Parametric and Nonparametric Covariate Balancing Propensity Score for General Treatment Regimes∗

Propensity score matching and weighting are popular methods when estimating causal effects in observational studies. Beyond the assumption of unconfoundedness, however, these methods also require the model for propensity score to be correctly specified. The recently proposed covariate balancing propensity score (CBPS) methodology weakens this assumption by directly optimizing sample covariate balance between the treatment and control groups. In this paper, we generalize the CBPS to non-binary treatment regimes. While extensions of propensity score methods to general treatment regimes have been proposed, many applied researchers dichotomize non-binary treatments in order to use propensity score methods. We propose to estimate the generalized propensity score such that after weighting the association between covariates and the treatment is minimized. We further develop a non-parametric alternative without requiring a model for the propensity score. While promising, this approach is computationally demanding. Two applications demonstrate that the generalized CBPS methodology significantly improves covariate balance and offer substantive insights the original analyses fail to identify. The proposed methodology is implemented through publicly available open-source software.