Uncertainty Quantification in Zip Code Tabulation Area-Level Breast Cancer Screening: A Bayesian Geospatial Analysis...

Geographic variation (GV) in screening patterns for breast cancer exists among Zip Code Tabulation Areas (ZCTAs) in Florida, but most spatial analyses are based on frequentist point estimates which do not formally represent uncertainty. This study used a three-stage analytical approach to the breast cancer screening data at the zip code tract (ZCTA) level in Hillsborough County, Florida (n = 55 ZCTAs): first, a frequentist Poisson regression was applied with diagnostics for multicollinearity; second, global spatial autocorrelation (GSA) analysis was conducted using Moran's I; and third, a Bayesian Poisson and a Bayesian negative binomial regression were performed, both estimated via the No-U-Turn Sampler in the brms/Stan framework. In ArcGIS Pro 3.6, spatial analyses were carried out. The dependent variable was the number of breast cancer screening exams conducted at the ZCTA level over the study period. Across all racial/ethnic subgroups, the observed number of screenings was correlated with the number of females in the household, while no independent correlation was found for median household income, insurance status or age by stratum variables after adjustment. There was no significant and strong spatial autocorrelation across the study area (Moran's I = 0.003, z = 0.326, p = 0.745). The Poisson model did best among the Bayesian models with a Bayesian R² of 0.91, RMSE of 5.40, and MBE of 0.02. The results show the usefulness of Bayesian uncertainty quantification in small area public health surveillance and offer a framework for quantifying geographic variation in screening activity in a probabilistic manner. The results only compare screening examination (not population-standardized screening rates) and should be considered to reflect screening volume rather than screening participation.