Optimal Full Matching

In an observational study the distribution of outcomes and covariates for units receiving the treatment condition may differ greatly from the distribution of outcomes and covariates for units receiving the control condition. Simple estimates of treatment effects or tests of hypotheses for causal effects may be confounded if appropriate adjustment is not applied. In this chapter, we discuss optimal full matching, a particular form of statistical matching to control for background imbalances in covariates or treatment probabilities. Ideally, the matched sets would be homogeneous on background variables and the probability of receiving the treatment condition. In practice, such precise matching is frequently not possible, which suggests matches that minimize observed discrepancies. Optimal full matches can be found efficiently in moderate sized problems on modern hardware, and the algorithm permits researcher control of matched sets that can be used to control which units are matched and also reduce the complexity of large problems. The algorithms for optimal full matches are readily available in existing software packages and are easily extended to include additional constraints on acceptable matches. We conclude with a brief discussion of the use of matches in outcome analysis, a simulation study, and an overview of recent developments in the field.