Normalized Power Prior Bayesian Analysis

• Activity Number: 290 - Advanced Bayesian Topics (Part 3)
• Type: Contributed
• Date/Time: Wednesday, August 11, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Keying Ye* and Zifei Han and Yuyan Duan and Tianyu Bai
• Companies: The University of Texas at San Antonio and University of International Business and Economics and Novartis Inc. and FDA
• Keywords: Bayesian analysis; historical data; joint power prior; normalized power prior

Abstract

The elicitation of power priors, based on the availability of historical data, is realized by raising the likelihood function of the historical data to a fractional power, which quantifies the degree of discounting of the historical information in making inference with the current data. In this study, we investigate a normalized power prior approach which obeys the likelihood principle and is a modified form of the joint power prior. The optimality properties of the normalized power prior in the sense of minimizing the weighted Kullback-Leibler divergences are investigated. By examining the posteriors of several commonly used distributions, we show that the discrepancy between the historical and the current data can be well quantified by the power parameter under the normalized power prior setting. Efficient algorithm to compute the scale factor is also proposed. In addition, we illustrate the use of the normalized power prior to Bayesian analysis with several data examples and provide an implementation with an R package NPP.