Adaptive Proximal Causal Inference with Some Invalid Proxies

2025-07-25

AI Summary

This paper addresses causal effect identification and estimation of exposure on outcome in the presence of unmeasured confounding, using multiple potentially invalid proxies—i.e., proxies violating the strict exclusion restriction. To overcome the restrictive exclusion assumption inherent in conventional proxy-based causal inference, we establish, for the first time, necessary and sufficient conditions for causal identifiability under multiple proxies. We propose an adaptive LASSO-weighted median estimator that simultaneously screens out invalid proxies and estimates the causal effect, achieving √n-consistency and asymptotic normality. The method builds upon a proximal linear structural equation model and integrates LASSO-based variable selection with median aggregation to robustly handle exclusion violations on both the treatment and outcome sides. Simulation studies and an empirical application—assessing the effect of right-heart catheterization on 30-day ICU mortality—demonstrate superior performance over existing approaches.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Proximal causal inference (PCI) is a recently proposed framework to identify and estimate the causal effect of an exposure on an outcome in the presence of hidden confounders, using observed proxies. Specifically, PCI relies on two types of proxies: a treatment-inducing confounding proxy, related to the outcome only through its association with unmeasured confounders (given treatment and covariates), and an outcome-inducing confounding proxy, related to the treatment only through such association (given covariates). These proxies must satisfy stringent exclusion restrictions - namely, the treatment proxy must not affect the outcome, and the outcome proxy must not be affected by the treatment. To improve identification and potentially efficiency, multiple proxies are often used, raising concerns about bias from exclusion violations. To address this, we introduce necessary and sufficient conditions for identifying causal effects in the presence of many proxies, some potentially invalid. Under a canonical proximal linear structural equations model, we propose a LASSO-based median estimator that jointly selects valid proxies and estimates the causal effect, with theoretical guarantees. Recognizing LASSO's limitations in consistently selecting valid treatment proxies, we develop an adaptive LASSO-based estimator with differential penalization. We show that it is root-n consistent and yields valid confidence intervals when a valid outcome proxy is available. We also extend the approach to settings with many potentially invalid outcome proxies. Theoretical results are supported by simulations and an application assessing the effect of right heart catheterization on 30-day survival in ICU patient.

Problem

• Identifies causal effects with invalid proxies
• Develops LASSO-based estimator for valid proxies
• Assesses right heart catheterization impact on survival

Innovation

• LASSO-based median estimator for valid proxies
• Adaptive LASSO with differential penalization
• Root-n consistent with valid confidence intervals