arXiv subjects

Sophie M. Woodward

Publications and source records attributed to Sophie M. Woodward.

2 recordsLinked to original sources

arXiv2025

Understanding Spatial Regression Models from a Weighting Perspective in an Observational Study of Superfund Remediation

A key challenge in environmental health research is unmeasured spatial confounding, driven by unobserved spatially structured variables that influence both treatment and outcome. A common approach is to fit a spatial regression that models the outcome as a linear function of treatment and covariates, with a spatially structured error term to account for unmeasured spatial confounding. However, it remains unclear to what extent spatial regression actually accounts for such forms of confounding in finite samples, and whether this regression adjustment can be reformulated from a design-based perspective. Motivated by an observational study on the effect of Superfund site remediation on birth outcomes, we present a weighting framework for causal inference that unifies three canonical classes of spatial regression models$\unicode{x2013}$random effects, conditional autoregressive, and Gaussian process models$\unicode{x2013}$and reveals how they implicitly construct causal contrasts across space. Specifically, we show that: (i) the spatial error term induces approximate balance on a latent set of covariates and therefore adjusts for a specific form of unmeasured confounding; and (ii) the covariance structure of the spatial error can be equivalently represented as regressors in a linear model. Building on these insights, we introduce a new estimator that jointly addresses multiple forms of unmeasured spatial confounding and develop visual diagnostics. Using our new estimator, we find evidence of a small but beneficial effect of remediation on the percentage of small vulnerable newborns.

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arXiv2025

An Instrumental Variables Framework to Unite Spatial Confounding Methods

Studies investigating the causal effects of spatially varying exposures on outcomes often rely on observational and spatially indexed data. A prevalent challenge is unmeasured spatial confounding, where an unobserved spatially varying variable affects both exposure and outcome, leading to biased estimates and invalid confidence intervals. There is a very large literature on spatial statistics that attempts to address unmeasured spatial confounding bias; most of this literature is not framed in the context of causal inference and relies on strict assumptions. In this paper, we propose an instrumental variables (IV) framework that unifies and extends existing methods for addressing unmeasured spatial confounding bias. This framework reveals that many spatial confounding methods can be viewed as IV methods, in which small-scale spatial variation in exposure operates as the instrument, providing a common theoretical foundation for approaches that previously appeared distinct. The framework clarifies that these methods share a common set of assumptions and differ primarily in how small-scale spatial variation is defined, while offering a general strategy for constructing instruments. It also extends to identify and estimate a broad class of causal effects, including the exposure response curve, without requiring a linear outcome model. We apply our methodology in simulation and to a national data set of 33,255 zip codes to estimate the effect of enforcing air pollution exposure levels below 6-12 $μg/m^3$ on all-cause mortality while adjusting for unmeasured spatial confounding.

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