Abstract
District hospital systems in low-resource settings face persistent challenges in operational efficiency, yet robust methodologies for quantifying longitudinal efficiency gains are underdeveloped. Existing approaches often lack the temporal granularity and predictive validity required for strategic resource planning. This study aimed to methodologically evaluate a novel time-series forecasting model designed to measure and project efficiency gains within district-level healthcare delivery systems. The objective was to assess the model's predictive accuracy and its utility for long-term operational planning. We conducted an intervention study applying a seasonal autoregressive integrated moving average with exogenous variables (SARIMAX) model, specified as $\phi(B)\Phi(B^s)\nabla^d\nablas^D yt = \theta(B)\Theta(B^s)\epsilont + \beta Xt$, to longitudinal administrative data. Model performance was evaluated using rolling-origin forecast evaluation, with uncertainty quantified via 95% prediction intervals and robust standard errors. The forecasting model demonstrated a mean absolute percentage error of 8.7% for key efficiency metrics over a five-year projection horizon. A core finding was a projected 12.3% cumulative efficiency gain in resource utilisation, with prediction intervals indicating the estimate's robustness to stochastic shocks in supply chains. The proposed time-series model provides a statistically rigorous and operationally actionable tool for measuring historical and forecasting future efficiency trajectories in complex healthcare systems. Health system planners should integrate such forecasting models into medium-term expenditure frameworks. Further research should validate the model's transferability to other public service sectors within food and health systems. health systems efficiency, time-series forecasting, operational research, resource allocation, predictive modelling, SARIMAX This paper provides a novel methodological framework for disentangling trend, seasonal, and policy-driven components of efficiency gains in low-resource health systems, moving beyond static cross-sectional assessments.