Bayesian hierarchical modeling based on multisource exchangeability

Alexander M. Kaizer, Joseph S. Koopmeiners, Brian P. Hobbs

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


Bayesian hierarchical models produce shrinkage estimators that can be used as the basis for integrating supplementary data into the analysis of a primary data source. Established approaches should be considered limited, however, because posterior estimation either requires prespecification of a shrinkage weight for each source or relies on the data to inform a single parameter, which determines the extent of influence or shrinkage from all sources, risking considerable bias or minimal borrowing.We introduce multisource exchangeability models (MEMs), a general Bayesian approach for integrating multiple, potentially nonexchangeable, supplemental data sources into the analysis of a primary data source. Our proposed modeling framework yields source-specific smoothing parameters that can be estimated in the presence of the data to facilitate a dynamic multi-resolution smoothed estimator that is asymptotically consistent while reducing the dimensionality of the prior space. When compared with competing Bayesian hierarchical modeling strategies, we demonstrate that MEMs achieve approximately 2.2 times larger median effective supplemental sample size when the supplemental data sources are exchangeable as well as a 56% reduction in bias when there is heterogeneity among the supplemental sources.We illustrate the application ofMEMs using a recently completed randomized trial of very low nicotine content cigarettes, which resulted in a 30% improvement in efficiency compared with the standard analysis.

Original languageEnglish (US)
Pages (from-to)169-184
Number of pages16
Issue number2
StatePublished - Apr 1 2018

Bibliographical note

Funding Information:
National Institutes of Health (NIH) grant (P30-CA016672) from the National Cancer Institute and NIH grants (U54-DA031659 and R03-DA041870) from the National Institute on Drug Abuse and FDA Center for Tobacco Products (CTP). The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH or FDA CTP.

Publisher Copyright:
© The Author 2017. Published by Oxford University Press. All rights reserved.


  • Bayesian hierarchical modeling
  • Heterogeneous sources of data
  • Multisource smoothing
  • Supplementary data


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