A Longitudinal Bayesian Hierarchical Model for the Cost-Effectiveness of District Hospital Systems in Rwanda, 2000–2026

{ "background": "District hospitals are critical nodes in health and food systems, linking clinical care with nutrition and agricultural extension services. Evaluating their long-term cost-effectiveness is essential for sustainable system investment, yet longitudinal analyses in low-resource settings are hampered by sparse, heterogeneous data.", "purpose and objectives": "This study aimed to develop and apply a novel Bayesian hierarchical model to assess the longitudinal cost-effectiveness of district hospital systems, providing a robust framework for policy evaluation under data scarcity.", "methodology": "A longitudinal study design was employed, utilising panel data on hospital expenditures and outcome proxies. The core methodological innovation is a Bayesian hierarchical model: yit \~ (\ + \ + it\\γ, \σ²), with \ \~ (\μ\α, \τ\α²), where i indexes hospitals and t time. This estimates hospital-specific (\) and temporal (\βₜ) effects, with posterior distributions quantifying all parameter uncertainty.", "findings": "The model successfully synthesised fragmented data, revealing a sustained positive trend in cost-effectiveness across the study period. A key quantitative finding is that the posterior probability of a positive system-wide trend exceeded 0.95. The analysis identified operational scale as a dominant driver of efficiency gains.", "conclusion": "The Bayesian hierarchical approach offers a statistically rigorous solution for longitudinal health systems research where conventional methods are challenged by data limitations, demonstrating improved inferential capacity over time.", "recommendations": "Health and agricultural policy planners should adopt similar Bayesian modelling techniques for long-term performance tracking of integrated service delivery units. Investment should prioritise scalable operational protocols identified by the model.", "key words": "Bayesian hierarchical model, cost-effectiveness analysis, health systems research, longitudinal data, sub-Saharan Africa", "contribution statement": "This paper provides a novel methodological framework for longitudinal cost-effectiveness analysis in