Selecting a Scale for Spatial Confounding Adjustment

Abstract

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 fine particulate matter and blood pressure in a cohort of United States women.

Keywords: Air Pollution Epidemiology; Confounding; Regression Splines; Spatial Filtering.

Fig. 1.

Estimated difference in SBP (in mmHg) associated with a difference of 10 μg/m³ in annual average ambient PM_2.5, when adjusting for TPRS with varying values of df in the outcome model. The square marker (■) at df = 0 is the estimate without spatial adjustment and has error bars indicating a 95% confidence interval. The thick black curve (▬) represents estimates for different choices of df and the thin black curves (—) represent point-wise 95% confidence intervals.

Fig. 2.

Effective bandwidth (a) by df for TPRS and (b) by frequency for HPF on a 512 × 512 grid over the unit square.

Fig. 3.

Estimates (—) of β in Simulation 1 when pre-adjusting exposure with different choices of spatial basis (panel columns) and different underlying confounding surfaces (panel rows). The far left column shows the unadjusted estimate. The dashed lines (---) and error bars indicate 2x the standard error. The true parameter value β = 1 is plotted as a dotted line (.........).

Fig. 4.

Estimates (—) of β in Simulation 2 when pre-adjusting exposure with different choices of spatial basis (panel columns) and different underlying confounding surfaces (panel rows). The far left column shows the unadjusted estimate. The dashed lines (---) and error bars indicate 2x the standard error. The true parameter value β = 1 is plotted as a dotted line (.........).

Fig. 5.

Estimates (▬) and pointwise confidence intervals (— ) of the association between SBP and PM_2.5 for different amounts of confounding adjustment using TPRS. The horizontal line (---) is at zero.

Fig. 6.

Estimates (▬ ) and pointwise confidence intervals (— ) of the association between SBP and PM_2.5 for different amounts of confounding adjustment using Fourier and wavelet filtering. The horizontal line (---) is at zero.