Discovering Causal Relationships using Proxy Variables under Unmeasured Confounding

TL;DR

This paper introduces a flexible nonparametric method for discovering causal relationships using negative controls, effectively addressing unmeasured confounding in both discrete and continuous data settings.

Contribution

It presents a novel integral equation-based identification approach and a kernel testing procedure that work with a single negative control outcome, extending to negative control exposure when needed.

Findings

Effective in both discrete and continuous settings

Outperforms existing methods in efficiency

Validated on real-world datasets

Abstract

Inferring causal relationships between variable pairs in the observational study is crucial but challenging, due to the presence of unmeasured confounding. While previous methods employed the negative controls to adjust for the confounding bias, they were either restricted to the discrete setting (i.e., all variables are discrete) or relied on strong assumptions for identification. To address these problems, we develop a general nonparametric approach that accommodates both discrete and continuous settings for testing causal hypothesis under unmeasured confounders. By using only a single negative control outcome (NCO), we establish a new identification result based on a newly proposed integral equation that links the outcome and NCO, requiring only the completeness and mild regularity conditions. We then propose a kernel-based testing procedure that is more efficient than existing moment-restriction methods. We derive the asymptotic level and power properties for our tests. Furthermore, we examine cases where our procedure using only NCO fails to achieve identification, and introduce a new procedure that incorporates a negative control exposure (NCE) to restore identifiability. We demonstrate the effectiveness of our approach through extensive simulations and real-world data from the Intensive Care Data and World Values Survey.