Optimal Matching for Observational Studies

TLDR

Matching is widely used in observational studies, yet greedy stepwise procedures often produce suboptimal samples that could be improved by reassigning controls, and computational efficiency is a concern. The study applies network flow theory to obtain optimal matched samples. The authors combine statistical matching and graph‑matching algorithms, reviewing both literatures, to formulate optimal matching via network flow. Optimal matched‑pair samples are obtained, and the approach also yields optimal constructions for several previously unstudied statistical matching problems, including multiple controls, variable numbers of controls, and balanced samples combining pair and frequency matching.

Abstract

Abstract Matching is a common method of adjustment in observational studies. Currently, matched samples are constructed using greedy heuristics (or "stepwise" procedures) that produce, in general, suboptimal matchings. With respect to a particular criterion, a matched sample is suboptimal if it could be improved by changing the controls assigned to specific treated units, that is, if it could be improved with the data at hand. Here, optimal matched samples are obtained using network flow theory. In addition to providing optimal matched-pair samples, this approach yields optimal constructions for several statistical matching problems that have not been studied previously, including the construction of matched samples with multiple controls, with a variable number of controls, and the construction of balanced matched samples that combine features of pair matching and frequency matching. Computational efficiency is discussed. Extensive use is made of ideas from two essentially disjoint literatures, namely statistical matching in observational studies and graph algorithms for matching. The article contains brief reviews of both topics.