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The Central Role of Bayes’ Theorem for Joint Estimation of Causal Effects and Propensity Scores

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  • Corwin Matthew Zigler

Abstract

Although propensity scores have been central to the estimation of causal effects for over 30 years, only recently has the statistical literature begun to consider in detail methods for Bayesian estimation of propensity scores and causal effects. Underlying this recent body of literature on Bayesian propensity score estimation is an implicit discordance between the goal of the propensity score and the use of Bayes’ theorem. The propensity score condenses multivariate covariate information into a scalar to allow estimation of causal effects without specifying a model for how each covariate relates to the outcome. Avoiding specification of a detailed model for the outcome response surface is valuable for robust estimation of causal effects, but this strategy is at odds with the use of Bayes’ theorem, which presupposes a full probability model for the observed data that adheres to the likelihood principle. The goal of this article is to explicate this fundamental feature of Bayesian estimation of causal effects with propensity scores to provide context for the existing literature and for future work on this important topic.[Received June 2014. Revised September 2015.]

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  • Corwin Matthew Zigler, 2016. "The Central Role of Bayes’ Theorem for Joint Estimation of Causal Effects and Propensity Scores," The American Statistician, Taylor & Francis Journals, vol. 70(1), pages 47-54, February.
    • Handle: RePEc:taf:amstat:v:70:y:2016:i:1:p:47-54
    DOI: 10.1080/00031305.2015.1111260
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    1. Brumback, Babette A., 2009. "A note on using the estimated versus the known propensity score to estimate the average treatment effect," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 537-542, February.
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    2. F. Swen Kuh & Grace S. Chiu & Anton H. Westveld, 2019. "Modeling National Latent Socioeconomic Health and Examination of Policy Effects via Causal Inference," Papers 1911.00512, arXiv.org.
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    5. Brian J. Reich & Shu Yang & Yawen Guan & Andrew B. Giffin & Matthew J. Miller & Ana Rappold, 2021. "A Review of Spatial Causal Inference Methods for Environmental and Epidemiological Applications," International Statistical Review, International Statistical Institute, vol. 89(3), pages 605-634, December.

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