Bayesian estimation of the average treatment effect on the treated using inverse weighting

Stat Med. 2019 Jun 15;38(13):2447-2466. doi: 10.1002/sim.8121. Epub 2019 Mar 11.


We develop a Bayesian approach to estimate the average treatment effect on the treated in the presence of confounding. The approach builds on developments proposed by Saarela et al in the context of marginal structural models, using importance sampling weights to adjust for confounding and estimate a causal effect. The Bayesian bootstrap is adopted to approximate posterior distributions of interest and avoid the issue of feedback that arises in Bayesian causal estimation relying on a joint likelihood. We present results from simulation studies to estimate the average treatment effect on the treated, evaluating the impact of sample size and the strength of confounding on estimation. We illustrate our approach using the classic Right Heart Catheterization data set and find a negative causal effect of the exposure on 30-day survival, in accordance with previous analyses of these data. We also apply our approach to the data set of the National Center for Health Statistics Birth Data and obtain a negative effect of maternal smoking during pregnancy on birth weight.

Keywords: Bayesian inference; causal inference; inverse probability weighting; observational study; propensity score.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Bayes Theorem*
  • Bias
  • Birth Weight
  • Cardiac Catheterization / statistics & numerical data
  • Computer Simulation
  • Confounding Factors, Epidemiologic
  • Female
  • Humans
  • Infant, Newborn
  • Observational Studies as Topic
  • Pregnancy
  • Propensity Score
  • Sample Size
  • Smoking / adverse effects
  • Survival Analysis