A comparison of parametric propensity score‐based methods for causal inference with multiple treatments and a binary outcome

We consider comparative effectiveness research (CER) from observational data with two or more treatments. In observational studies, the estimation of causal effects is prone to bias due to confounders related to both treatment and outcome. Methods based on propensity scores are routinely used to correct for such confounding biases. A large fraction of propensity score methods in the current literature consider the case of either two treatments or continuous outcome. There has been extensive literature with multiple treatment and binary outcome, but interest often lies in the intersection, for which the literature is still evolving. The contribution of this article is to focus on this intersection and compare across methods, some of which are fairly recent. We describe propensity-based methods when more than two treatments are being compared, and the outcome is binary. We assess the relative performance of these methods through a set of simulation studies. The methods are applied to assess the effect of four common therapies for castration-resistant advanced-stage prostate cancer. The data consist of medical and pharmacy claims from a large national private health insurance network, with the adverse outcome being admission to the emergency room within a short time window of treatment initiation.