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

TL;DR

This paper introduces a spectral domain approach to adjust for unmeasured spatial confounding in multivariate environmental health studies, enabling more accurate causal inference across multiple exposures and outcomes.

Contribution

It proposes a novel tensor-based spectral method with shrinkage priors to separate spatial scales and mitigate confounding bias in complex spatial regression models.

Findings

Effective in simulations for reducing confounding bias.

Improves causal interpretation of exposure effects.

Demonstrated on disaster resilience and chronic disease data.

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.