Bayesian inference of interval-censored data with an application to HIV population surveys: a simulation study comparing Hamiltonian Monte Carlo and Metropolis–Hastings sampling algorithms

HIV incidence estimation in population-based surveys often relies on interval-censored seroconversion times and complex survey designs, requiring computationally efficient Bayesian methods. We compared the computational efficiency and inferential performance of Hamiltonian Monte Carlo (HMC) and Metropolis–Hastings (MH) for Bayesian analysis of interval-censored HIV seroconversion times using a weighted log-logistic accelerated failure-time model. We conducted a simulation study of 5,400 datasets varying sample size, censoring, and weight dispersion under identical likelihoods, priors, diagnostics, and convergence criteria for both samplers, and applied the same model to the Zimbabwe PHIA 2020 survey (ZIMPHIA). Performance was assessed using efficiency (effective sample size per second, ESS/s), accuracy, interval calibration, and standard convergence diagnostics. HMC delivered substantially higher sampling efficiency across scenarios while producing comparable point estimates, uncertainty, and coverage. On ZIMPHIA ( \(n = 16{,}554\) ), HMC delivered \({~ }72{× }\) higher effective sample size per second than MH for \(β ₛₑₓ\) , equivalent to 1.43 vs 31.83 minutes of wall time at matched effective sample sizes. HMC is a practical default for weighted, interval-censored survival analysis in HIV surveys, with benefits that increase with sample size and weight variability.