Abstract
{ "background": "The evaluation of health system adoption in low-resource settings requires robust statistical methods to handle sparse, multi-level data and quantify uncertainty. Existing approaches often fail to adequately model the hierarchical structure of community-level interventions and their temporal evolution.", "purpose and objectives": "This study presents a novel Bayesian hierarchical model to methodologically assess the adoption dynamics of community health centre systems. The objective is to provide a rigorous framework for estimating adoption rates and their predictors while fully characterising uncertainty.", "methodology": "We developed a Bayesian hierarchical model specified as $y{it} \\sim \\text{Binomial}(n{it}, \\theta{it})$, $\\text{logit}(\\theta{it}) = \\alpha + \\beta X{it} + ui + vt$, with $ui \\sim \\mathcal{N}(0, \\sigmau^2)$ and $vt \\sim \\text{AR}(1)$. The model was fitted using Hamiltonian Monte Carlo, with convergence assessed via $\\hat{R}$ statistics. The analysis utilised national administrative panel data.", "findings": "The model successfully quantified adoption trajectories and key drivers. Posterior distributions indicated a strong positive association between trained workforce density and adoption probability, with a mean coefficient of 0.85 (95% credible interval: 0.72 to 0.99). Adoption rates showed significant spatial clustering, with the posterior probability of a district-level random effect exceeding zero being above 0.95 for over a third of administrative units.", "conclusion": "The proposed Bayesian hierarchical model offers a statistically sound methodological framework for evaluating health system adoption, effectively handling complex dependencies and providing probabilistic interpretations crucial for policy planning.", "recommendations": "Researchers evaluating similar community-based health interventions should adopt Bayesian hierarchical modelling to incorporate multi-level uncertainty. Policymakers should utilise the probabilistic outputs, such as credible intervals, for risk-aware planning and resource allocation.", "key words": "Bayesian inference, hierarchical modelling, health systems research, adoption evaluation,