Approaches to spatial confounding in geostatistics

Research in the past few decades has discussed the concept of "spatial confounding" but has provided conflicting definitions and proposed solutions, some of which do not address the issue of confounding as it is understood in the field of 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 smoothness of the confounder as a function of space, we show that spatial covariates (e.g., latitude and longitude) can be handled as typical covariates by algorithms popular in causal inference. We focus on "double machine learning" (DML) by which flexible models are fit for both the exposure and outcome variables to arrive at a causal estimator with favorable convergence properties. These models avoid restrictive assumptions, such as linearity and heterogeneity, which are present in linear models typically employed in spatial statistics and which can lead to strong bias when violated. We demonstrate the advantages of the DML approach analytically and via extensive simulation studies.