Spatial Causal Tensor Completion for Multiple Exposures and Outcomes: An Application to the Health Effects of PFAS Pollution

2026-03-17

AI Summary

This study addresses the challenge of jointly estimating causal effects of multiple PFAS exposures on multiple health outcomes in the presence of unobserved spatial confounding and pervasive missingness in potential outcomes. To tackle this, the authors propose a spatial causal tensor completion framework that integrates low-rank tensor modeling with spectral adjustment based on graph Laplacian eigenvectors. This approach uniquely combines tensor completion with spectral correction to approximately control for latent spatial confounders while enabling multi-exposure–multi-outcome causal inference. An efficient optimization procedure is implemented via projected gradient descent. Simulation studies demonstrate the method’s superior performance, and its application to national PFAS monitoring data reveals more conservative and robust causal associations between PFOA/PFOS and thirteen chronic diseases.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Per- and polyfluoroalkyl substances (PFAS) are typically encountered as mixtures of distinct chemicals with distinct effects on multiple health outcomes. Estimating joint causal effects using spatially-dependent observed data is challenging. We propose a spatial causal tensor completion framework that jointly models multiple exposures and outcomes within a low-rank tensor structure, while adjusting for observed confounders and latent spatial confounders. This method combines a low-rank tensor representation to pool information across exposures and outcomes with a spectral adjustment step that incorporates graph-Laplacian eigenvectors to approximate unmeasured spatial confounders, implemented via a projected-gradient descent algorithm. This framework enables causal inference in the presence of unmeasured spatial confounding and pervasive missingness of potential outcomes. We establish theoretical guarantees for the estimator and evaluate its finite-sample performance through extensive simulations. In an application to national PFAS monitoring data, our approach yields more conservative and credible causal relationships between PFOA and PFOS exposure and 13 chronic disease outcomes compared with existing alternatives.

Problem

• causal inference
• spatial confounding
• tensor completion
• multiple exposures
• missing outcomes

Innovation

• spatial causal inference
• tensor completion
• low-rank structure
• unmeasured spatial confounding
• graph Laplacian