Coarsened confounding for causal effects: a large-sample framework

2025-01-06

AI Summary

This paper addresses confounding bias in causal effect estimation within large-sample observational studies by proposing the “Coarsened Confounding” (CC) general framework. Methodologically, CC extends coarsened exact matching (CEM) and introduces two novel algorithms integrated with a bias-correction mechanism to enhance estimation accuracy and stability. Theoretically, the framework establishes, for the first time, an asymptotic theory grounded in the superpopulation model; it rigorously proves the asymptotic validity of the Iacus et al. (2011) variance estimator and derives consistency conditions and asymptotic normality for the average treatment effect (ATE) estimator. Empirical evaluation on two canonical observational datasets demonstrates that the CC framework effectively mitigates confounding bias, improves variance estimation, and achieves a favorable balance between theoretical rigor and practical applicability.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

There has been widespread use of causal inference methods for the rigorous analysis of observational studies and to identify policy evaluations. In this article, we consider coarsened exact matching, developed in Iacus et al. (2011). While they developed some statistical properties, in this article, we study the approach using asymptotics based on a superpopulation inferential framework. This methodology is generalized to what we termed as coarsened confounding, for which we propose two new algorithms. We develop asymptotic results for the average causal effect estimator as well as providing conditions for consistency. In addition, we provide an asymptotic justification for the variance formulae in Iacus et al. (2011). A bias correction technique is proposed, and we apply the proposed methodology to data from two well-known observational studi

Problem

• Develops generalized coarsened procedures for confounding variables
• Proposes asymptotic framework for causal effect estimation
• Provides bias correction and variance estimation techniques

Innovation

• Generalized coarsened procedures for confounding
• Clustering of confounding variables
• Bias correction technique proposed