Bayesian Spatial Modeling of HIV Counts Using Flexible Zero-Inflated Models

This study develops a Bayesian spatial modeling framework to analyze HIV-related mortality across 61 counties in New York State, addressing key challenges in epidemiological count data: zero inflation, dispersion heterogeneity, and spatial dependence. We compare four models, including zero-inflated negative binomial (ZINB), hurdle Poisson, hurdle negative binomial, and zero-inflated Conway–Maxwell–Poisson (ZI-CMP), each incorporating conditional autoregressive spatial priors to account for regional correlation and unobserved heterogeneity. Diagnostic analysis confirms substantial zero-inflation and varying dispersion, justifying the use of zero-inflated and hurdle formulations. Convergence is evaluated using trace plots, Brooks-Gelman diagnostics, and Rˆ statistics. Model comparison based on deviance information criterion (DIC) and conditional predictive ordinate (CPO) identifies ZI-CMP as the best-fitting model (DIC = 167.85; mean CPO = 0.4777). Posterior inference reveals that poverty is positively associated with HIV mortality, whereas income inequality shows a negative marginal effect that becomes strongly positive through interaction with poverty, indicating compounded risk in highly disadvantaged counties. Spatial effects exhibit marked geographic clustering, suggesting unobserved local influences such as healthcare access and social vulnerability.