Matching algorithms for causal inference with multiple treatments

Randomized clinical trials are ideal for estimating causal effects, because the distributions of background covariates are similar in expectation across treatment groups. When estimating causal effects using observational data, matching is a commonly used method to replicate the covariate balance achieved in a randomized clinical trial. Matching algorithms have a rich history dating back to the mid-1900s but have been used mostly to estimate causal effects between two treatment groups. When there are more than two treatments, estimating causal effects requires additional assumptions and techniques. We propose several novel matching algorithms that address the drawbacks of the current methods, and we use simulations to compare current and new methods. All of the methods display improved covariate balance in the matched sets relative to the prematched cohorts. In addition, we provide advice to investigators on which matching algorithms are preferred for different covariate distributions.