Effect of spatial scale on bias in models with spatial confounding

When unmeasured confounders vary spatially, a common technique in spatial epidemiology is to try to account for the unmeasured confounding by modeling residual spatial correlation. Previous work in the temporal setting indicates that when the variable of interest has an uncorrelated component then such an approach can minimize bias. Here I consider the situation that the variable of interest varies at multiple spatial scales but may not have a non-spatial component. I develop a framework for understanding bias using a simple generalized least squares model with data collected at point locations and fixed and known spatial scales. I show that bias is substantial even when the scales are known, unless the variable of interest has an unconfounded component that varies at a finer spatial scale than the confounder. Using simulation I consider the effect of estimating the scale of the residual spatial correlation on bias. The implication for data aggregated into areal units under s

tandard conditional autoregressive models is that these models are unlikely to account for unmeasured confounding. I suggest diagnostics and sensitivity analyses to understand whether it is possible to account for spatial confounding in any given application.