Matching to estimate the causal effects from multiple treatments

The propensity score is a common tool for estimating the causal effect of a binary treatment using observational data. In this setting, matched methods, defined as either individual matching, subclassifying, or using inverse probability weighting on the propensity score, can reduce the initial covariate bias between the treatment and control groups. With more than two treatment options, however, matched methods require additional assumptions and techniques, the implementations of which have varied across disciplines, including public health and economics. This paper blends current methods together, identifying and contrasting the treatment effects each one estimates. Further, we propose a matching technique for use with multiple, nominal categorical treatments, and use simulations to show improved covariate similarity between those in the matched sets compared both the pre-matched cohort and to other current matching strategies. In summary, this manuscript provides a central location for those looking how to notate and use causal methods for categorical treatments. (< 150 words)