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.

翻译：匹配是观察性研究中广泛使用的因果推断研究设计。它通过基于协变量邻近性构建处理组与对照组的匹配集，旨在模拟随机化实验。理想情况下，处理单元与对照单元在协变量上实现精确匹配，随后可在可忽略性假设下如同随机化实验般进行基于随机化的处理效应推断。然而，当存在连续协变量或大量协变量时，匹配通常是非精确的。先前研究只要满足某些协变量平衡标准，就会在下游的基于随机化推断中常规性地忽略非精确匹配问题。近期研究发现，这种常规做法可能导致严重偏差。为此，学者们提出了新的推断方法以校正非精确匹配引起的偏差。然而，这些推断方法主要关注恒定处理效应（即费希尔强零假设），并不直接适用于平均处理效应（即奈曼弱零假设）。为解决此问题，我们提出了一个新框架——逆匹配后概率加权（IPPW）——用于非精确匹配下基于随机化的平均处理效应推断。与常规使用的基于均值差估计量的随机化推断框架相比，我们提出的IPPW框架能显著减少非精确匹配导致的偏差并提升覆盖率。我们还开发了开源R软件包RIIM（非精确匹配下的随机化推断）以实现所提方法。