Covariate Balancing Propensity Score

Abstract

Summary The propensity score plays a central role in a variety of causal inference settings. In particular, matching and weighting methods based on the estimated propensity score have become increasingly common in the analysis of observational data. Despite their popularity and theoretical appeal, the main practical difficulty of these methods is that the propensity score must be estimated. Researchers have found that slight misspecification of the propensity score model can result in substantial bias of estimated treatment effects. We introduce covariate balancing propensity score (CBPS) methodology, which models treatment assignment while optimizing the covariate balance. The CBPS exploits the dual characteristics of the propensity score as a covariate balancing score and the conditional probability of treatment assignment. The estimation of the CBPS is done within the generalized method‐of‐moments or empirical likelihood framework. We find that the CBPS dramatically improves the poor empirical performance of propensity score matching and weighting methods reported in the literature. We also show that the CBPS can be extended to other important settings, including the estimation of the generalized propensity score for non‐binary treatments and the generalization of experimental estimates to a target population. Open source software is available for implementing the methods proposed.

Empirical Likelihood Methods for Complex Surveys With Data Missing-by-Design

“…In other words, the covariates need to be balanced between the two groups. Balancing covariates through propensity scores has been studied by several authors, including Austin (2008Austin ( , 2009), Imai and Ratkovic (2014) and Li, Morgan and Zaslavsky (2015). Rosenbaum and Rubin (1984) proposed using subclassification based on propensity scores, and Zanutto, Lu and Hornik (2005) provided an application of the subclassification method.…”

Pharmacological Treatment of Adult Attention-Deficit/Hyperactivity Disorder (ADHD) in a Longitudinal Observational Study: Estimated Treatment Effect Strengthened by Improved Covariate Balance

“…The popular marginal structural model (MSM) for causal inference, of Robins et al, adjusts for time-varying confounding, but suffers from lack of robustness for misspecification in the weights. Recent work by Imai and Ratkovic [1] [2] achieves robustness in the MSM, through improved covariate balance (CBMSM). The CBMSM (freely available software) was compared with a standard fit of a MSM and a naive regression model, to give a robust estimate of the true treatment effect in 250 previously non-medicated adults, treated for one year, in a specialized ADHD outpatient clinic in Norway.…”

Comments: Improving Weighting Methods for Causal Mediation Analysis

“…Thus, what the CBPS estimation accomplishes is to estimate the propensity score such that the covariate balance is optimized. Imai and Ratkovic (2012) found that the resulting CBPS dramatically improves the empirical performance of propensity score weighting methods and overcomes the critiques of Kang and Schafer (2007).…”

“…As discussed in Imai and Ratkovic (2012), the CBPS can be easily extended to nonbinary treatment regimes, which implies that it can be applied to the RMPW estimation even when the mediator is not binary. In particular, instead of fitting the ordered logistic regression via maximum likelihood as suggested by the authors, we can use the GMM estimation based on the following moment conditions.…”

“…To address this issue, Imai and Ratkovic (2012) proposed the covariate balancing propensity score (CBPS) estimation as the robust parametric estimation strategy for the propensity score. The idea is to exploit the dual characteristics of the propensity score as the conditional probability of treatment assignment and a balancing score: If the propensity score is correctly estimated, it should predict the treatment assignment Z and balance the covariate distribution between the treatment and control groups (once the covariates X 294 K. Imai are appropriately weighted via the inverse of the propensity score).…”