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Causal Inference in Observational Studies with Non-Binary Treatments

Propensity score methods have become a part of the standard toolkit for applied researchers who wish to ascertain causal effects from observational data. While they were originally developed for binary treatments, several researchers have proposed generalizations of the propensity score methodology for non-binary treatment regimes. Such extensions have widened the applicability of propensity score methods and are indeed becoming increasingly popular themselves. In this article, we closely examine the two main generalizations of propensity score methods, namely, the propensity function (P-FUNCTION) of Imai and van Dyk (2004) and the generalized propensity score (GPS) of Hirano and Imbens (2004), along with recent extensions of the GPS that aim to improve its robustness. We compare the assumptions, theoretical properties, and empirical performance of these alternative methodologies. On a theoretical level, the GPS and its extensions are advantageous in that they can be used to estimate the full dose response function rather than the simple average treatment effect that is typically estimated with the P-FUNCTION. Unfortunately, our analysis shows that in practice response models often used with the original GPS are less flexible than those typically used with propensity score methods and are prone to misspecification. We compare new and existing methods that improve the robustness of the GPS and propose methods that use the P-FUNCTION to estimate the dose response function. We illustrate our findings and proposals through simulation studies, including one based on an empirical application.