A Bayesian spatial measurement error approach to incorporate heterogeneous population-at-risk uncertainty in estimating small-area opioid mortality rates

Monitoring small-area geographical population trends in opioid mortality has significant implications for informing preventative resource allocation. A common approach to estimating small-area opioid mortality uses a standard disease mapping method where population-at-risk estimates (denominators) are treated as fixed. This assumption ignores the uncertainty in small-area population estimates, potentially biasing risk estimates and underestimating their uncertainties. We compare a Bayesian Spatial Berkson Error model and a Bayesian Spatial Classical Error model to a naive approach that treats denominators as fixed. Using simulations, we illustrate potential bias from ignored population-at-risk uncertainty. We apply these methods to obtain 2020 opioid mortality risk estimates for 159 counties in Georgia. Assessing differences in bias and uncertainty across approaches can improve the accuracy of small-area opioid risk estimates, guiding public health interventions, policies, and resource allocation.