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.