Optimal Full Matching and Related Designs via Network Flows

In the matched analysis of an observational study, confounding on covariates X is addressed by comparing members of a distinguished group (Z = 1) to controls (Z = 0) only when they belong to the same matched set. The better matchings, therefore, are those whose matched sets exhibit both dispersion in Z and uniformity in X. For dispersion in Z, pair matching is best, creating matched sets that are equally balanced between the groups; but actual data place limits, often severe limits, on matched pairs' uniformity in X. At the other extreme is full matching, the matched sets of which are as uniform in X as can be, while often so poorly dispersed in Z as to sacrifice efficiency.This article presents an algorithm…