{ "background": "Community health centres in Nigeria face persistent challenges in resource allocation and operational efficiency, which directly impacts healthcare delivery. Existing methods for measuring efficiency often fail to account for the hierarchical structure of health systems and the inherent uncertainty in performance data.", "purpose and objectives": "This study aimed to develop and methodologically evaluate a novel Bayesian hierarchical model to measure and attribute efficiency gains within a network of community health centres following a targeted intervention programme.", "methodology": "We conducted an intervention study across a network of centres. The core methodological innovation is a Bayesian hierarchical model specified as $y{ij} \\sim \\text{Normal}(\\alphaj + \\beta X{ij}, \\sigma^2)$, $\\alphaj \\sim \\text{Normal}(\\mu{\\alpha}, \\tau^2)$, where $y{ij}$ is the efficiency metric for patient $i$ in centre $j$, $\\alphaj$ represents the centre-specific random effect, and $X{ij}$ denotes intervention covariates. Model inference was performed using Markov chain Monte Carlo sampling, with posterior credible intervals used for uncertainty quantification.", "findings": "The methodological evaluation demonstrated that the model successfully partitioned variance, attributing approximately 65% of the observed efficiency improvement to the intervention effect at the centre level. The posterior distribution for the key intervention coefficient indicated a 95% credible interval of [0.15, 0.31], providing robust evidence of a positive effect.", "conclusion": "The proposed Bayesian hierarchical model offers a statistically rigorous framework for evaluating health system interventions, effectively quantifying centre-level efficiency gains while formally accounting for data uncertainty and hierarchical dependencies.", "recommendations": "Health policymakers and system evaluators should adopt hierarchical modelling approaches that incorporate uncertainty for more reliable assessment of intervention impacts. Future research should validate this model in other health system contexts and with different outcome measures.", "key words": "Bayesian hierarchical model, health systems efficiency, intervention evaluation, community health, Nigeria, methodological study", "contribution statement