Approaches to spatial confounding in geostatistics

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 do not address the issue of confounding as it is understood in causal inference. We give a clear account of spatial confounding as the existence of an unmeasured confounding variable with a spatial structure. Under certain conditions, including the measurability of the confounder as a function of space, we show that spatial covariates (e.g. latitude and longitude) can be handled by existing causal inference estimation procedures. We 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. These models avoid 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.