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Primary Submission Category: Matching

Bias Correction for Randomization-Based Inference in Imperfectly Matched Observational Studies: Oracles, Practices, and Simulations

Authors: Jianan Zhu, Siyu Heng,

Presenting Author: Jianan Zhu*

In causal inference, matching is one of the most widely used methods to mimic a randomized experiment with observational data. Ideally, treated subjects are perfectly matched with controls for the confounders, and randomization-based inference can therefore be conducted. However, imperfect matching is typically expected in practice, especially with continuous or many confounders. Previous imperfectly matched studies have routinely treated the downstream randomization-based inference as if the confounders were perfectly matched. In this work, we propose a bias correction framework for randomization-based inference with imperfectly matched datasets to further reduce confounding bias after matching. First, we derive the unbiased oracle randomization-based inference procedure with imperfect matching under oracle propensity scores. Second, based on the derived oracle inference procedure, we give some practical proposals for bias correction for imperfect matching by replacing oracle propensity scores with estimated ones. Third, we conduct simulation studies to compare the performances of various practices of randomization-based inference, including the previous practice of ignoring imperfect matching and our proposed practices of bias correction for imperfect matching. Our framework works for most existing matching designs and covers both Fisher’s sharp null and Neyman’s weak null.