Network flow methods for the minimum covariate imbalance problem

In an observational study, one is given disjoint samples of treatment units and control (untreated) units, the goal to compare outcomes between two in order estimate a effect. A complication that often differ on important pre-treatment attributes, these differences, referred as covariate imbalance, can bias estimate. One method correct for imbalance select subset sample has minimum with respect sample, then use this estimating While optimization problem NP-hard general, certain special cases be solved efficiently. Specifically, variant easy solve, three or more covariates NP-hard, solvable polynomial time. We present several network flow formulations minimizing nominal covariates. First, we cost formulation solving constraint must have same size sample. derive improved maximum formulation. For alternate restrictions subset, proportional objective which leads non-integral supplies demands preceding formulations. ensures integrality solves