Propensity-score based methods for causal inference in observational studies with non-binary treatments

Propensity score methods are a part of the standard toolkit for applied researchers who wish to ascertain causaleffects from observational data. While they were originally developed for binary treatments, several researchershave proposed generalizations of the propensity score methodology for non-binary treatment regimes. Suchextensions have widened the applicability of propensity score methods and are indeed becoming increasinglypopular themselves. In this article, we closely examine two methods that generalize propensity scores in thisdirection, namely, the propensity function (pf), and the generalized propensity score (gps), along with twoextensions of thegpsthat aim to improve its robustness. We compare the assumptions, theoretical properties,and empirical performance of these methods. On a theoretical level, thegpsand its extensions are advantageousin that they are designed to estimate the full dose response function rather than the average treatment effectthat is estimated with thepf. We comparegpswith a newpfmethod, both of which estimate the doseresponse function. We illustrate our findings and proposals through simulation studies, including one based onan empirical study about the effect of smoking on healthcare costs. While our proposedpf-based estimatorpreforms well, we generally advise caution in that all available methods can be biased by model misspecificationand extrapolation