Randomization-Based Inference for Average Treatment Effect in Inexactly Matched Observational Studies

Matching is a widely used causal inference study design in observational studies. It seeks to mimic a randomized experiment by forming matched sets of treated and control units based on proximity in covariates. Ideally, treated units are exactly matched with controls for the covariates, and randomization-based inference for the treatment effect can then be conducted as in a randomized experiment under the ignorability assumption. However, matching is typically inexact when continuous covariates or many covariates exist. Previous studies have routinely ignored inexact matching in the downstream randomization-based inference as long as some covariate balance criteria are satisfied. Some recent studies found that this routine practice can cause severe bias. They proposed new inference methods for correcting for bias due to inexact matching. However, these inference methods focus on the constant treatment effect (i.e., Fisher's sharp null) and are not directly applicable to the average treatment effect (i.e., Neyman's weak null). To address this problem, we propose a new framework - inverse post-matching probability weighting (IPPW) - for randomization-based average treatment effect inference under inexact matching. Compared with the routinely used randomization-based inference framework based on the difference-in-means estimator, our proposed IPPW framework can substantially reduce bias due to inexact matching and improve the coverage rate. We have also developed an open-source R package RIIM (Randomization-Based Inference under Inexact Matching) for implementing our methods.