Selecting a Scale for Spatial Confounding Adjustment

Unmeasured, spatially-structured factors can confound associations between spatial environmental exposures and health outcomes. Adding flexible splines to a regression model is a simple approach for spatial confounding adjustment, but the spline degrees of freedom do not provide an easily interpretable spatial scale. We describe a method for quantifying the extent of spatial confounding adjustment in terms of the Euclidean distance at which variation is removed. We develop this approach for confounding adjustment with splines and using Fourier and wavelet filtering. We demonstrate differences in the spatial scales these bases can represent and provide a comparison of methods for selecting the amount of confounding adjustment. We find the best performance for selecting the amount of adjustment using an information criterion evaluated on an outcome model without exposure. We apply this method to spatial adjustment in an analysis of particulate matter and blood pressure in a cohort of United States women.