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

Matching is a commonly used causal inference framework in observational studies. By pairing individuals with different treatment values but with the same values of covariates (i.e., exact matching), the sample average treatment effect (SATE) can be consistently estimated and inferred using the classic Neyman-type (difference-in-means) estimator and confidence interval. However, inexact matching typically exists in practice and may cause substantial bias for the downstream treatment effect estimation and inference. Many methods have been proposed to reduce bias due to inexact matching in the binary treatment case. However, to our knowledge, no existing work has systematically investigated bias due to inexact matching in the continuous treatment case. To fill this blank, we propose a general framework for reducing bias in inexactly matched observational studies with continuous treatments. In the matching stage, we propose a carefully formulated caliper that incorporates the information of both the paired covariates and treatment doses to better tailor matching for the downstream SATE estimation and inference. In the estimation and inference stage, we propose a bias-corrected Neyman estimator paired with the corresponding bias-corrected variance estimator to leverage the information on propensity density discrepancies after inexact matching to further reduce the bias due to inexact matching. We apply our proposed framework to COVID-19 social mobility data to showcase differences between classic and bias-corrected SATE estimation and inference.