A causal inference framework for spatial confounding

Over the past few decades, addressing "spatial confounding" has become a major topic in spatial statistics. However, the literature has provided conflicting definitions, and many proposed solutions are tied to specific analysis models and do not address the issue of confounding as it is understood in causal inference. We offer an analysis-model-agnostic definition of spatial confounding as the existence of an unmeasured causal confounder variable with a spatial structure. We present a causal inference framework for nonparametric identification of the causal effect of a continuous exposure on an outcome in the presence of spatial confounding. In particular, we identify two critical additional assumptions that allow the use of the spatial coordinates as a proxy for the unmeasured spatial confounder: the measurability of the confounder as a function of space, which is required for conditional ignorability to hold, and the presence of a non-spatial component in the exposure, required for positivity to hold. We also propose studying a causal estimand based on a "shift intervention" that requires less stringent identifying assumptions than traditional estimands. We then turn to estimation and focus on "double machine learning" (DML), a procedure in which flexible models are used to regress both the exposure and outcome variables on confounders to arrive at a causal estimator with favorable robustness properties and convergence rates. This procedure avoids restrictive assumptions, such as linearity and effect homogeneity, which are typically made in spatial models and which can lead to bias when violated. We demonstrate the advantages of the DML approach analytically and via extensive simulation studies. We apply our methods and reasoning to a study of the effect of fine particulate matter exposure during pregnancy on birthweight in California.