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

TL;DR

This paper introduces a new inverse post-matching probability weighting method for more accurate randomization-based inference of average treatment effects in observational studies with inexact matching.

Contribution

It extends randomization-based inference methods to handle inexact matching for average treatment effects, addressing a gap in existing approaches focused on constant effects.

Findings

The proposed method reduces bias compared to conventional approaches.

Simulation results show improved coverage rates with the new method.

Theoretical analysis supports the effectiveness of the approach.

Abstract

Matching is a widely used causal inference design that aims to approximate a randomized experiment using observational data by forming matched sets of treated and control units based on similarities in their covariates. Ideally, treated units are exactly matched with controls on these covariates, enabling randomization-based inference for treatment effects as in a randomized experiment, under the assumption of no unobserved covariates. However, inexact matching often occurs, leading to residual covariate imbalance after matching. Previous matched studies have typically overlooked this issue and relied on conventional randomization-based inference, assuming that some covariate balance criteria are met. Recent research, however, has shown that this approach can introduce significant bias and proposed methods to correct for bias arising from inexact matching in randomization-based inference. These methods, however, are primarily focused on the constant treatment effect and its extensions (i.e., Fisher's sharp null) and do not apply to average treatment effects (i.e., Neyman's weak null). To address this gap, we introduce a new method--inverse post-matching probability weighting--for conducting randomization-based inference for average treatment effects under inexact matching. Our theoretical and simulation results indicate that, compared to conventional randomization-based inference methods, our approach significantly reduces bias and improves coverage rates in the presence of inexact matching.