Abstract
{ "background": "District hospital systems are critical nodes in national health and food security networks, yet robust methodologies for quantifying their operational reliability across diverse regions are lacking. Existing assessments often rely on aggregate indicators that mask local variability and uncertainty.", "purpose and objectives": "This case study presents and validates a novel Bayesian hierarchical modelling framework for assessing the spatio-temporal reliability of district hospital systems, using the Senegalese context as a methodological proving ground.", "methodology": "We developed a Bayesian hierarchical model where the log-odds of system failure for hospital $i$ in region $j$ at time $t$ is given by $\\text{logit}(p{ijt}) = \\alpha + \\beta X{ijt} + uj + vt + \\epsilon{ijt}$, with $uj \\sim N(0, \\sigma^2u)$ and $vt \\sim N(v{t-1}, \\sigma^2v)$. The model integrates administrative data on resource availability, staffing, and case-loads. Posterior distributions were estimated using Markov chain Monte Carlo sampling.", "findings": "The model successfully quantified substantial regional heterogeneity in reliability, with posterior probabilities of system failure in a given year ranging from 0.08 to 0.35 across different administrative zones. A key finding was a strong positive association between integrated logistics support for nutritional therapeutics and system reliability, with a posterior mean odds ratio of 2.15 (95% credible interval: 1.72 to 2.65).", "conclusion": "The Bayesian hierarchical framework provides a statistically rigorous tool for capturing uncertainty and spatial dependence in health system performance, offering superior insights for targeted intervention compared to conventional methods.", "recommendations": "Health and agricultural policy planners should adopt similar probabilistic modelling approaches to prioritise resource allocation. Future research should integrate direct food security and community health outcome data into the reliability model.", "key words": "health systems resilience, Bayesian statistics, spatio-temporal modelling, resource allocation, West