Per- and polyfluoroalkyl substances -- PFAS, the “forever chemicals” -- contaminate water systems in spatial patterns that correlate with industrial activity, population density, and geological features. These same features also correlate with health outcomes through pathways that have nothing to do with PFAS exposure. Xiaodan Zhou, Brian Reich, and Shu Yang address this confounding by embedding the causal problem in a low-rank tensor structure and adjusting for unmeasured spatial confounders using graph-Laplacian eigenvectors extracted from geographic proximity.
The key move is treating geography itself as the hidden confounder. Standard causal inference assumes you can list and measure the confounders or use instruments to bypass them. But PFAS exposure patterns are spatially structured in ways that overlap with hundreds of unmeasured determinants of chronic disease -- proximity to highways, socioeconomic gradients, legacy industrial contamination, local dietary patterns. The authors' spectral adjustment approximates these unmeasured spatial confounders by capturing the dominant modes of geographic variation. The low-rank tensor simultaneously consolidates information across 13 disease outcomes and multiple PFAS compounds, recognizing that the exposure-response relationships share structure. When applied to national monitoring data, the method yields more conservative causal estimates than alternatives -- meaning that simpler methods were likely attributing spatial correlation to PFAS when it belonged to the landscape. The geography that delivers the contaminant also delivers a hundred other causes, and disentangling them requires treating the map as a variable, not a backdrop.
(arXiv:2603.16854)