An Instrumental Variables Framework to Unite Spatial Confounding Methods

Abstract: Studies investigating the causal effects of spatially varying exposures on human health 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 introduce a foundational instrumental variables (IV) framework that unites many of the existing approaches designed to account for unmeasured spatial confounding bias. Using the newly introduced framework, we show that many existing approaches are in fact IV methods, where small-scale variation in exposure is the instrument. By mapping each approach to our framework, we explicitly derive its underlying assumptions and estimation strategy. We further provide theoretical arguments that enable the IV framework to identify a general class of causal effects, including the exposure response curve, without assuming a linear outcome model. We apply our methodology to a national data set of 33,255 zip codes to estimate the effect of enforcing air pollution exposure levels below 6-12 $\mu g/m^3$ on all-cause mortality while adjusting for unmeasured spatial confounding.