{ "background": "Evaluating the adoption of community health centre (CHC) systems in sub-Saharan Africa is critical for improving healthcare delivery, yet existing methods often fail to account for complex, nested data structures and inherent uncertainty in measurement.", "purpose and objectives": "This methodological case study presents a novel Bayesian hierarchical model to measure and analyse the adoption rates of CHC systems, demonstrating its application to a real-world evaluation in Tanzania.", "methodology": "We developed a three-level hierarchical logistic model. Let $y{ij} \\sim \\text{Bernoulli}(p{ij})$ be the adoption status for facility $i$ in district $j$, with $\\text{logit}(p{ij}) = \\alpha{j[i]} + \\beta X{ij}$. The district-level intercepts are modelled as $\\alphaj \\sim \\text{Normal}(\\mu{\\alpha}, \\sigma{\\alpha}^2)$, with weakly informative priors. Inference is based on posterior distributions derived via Markov chain Monte Carlo sampling.", "findings": "The model quantified substantial heterogeneity in adoption probabilities across districts, with posterior credible intervals for district-level random effects indicating where interventions were most and least effective. A key finding was that the estimated national adoption rate had a 95% posterior credible interval of 0.42 to 0.51, highlighting significant uncertainty absent from prior analyses.", "conclusion": "The Bayesian hierarchical framework provides a robust, interpretable method for assessing health system adoption, formally incorporating variability at multiple administrative levels and quantifying uncertainty in a way that directly informs policy.", "recommendations": "Researchers evaluating complex health interventions should adopt similar hierarchical modelling approaches to account for data structure. Policymakers should request probabilistic estimates, like credible intervals, to better understand the range of potential outcomes for decisions.", "key words": "Bayesian statistics, hierarchical modelling, health systems research, adoption evaluation, sub-Saharan Africa, uncertainty quantification", "contribution statement": "This study provides a novel, general