Optimal nonbipartite matching and its statistical applications. Matching is a powerful statistical tool in design and analysis. Conventional two-group, or bipartite, matching has been widely used in practice. However, its utility is limited to simpler designs. In contrast, nonbipartite matching is not limited to the two-group case, handling multiparty matching situations. It can be used to find the set of matches that minimize the sum of distances based on a given distance matrix. It brings greater flexibility to the matching design, such as multigroup comparisons. Thanks to improvements in computing power and freely available algorithms to solve nonbipartite problems, the cost in terms of computation time and complexity is low. This article reviews the optimal nonbipartite matching algorithm and its statistical applications, including observational studies with complex designs and an exact distribution-free test comparing two multivariate distributions. We also introduce an R package that performs optimal nonbipartite matching. We present an easily accessible web application to make nonbipartite matching freely available to general researchers.

References in zbMATH (referenced in 9 articles )

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  1. Biswas, Munmun; Sarkar, Soham; Ghosh, Anil K.: On some exact distribution-free tests of independence between two random vectors of arbitrary dimensions (2016)
  2. Petrie, Adam: Graph-theoretic multisample tests of equality in distribution for high dimensional data (2016)
  3. Sauppe, Jason J.; Jacobson, Sheldon H.; Sewell, Edward C.: Complexity and approximation results for the balance optimization subset selection model for causal inference in observational studies (2014)
  4. Zubizarreta, José R.; Paredes, Ricardo D.; Rosenbaum, Paul R.: Matching for balance, pairing for heterogeneity in an observational study of the effectiveness of for-profit and not-for-profit high schools in Chile (2014)
  5. Zubizarreta, José R.; Small, Dylan S.; Rosenbaum, Paul R.: Isolation in the construction of natural experiments (2014)
  6. Rosenbaum, Paul R.: Impact of multiple matched controls on design sensitivity in observational studies (2013)
  7. Zubizarreta, José R.; Small, Dylan S.; Goyal, Neera K.; Lorch, Scott; Rosenbaum, Paul R.: Stronger instruments via integer programming in an observational study of late preterm birth outcomes (2013)
  8. Heller, R.; Gorfine, M.; Heller, Y.: A class of multivariate distribution-free tests of independence based on graphs (2012)
  9. Yang, Dan; Small, Dylan S.; Silber, Jeffrey H.; Rosenbaum, Paul R.: Optimal matching with minimal deviation from fine balance in a study of obesity and surgical outcomes (2012)