Estimating Global HIV Prevalence in Key Populations: A Cross-Population Hierarchical Modeling Approach

Key populations at high risk of HIV infection are critical for understanding and monitoring HIV epidemics, but global estimation is hampered by sparse, uneven data. We analyze data from 199 countries for female sex workers (FSW), men who have sex with men (MSM), and people who inject drugs (PWID) over 2011-2021, and introduce a cross-population hierarchical model that borrows strength across countries, years, and populations. The model combines region- and population-specific means with country random effects, temporal dependence, and cross-population correlations in a Gaussian Markov random-field formulation on the log-prevalence scale. In 5-fold cross-validation, the approach outperforms a regional-median baseline and reduced variants (65 percent reduction in cross-validated MSE) with well-calibrated posterior predictive coverage (93 percent). We map the 2021 prevalence and quantify the change between 2011 and 2021 using posterior prevalence ratios to identify countries with substantial increases or decreases. The framework yields globally comparable and uncertainty-quantified country-by-year prevalence estimates, enhancing evidence for resource allocation and targeted interventions for marginalized populations where routine data are limited.