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Motivated by a study exploring differences in glycemic control between non-Hispanic black and non-Hispanic white veterans with type 2 diabetes, we aim to address a type of confounding that arises in spatially referenced observational studies. Specifically, we develop a spatial doubly robust propensity score estimator to reduce bias associated with geographic confounding, which occurs when measured or unmeasured confounding factors vary by geographic location, leading to imbalanced group comparisons. We augment the doubly robust estimator with spatial random effects, which are assigned conditionally autoregressive priors to improve inferences by borrowing information across neighboring geographic regions. Through a series of simulations, we show that ignoring spatial variation results in increased absolute bias and mean squared error, while the spatial doubly robust estimator performs well under various levels of spatial heterogeneity and moderate sample sizes. In the motivating application, we construct three global estimates of the risk difference between race groups: an unadjusted estimate, a doubly robust estimate that adjusts only for patient-level information, and a hierarchical spatial doubly robust estimate. Results indicate a gradual reduction in the risk difference at each stage, with the inclusion of spatial random effects providing a 20% reduction compared to an estimate that ignores spatial heterogeneity. Smoothed maps indicate poor glycemic control across Alabama and southern Georgia, areas comprising the so-called "stroke belt." These results suggest the need for community-specific interventions to target diabetes in geographic areas of greatest need.

Addressing geographic confounding through spatial propensity scores: a study of racial disparities in diabetes