Optimization Techniques in Multivariate Matching

Optimization techniques for multivariate matching in observational studies are widely used and extensively developed, and the subject continues to grow at a quick pace. This chapter reviews some of this technical background at a level appropriate for a PhD student in statistics. It assumes no background in combinatorial optimization, and the chapter may serve as an entry point to the literature on combinatorial optimization for a student of statistics. Matching is used to achieve a variety of goals. Mostly commonly, it is used to reduce confounding from measured covariates in observational studies. There are several algorithms for finding an optimal assignment. A typical strategy for solving a new combinatorial optimization problem is to reduce it to a previously solved problem. In some contexts, there are some treated individuals who are unlike all controls in terms of observed covariates.