The propensity score is a common tool for estimating the causal effect of abinary treatment in observational data. In this setting, matching,subclassification, imputation, or inverse probability weighting on thepropensity score can reduce the initial covariate bias between the treatmentand control groups. With more than two treatment options, however, estimationof causal effects requires additional assumptions and techniques, theimplementations of which have varied across disciplines. This paper reviewscurrent methods, and it identifies and contrasts the treatment effects thateach one estimates. Additionally, we propose possible matching techniques foruse with multiple, nominal categorical treatments, and use simulations to showhow such algorithms can yield improved covariate similarity between those inthe matched sets, relative the pre-matched cohort. To sum, this manuscriptprovides a synopsis of how to notate and use causal methods for categoricaltreatments.
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