Discovering Causal Relationships using Proxy Variables under Unmeasured Confounding

2025-10-20

AI Summary

This paper addresses nonparametric causal inference in observational studies with unmeasured confounding. We propose a novel identification framework grounded in negative control variables, formulated as an integral equation. Under mild regularity conditions and using only one negative control outcome variable, our approach achieves nonparametric identification of causal effects for both discrete and continuous treatments. Incorporating a negative control exposure variable further enables identification in settings where conventional methods fail, substantially relaxing standard assumptions such as completeness and the existence of strong instrumental variables. We construct a test statistic via kernel estimation and establish its asymptotic unbiasedness under the null and uniform consistency against local alternatives. Extensive simulations and empirical applications—including ICU data and the World Values Survey—demonstrate that our method outperforms existing moment-based approaches in both statistical power and robustness.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

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.

Problem

• Tests causal relationships under unmeasured confounding using proxy variables
• Develops nonparametric approach for discrete and continuous variable settings
• Uses negative control outcomes and exposures to achieve identifiability

Innovation

• Nonparametric approach for causal testing under unmeasured confounders
• Kernel-based testing procedure using negative control outcome
• Combined negative control exposure to restore identifiability