State-Level Heterogeneity in the Syphilis–HIV Association Across US Counties: A Bayesian Hierarchical Analysis

Background: The syphilis–HIV co-epidemic in the United States is geographically uneven. We examined county-level associations between syphilis burden and HIV diagnosis rates using Bayesian hierarchical models that account for state-level clustering. Methods: We analyzed 2023 county-level data from AIDSVu and CDC STI Surveillance ( n = 2,009 counties; 50 states and Puerto Rico). A linear model with a state-level random intercept was extended to allow the syphilis coefficient to vary by state (random slope), and a negative binomial model with a population offset was fit separately ( n = 1,976; Puerto Rico excluded due to unavailable population estimates). Adjustment variables included poverty, insurance coverage, income, unemployment, and urbanicity. Residual spatial autocorrelation was assessed with Moran’s I on county adjacency. Results: A one standard deviation increase in county syphilis rate was associated with 1.79 additional HIV diagnoses per 100,000 (95% credible interval [CrI]: 1.28, 2.31) in the linear model, and an incidence rate ratio of 1.35 (95% CrI: 1.27, 1.44) in the negative binomial model. State random intercepts ranged from +14.3 (Mississippi) to − 5.6 (Puerto Rico). Random slopes showed detectable heterogeneity in the association itself ( τ̂ 2 = 7.45; 95% CrI: 3.57, 13.76), though without decisively improving predictive fit over a random-intercept-only model (LOO-CV ELPD difference = − 15.0, SE = 35.1). Residual spatial autocorrelation remained after accounting for state clustering (Moran’s I = 0.099, p < 0.001). Conclusions: County-level syphilis burden is associated with HIV diagnosis rates after accounting for state-level clustering. Evidence of both varying baseline burden and a modestly varying association across states, together with residual geographic dependence beyond state boundaries, suggests state random intercepts capture much but not all relevant spatial structure.