  Randomized clinical trials (RCTs) 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 RCT. 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 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 pre-matched
cohorts. In addition, we provide advice to investigators on which matching
algorithms are preferred for different covariate distributions.
