JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1161 10.6339/24-JDS1161 Data Science Reviews Power Priors for Leveraging Historical Data: Looking Back and Looking Forward✩ ChenMing-Huiming-hui.chen@uconn.edu∗ GuanZhe LinMin SunMaxfor the Alzheimer’s Disease Neuroimaging Initiative Department of Statistics, University of Connecticut, Storrs, CT 06269-4120, United States

Data used in preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf

Corresponding author. Email: ming-hui.chen@uconn.edu. 202531122024231130 Supplementary Material

The posterior densities in Figure 2 and the posterior estimates reported in Table 5 are computed using SAS while the posterior estimates in Table 6 are obtained either analytically or using R. Additional tables and figures for MCMC convergence checks, which show good convergence and mixing of MCMC samples, are provided in Supplementary Material Sections S.1. Section S.2 contains additional tables and figures for MCMC convergence checks for the ADNI data, which again show good convergence and mixing. Unfortunately, the ADNI data is proprietary. SAS code (Kociba_NTP_example.sas) for the Kociba and NTP data, R code (analysis_simulated_data.qmd) for ADNI results, and a simulated dataset (sim_data.csv) mimicking the ADNI data can be found at https://github.com/MinLinSTAT/PPreview. The posterior estimates of γ for the simulated dataset are given in Section S.3.

303202417122024 2025 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2025 Open access article under the CC BY license.

Historical data or real-world data are often available in clinical trials, genetics, health care, psychology, environmental health, engineering, economics, and business. The power priors have emerged as a useful class of informative priors for a variety of situations in which historical data are available. In this paper, an overview of the development of the power priors is provided. Various variations of the power priors are derived under a binomial regression model and a normal linear regression model. The development of software on the power priors is also briefly reviewed. Throughout this paper, the data from the Kociba study and the National Toxicology Program study as well as the data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study are used to demonstrate the derivations of the power priors and their variations. Detailed analyses of the data from these studies are carried out to further demonstrate the usefulness of the power priors and their variations in these real applications. Finally, the directions of future research on the power priors are discussed.

 Bayesian design of clinical trials borrowing-by-parts power priors discounting parameters informative priors partial borrowing power priors propensity score based power priors Data collection and sharing for this project was funded by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer’s Association; Alzheimer’s Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (www.fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimer’s Therapeutic Research Institute at the University of Southern California. 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