Bias Mitigation in Matched Observational Studies with Continuous Treatments: Calipered Non-Bipartite Matching and Bias-Corrected Estimation and Inference

Abstract: In matched observational studies with continuous treatments, individuals with different treatment doses but the same or similar covariate values are paired for causal inference. While inexact covariate matching (i.e., covariate imbalance after matching) is common in practice, previous matched studies with continuous treatments have often overlooked this issue as long as post-matching covariate balance meets certain criteria. Through re-analyzing a matched observational study on the social distancing effect on COVID-19 case counts, we show that this routine practice can introduce severe bias for causal inference. Motivated by this finding, we propose a general framework for mitigating bias due to inexact matching in matched observational studies with continuous treatments, covering the matching, estimation, and inference stages. In the matching stage, we propose a carefully designed caliper that incorporates both covariate and treatment dose information to improve matching for downstream treatment effect estimation and inference. For the estimation and inference, we introduce a bias-corrected Neyman estimator paired with a corresponding bias-corrected variance estimator. The effectiveness of our proposed framework is demonstrated through numerical studies and a re-analysis of the aforementioned observational study on the effect of social distancing on COVID-19 case counts. An open-source R package for implementing our framework has also been developed.