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

Thomas M. Menino Convention & Exhibition Center 

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 responses and exposures to the spectral domain to decorrelate the data and separate effects at different spatial resolutions. This transformation replaces the strict causal assumption of no unmeasured confounders with a more realistic assumption of local unconfoundedness, allowing for causal interpretation. 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. This enables us to identify low-rank structures, such as specific themes among disaster resilience impacting incidence of chronic diseases at particular scales. Combining spectral projections with low-rank modeling results in an efficient method is suitable for large datasets, offering interpretable epidemiological insights.

Spatial confounding

causal inference

exposure mixtures

unmeasured confounder

tensor decomposition