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

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.]

• Bayesian estimation
• Causal inference
• Model feedback

Additional information

Notes on contributors

Corwin Matthew Zigler

Corwin Matthew Zigler is Assistant Professor, Department of Biostatistics, Building 2, 4th Floor, 655 Huntington Avenue, Boston, MA 02115 (E-mail: [email protected]). Funding for this work provided by NCI P01 CA134294 and HEI 4909-RFA11-1/12-3. The author thanks Sebastien Haneuse, Francesca Dominici, and Matthew Cefalu for helpful comments and discussion that improved this article. Funding for this work provided by NCI P01 CA134294, HEI 4909, and NIH R01 GM111339.