Handling limited overlap in observational studies with cardinality matching

A common problem encountered in observational studies is limited overlap in covariate distributions across treatment groups. To address this problem, and avoid strong modeling assumptions, it has become common practice to restrict analyses to the portions of the treatment groups that overlap or, ultimately, are balanced in their covariate distributions. Often, this is done by matching on the estimated propensity score or coarsened versions of the observed covariates. A recent alternative methodology that, in a sense, encompasses these two approaches is cardinality matching. Cardinality matching is a flexible matching method that uses integer programming to find the largest matched sample that is balanced according to criteria specified before matching by the investigator. In this paper, we apply and illustrate the method of cardinality matching and show how to use it to directly balance several features of the covariates, including their trajectories in time and their distributions, without requiring exact matching. We demonstrate how cardinality matching addresses the problem of limited overlap using the original covariates, as opposed to a summarized or coarsened version of them. We discuss how this method can be extended to build matched samples that are not only balanced but also representative of a target population by design. We also show how this method enhances sensitivity analyses for hidden biases. We explain these advancements through an observational study of the electoral impact of the 2010 earthquake in Chile.