Polymatching algorithm in observational studies with multiple treatment groups

Matched designs are commonly used in non-randomized studies to evaluate causal effects for dichotomous treatment. Optimal matching algorithms have been devised to form matched pairs or sets between treatment and control groups in various designs, including 1-k matching and full matching. With multiple treatment arms, however, the optimal matching problem cannot be solved in polynomial-time. This is a major challenge for implementing matched designs with multiple arms, which are important for evaluating causal effects with different dose levels or constructing evidence factors with multiple control groups. A polymatching framework for generating matched sets among multiple groups is proposed. An iterative multi-way algorithm for implementation is developed, which takes advantage of the existing optimal two-group matching algorithm repeatedly. An upper bound for the total distance attained by our algorithm is provided to show that the distance result is close to the optimal solution. Simulation studies are conducted to compare the proposed algorithm with the nearest neighbor algorithm under different scenarios. The algorithm is also used to construct a difference-in-difference matched design among four groups, to examine the impact of Medicaid expansion on the health status of Ohioans.