On adaptive propensity score truncation in causal inference

Stat Methods Med Res. 2019 Jun;28(6):1741-1760. doi: 10.1177/0962280218774817. Epub 2018 Jul 11.


The positivity assumption, or the experimental treatment assignment (ETA) assumption, is important for identifiability in causal inference. Even if the positivity assumption holds, practical violations of this assumption may jeopardize the finite sample performance of the causal estimator. One of the consequences of practical violations of the positivity assumption is extreme values in the estimated propensity score (PS). A common practice to address this issue is truncating the PS estimate when constructing PS-based estimators. In this study, we propose a novel adaptive truncation method, Positivity-C-TMLE, based on the collaborative targeted maximum likelihood estimation (C-TMLE) methodology. We demonstrate the outstanding performance of our novel approach in a variety of simulations by comparing it with other commonly studied estimators. Results show that by adaptively truncating the estimated PS with a more targeted objective function, the Positivity-C-TMLE estimator achieves the best performance for both point estimation and confidence interval coverage among all estimators considered.

Keywords: Propensity score; adaptive truncation; collaborative targeted learning; experimental treatment assignment; positivity.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Algorithms
  • Bias
  • Causality
  • Humans
  • Likelihood Functions
  • Models, Statistical
  • Propensity Score*
  • Reproducibility of Results