Uncertainty Quantification in Zip Code Tabulation Area-Level Breast Cancer Screening: A Bayesian Geospatial Analysis in Hillsborough County, Florida

Breast cancer screening patterns exhibit geographic variation across Zip Code Tabulation Areas (ZCTAs) in Florida, yet most spatial analyses rely on frequentist point estimation without formally characterizing uncertainty. This study applied a three-stage analytical framework to ZCTA-level breast cancer screening data in Hillsborough County, Florida (n = 55 ZCTAs): frequentist Poisson regression with stepwise multicollinearity diagnostics, global spatial autocorrelation analysis using Moran’s I with inverse-distance weighting, and Bayesian Poisson and Bayesian negative binomial regression with Jeffreys non-informative priors estimated via the No-U-Turn Sampler in R (brms/Stan). Spatial analysis was conducted in ArcGIS Pro. Racial and ethnic female population counts for White, Black or African American, and Hispanic or Latino groups were the strongest and most consistent predictors of screening counts. Median household income, insurance status, and age-stratified variables showed no independent association at the ZCTA level. Global Moran’s I was near zero and non-significant (I = 0.003, z = 0.326, p = 0.745). The Bayesian Poisson model showed superior fit compared with the Bayesian negative binomial model (Bayesian R² = 0.91, DIC = 367.2, RMSE = 5.40, MBE = 0.02). These findings associate screening concentration with the geographic distribution of demographic groups and demonstrate the value of a Bayesian uncertainty-oriented framework for small-area public health analysis.