real data are presented.