Discussion of the manuscript: Spatial+ a novel approach to spatial confounding

Abstract: I congratulate Dupont, Wood and Augustin (DWA hereon) for providing an easy-to-implement method for estimation in the presence of spatial confounding, and for addressing some of the complicated aspects on the topic. The method regresses the covariate of interest on spatial basis functions and uses the residuals of this model in an outcome regression. The authors show that, if the covariate is not completely spatial, this approach leads to consistent estimation of the conditional association between the exposure and the outcome. Below I discuss conceptual and operational issues that are fundamental to inference in spatial settings: (i) the target quantity and its interpretability, (ii) the non-spatial aspect of covariates and their relative spatial scales, and (iii) the impact of spatial smoothing. While DWA provide some insights on these issues, I believe that the audience might benefit from a deeper discussion. In what follows, I focus on the setting where a researcher is interested in interpreting the relationship between a given covariate and an outcome. I refer to the covariate of interest as the exposure to differentiate it from the rest.