{ "background": "District hospital systems are critical nodes for healthcare delivery and food system resilience in Ethiopia, yet methodological inconsistencies in evaluating their operational yields hinder comparative analysis and improvement.", "purpose and objectives": "This systematic review aims to critically evaluate methodological approaches used in studies of district hospital system yields and to propose a robust Bayesian hierarchical modelling framework for synthesising evidence and estimating performance improvements.", "methodology": "We conducted a systematic search of multiple databases for studies reporting on yield metrics (e.g., bed turnover, outpatient throughput) in Ethiopian district hospitals. Eligible studies were appraised for methodological quality. We then constructed a Bayesian hierarchical model to integrate heterogeneous data, formalised as $y{ij} \\sim \\text{Normal}(\\thetaj, \\sigma^2), \\; \\thetaj \\sim \\text{Normal}(\\mu, \\tau^2)$, where $y{ij}$ is the $i$th yield observation in hospital $j$, with partial pooling of estimates $\\theta_j$ towards the grand mean $\\mu$.", "findings": "The methodological review identified substantial heterogeneity in yield definitions and study designs, limiting direct comparability. Application of the proposed model to extracted data indicated a pooled posterior estimate for relative yield improvement of 18.2% (95% credible interval: 12.1% to 24.7%) following specific interventions, with the hospital standard deviation $\\tau$ estimated at 0.15, indicating considerable residual heterogeneity.", "conclusion": "Existing literature is methodologically fragmented, but a Bayesian hierarchical approach provides a coherent framework for evidence synthesis and more reliable inference on system performance.", "recommendations": "Future research should adopt standardised yield indicators and employ hierarchical modelling techniques to account for inherent clustering and variability within the hospital system, enabling more valid cross-study comparisons and policy assessment.", "key words": "health systems research, Bayesian inference, evidence synthesis, healthcare efficiency, resource-limited settings", "contribution statement": "This paper provides the first