A Note on Optimal Matching With Variable Controls Using the Assignment Algorithm

The assignment algorithm is an old, well-known, widely implemented, fast, combinatorial algorithm for optimal matching in a bipartite graph. This note proposes a method for using the assignment algorithm to solve the problem of optimal matching with a variable number of controls, in which there is a choice not only of who to select as a control for each treated subject, but also of how many controls to have for each treated subject. The strategy uses multiple copies of treated subjects and sinks with zero cost to absorb extra controls. Also, it is shown that an optimal matching with variable numbers of controls cannot be obtained by starting with an optimal pair matching and adding the closest additional controls. An example involving mortality after surgery in Pennsylvania hospitals is used to illustrate the method.     

An Algorithm for Optimal Tapered Matching,With Application to Disparities in Survival

In a tapered matched comparison, one group of individuals, called the focal group, is compared to two or more nonoverlapping matched comparison groups constructed from one population in such a way that successive comparison groups increasingly resemble the focal group. An optimally tapered matching solves two problems simultaneously: it optimally divides the single comparison population into nonoverlapping comparison groups and optimally pairs members of the focal group with members of each comparison group. We show how to use the optimal assignment algorithm in a new way to solve the optimally tapered matching problem, with implementation in R. This issue often arises in studies of groups defined by race, gender, or other categorizations such that equitable public policy might require an understanding of the mechanisms that produce disparate outcomes, where certain specific mechanisms would be judged illegitimate, necessitating reform. In particular, we use data from Medicare and the SEER Program of the National Cancer Institute as part of an ongoing study of black-white disparities in survival among women with endometrial cancer.     

Miscellaneous classification results for 2-designs

An orderly algorithm combined with clique searching is used to show that there are—up to isomorphism, in all cases—325,062 resolvable 2-(16,4,2) designs with 339,592 resolutions, 19,072,802 2-(13,6,5) designs, and 15,111,019 2-(14,7,6) designs. Properties of the classified designs are further discussed.