Abstract
{ "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: $y{it} \\sim \\text{Normal}(\\alphai + \\betat + \\mathbf{X}{it}\\boldsymbol{\\gamma}, \\sigma^2)$, with $\\alphai \\sim \\text{Normal}(\\mu{\\alpha}, \\tau{\\alpha}^2)$, where $i$ indexes hospitals and $t$ time. This estimates hospital-specific ($\\alphai$) and temporal ($\\beta_t$) 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