Graded Matching for Large Observational Studies

Ruoqi Yu, Paul R. Rosenbaum

Research output: Contribution to journalArticlepeer-review


Observational studies of causal effects often use multivariate matching to control imbalances in measured covariates. For instance, using network optimization, one may seek the closest possible pairing for key covariates among all matches that balance a propensity score and finely balance a nominal covariate, perhaps one with many categories. This is all straightforward when matching thousands of individuals, but requires some adjustments when matching tens or hundreds of thousands of individuals. In various senses, a sparser network—one with fewer edges—permits optimization in larger samples. The question is: What is the best way to make the network sparse for matching? A network that is too sparse will eliminate from consideration possible pairings that it should consider. A network that is not sparse enough will waste computation considering pairings that do not deserve serious consideration. We propose a new graded strategy in which potential pairings are graded, with a preference for higher grade pairings. We try to match with pairs of the best grade, incorporating progressively lower grade pairs only to the degree they are needed. In effect, only sparse networks are built, stored and optimized. Two examples are discussed, a small example with 1567 matched pairs from clinical medicine, and a slightly larger example with 22,111 matched pairs from economics. The method is implemented in an R package RBestMatch available at Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1406-1415
Number of pages10
JournalJournal of Computational and Graphical Statistics
Issue number4
StatePublished - 2022
Externally publishedYes


  • Fine balance
  • Network optimization
  • Observational study
  • Optimal matching
  • Rank maximal matching

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics


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