MCMC-Based Bayesian Estimation for Nonlinear Mixed-Effects Models with Missing Data: A Study of Convergence and Computational Efficiency

Bayesian estimation of nonlinear mixed-effects models typically relies on Markov-Chain Monte Carlo (MCMC) methods due to the intractability of the posterior distribution. While widely used for longitudinal data with missing observations, the performance of MCMC algorithms is often taken for granted, despite their critical impact on inference quality. This paper investigates MCMC-based estimation for Bayesian nonlinear mixed-effects models with missing data, focusing on convergence behavior and computational efficiency. We propose a hybrid sampling framework that combines Gibbs sampling with Metropolis–Hastings (MH) and adaptive MH algorithms to improve mixing and stability. Convergence diagnostics, the effective sample size, and computational performance are systematically evaluated. Simulation studies assess the effects of the iteration length, burn-in proportion, and sample size, and the methodology is illustrated using orthodontic growth data and the Treatment of Lead-Exposed Children (TLC) trial.