Handling Limited Overlap in Observational Studies with Cardinality Matching

Abstract

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.

How did the COVID-19 pandemic impact the stress vulnerability of employed and non-employed nursing students in Romania?

“…Causal effects are defined as comparisons between possible outcomes in terms of expected values, median or odd-rations of an unit i and a group of N units [23]. Appendix 2 in S1 File describes the algorithm used in order to assess the impact of employment status on nursing students and the COVID-19 pandemic on their stress vulnerability.…”

Profile Matching for the Generalization and Personalization of Causal Inferences

“…In randomized or observational studies, this facilitates estimation of the TATE by selecting the covariate profile appropriately. Profile matching can be implemented directly via a new approach to matching (specifically, by solving a multidimensional knapsack problem; Kellerer et al 2004;Bennett et al 2020) or indirectly via existing software for cardinality matching (Zubizarreta et al 2014;Visconti and Zubizarreta 2018). In the Supplementary Materials we describe the technical details of these two approaches.…”

“…After using cardinality matching to find the largest pairwise matched samples that are balanced, we re-match the samples to minimize the covariate distances between the matched units. That is-cardinality matching produces equally-sized subsamples from two exposure groups, and re-matching allows us to find pairs of individuals (i.e., one from each exposure group) such that the overall sum of covariate distances across the matched pairs is minimized (Visconti and Zubizarreta 2018). Thus, the final re-matched sets consist of the same individuals-they are just paired, perhaps, differently.…”

“…Thus, the final re-matched sets consist of the same individuals-they are just paired, perhaps, differently. This re-matching reduces heterogeneity in the matched pairs and translates into less sensitivity to hidden bias if the covariates used to compute the distances are strong predictors of the outcome (Visconti and Zubizarreta 2018;Zubizarreta et al 2014). To achieve this property, we construct matched pairs based on the binary covariate indicating the occurrence of a past year major depressive episode, as this covariate is predictive of both outcomes.…”

Treatment Effect Estimation using Invariant Risk Minimization

“…Classical matching techniques match the samples from the treatment group and the control group using nearest neighbor matching [15,16] or optimal matching [17]. More recent methods match using the estimated propensity score [11], coarsened versions of the observed covariates [18], or cardinality matching [19].…”