Optimal Matching of an Optimally Chosen Subset in Observational Studies

An algorithm is proposed for optimally matching to controls an optimally chosen subset of treated subjects. The algorithm makes three optimal decisions at once: (i) the number of treated subjects to match, (ii) the identity of the treated subjects to match, and (iii) the identity of the controls with whom they are paired. The algorithm finds an optimal assignment for an augmented distance matrix. An example from critical care medicine is considered in detail. An R-workspace is available under “supplemental materials”; it can reproduce the matches in the example.