A Spectral Confounder Adjustment for Spatial Regression with Multiple Exposures and Outcomes

2025-06-11

AI Summary

In environmental health research, unobserved spatial confounding induces severe and heterogeneous bias in causal effect estimation for multiple exposures and multiple outcomes. To address this, we propose a spectral-domain tensor regression model: leveraging spatial spectral analysis, we formulate confounding effects as locally scale-decaying processes and represent exposure–outcome–spatial-scale relationships as a three-dimensional tensor. For the first time, we integrate CP decomposition with Bayesian shrinkage priors within a multi-task learning framework, enabling cross-dimensional information sharing and sparse regularization while preserving causal interpretability of local-scale coefficients. Simulation studies and real-world analyses of disaster resilience–chronic disease associations demonstrate that our method substantially reduces confounding bias and improves accuracy, robustness, and interpretability in identifying multi-exposure effects.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Causality
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Unmeasured spatial confounding complicates exposure effect estimation in environmental health studies. This problem is exacerbated in studies with multiple health outcomes and environmental exposure variables, as the source and magnitude of confounding bias may differ across exposure/outcome pairs. We propose to mitigate the effects of spatial confounding in multivariate studies by projecting to the spectral domain to separate relationships by the spatial scale and assuming that the confounding bias dissipates at more local scales. Under this assumption and some reasonable conditions, the random effect is uncorrelated with the exposures in local scales, ensuring causal interpretation of the regression coefficients. Our model for the exposure effects is a three-way tensor over exposure, outcome, and spatial scale. We use a canonical polyadic decomposition and shrinkage priors to encourage sparsity and borrow strength across the dimensions of the tensor. We demonstrate the performance of our method in an extensive simulation study and data analysis to understand the relationship between disaster resilience and the incidence of chronic diseases.

Problem

• Addressing unmeasured spatial confounding in environmental health studies
• Mitigating confounding bias in multiple exposures and outcomes analysis
• Separating spatial scale relationships to ensure causal coefficient interpretation

Innovation

• Spectral domain projection for spatial confounding
• Three-way tensor model for exposure effects
• Canonical polyadic decomposition with shrinkage priors