{ "background": "Community health centres are critical for primary care delivery in many African nations, yet robust methodological frameworks for evaluating their systemic impact on population health risks are lacking. Existing evaluations often rely on aggregate statistics that mask heterogeneity and uncertainty.", "purpose and objectives": "This study aimed to develop and apply a novel Bayesian hierarchical model to quantify the reduction in key health risks attributable to the community health centre system, using a national-scale dataset from Senegal.", "methodology": "We formulated a Bayesian hierarchical model where the log-odds of a health outcome for individual $i$ in district $j$ is modelled as $\\text{logit}(p{ij}) = \\alpha + \\beta X{ij} + uj + \\epsilon{ij}$, with $uj \\sim N(0, \\sigma^2u)$ representing district-level random effects. The model was fitted using Markov chain Monte Carlo simulation to data encompassing facility utilisation and maternal/child health outcomes.", "findings": "The model estimated a substantive reduction in the risk of unattended births, with a posterior mean odds ratio of 0.42 (95% credible interval: 0.38 to 0.47) associated with centre utilisation. This indicates that utilisation more than halved the odds of an unattended delivery. Significant geographical heterogeneity in system effectiveness was identified.", "conclusion": "The Bayesian hierarchical model provides a statistically robust framework for evaluating health system performance, revealing both substantial average risk reduction and important sub-national variation in the effectiveness of community-based care.", "recommendations": "Health policy should prioritise investments in areas with lower estimated random effects to reduce geographical inequities. The methodological framework should be adopted for routine performance monitoring and resource allocation planning.", "key words": "Bayesian hierarchical model, health systems evaluation, risk reduction, community health, primary care, Senegal", "contribution statement": "This paper introduces a novel application of Bayesian hierarchical modelling for health systems evaluation in a low-resource setting, providing a template for