Gaining relevance from the random: Interpreting observed spatial heterogeneity

In Bayesian disease mapping, spatial random effects are used to account for confounding in the data so that reasonable estimates for the fixed effects can be obtained. Typically, the spatial random effects are mapped and qualitative comments are made related to an increase or decrease in risk for certain areas. The approach outlined here illustrates how a quantitative secondary assessment can be applied to make more useful and applicable inference related to these spatial random effects. We are able to recover important but unmeasured or unincluded risk factors via a secondary model fit. Results from the secondary model fit can determine association between spatial region-level risk factors and the estimated spatial random effects. We believe this work presents a useful, quantitative technique highlighting the importance and applicability of spatial random effects as well as illustrates how these methods lead to more interpretable conclusions.