Borrowing from supplemental sources to estimate causal effects from a primary data source

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5 Scopus citations


The increasing multiplicity of data sources offers exciting possibilities in estimating the effects of a treatment, intervention, or exposure, particularly if observational and experimental sources could be used simultaneously. Borrowing between sources can potentially result in more efficient estimators, but it must be done in a principled manner to mitigate increased bias and Type I error. Furthermore, when the effect of treatment is confounded, as in observational sources or in clinical trials with noncompliance, causal effect estimators are needed to simultaneously adjust for confounding and to estimate effects across data sources. We consider the problem of estimating causal effects from a primary source and borrowing from any number of supplemental sources. We propose using regression-based estimators that borrow based on assuming exchangeability of the regression coefficients and parameters between data sources. Borrowing is accomplished with multisource exchangeability models and Bayesian model averaging. We show via simulation that a Bayesian linear model and Bayesian additive regression trees both have desirable properties and borrow under appropriate circumstances. We apply the estimators to recently completed trials of very low nicotine content cigarettes investigating their impact on smoking behavior.

Original languageEnglish (US)
Pages (from-to)5115-5130
Number of pages16
JournalStatistics in Medicine
Issue number24
Early online dateJun 22 2021
StatePublished - Oct 30 2021

Bibliographical note

Funding Information:
This research was partially funded by NIH under grants P30‐CA077598, R01‐CA214824, and R01‐CA225190 from the National Cancer Institute and R03‐DA041870, R01‐DA046320, and U54‐DA031659 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:
© 2021 John Wiley & Sons Ltd.


  • Bayesian additive regression trees
  • Bayesian linear model
  • Bayesian model averaging
  • borrowing
  • causal inference
  • multisource exchangeability models


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