{ "background": "District hospital systems in Ghana face persistent challenges in resource allocation and operational efficiency. Existing methods for measuring efficiency gains often fail to account for the hierarchical structure of health system data and inherent uncertainty, limiting their utility for evidence-based management.", "purpose and objectives": "This study aimed to methodologically evaluate a novel Bayesian hierarchical model designed to measure efficiency gains within these complex systems, assessing its applicability and inferential advantages over conventional approaches.", "methodology": "We conducted an intervention study applying the model to operational data from a network of district hospitals. The core model is specified as $y{ij} \\sim N(\\beta{0j} + X{ij}\\beta, \\sigma^2)$, with $\\beta{0j} \\sim N(\\gamma0 + Zj\\gamma, \\tau^2)$, where $i$ indexes individual hospital units and $j$ indexes districts. Efficiency was measured via a stochastic frontier analysis framework integrated within this hierarchy. Model performance was evaluated using posterior predictive checks and comparisons of credible interval widths.", "findings": "The model successfully quantified efficiency, revealing a posterior probability of 0.87 that the intervention led to a positive median efficiency gain across districts. Crucially, it provided more precise and probabilistically interpretable estimates than frequentist counterparts, with credible intervals for district-level random effects being on average 15% narrower, reflecting the model's ability to share strength across clusters.", "conclusion": "The Bayesian hierarchical model offers a statistically robust and methodologically superior framework for measuring efficiency in complex health systems, effectively handling multi-level data and providing direct probabilistic inference.", "recommendations": "Health system researchers and policymakers should adopt similar hierarchical modelling approaches to better capture uncertainty and heterogeneity when evaluating interventions. Future work should validate the model across different sub-Saharan African contexts.", "key words": "health systems efficiency, Bayesian statistics, hierarchical modelling, stochastic frontier analysis, resource allocation, Ghana", "contribution statement": "This paper introduces and validates a novel