A time-series forecasting model for the cost-effectiveness evaluation of district hospital systems in Kenya: a methodological appraisal, 2000–2026

District hospitals are critical nodes in Kenya's healthcare system, yet persistent challenges in resource allocation and financial sustainability necessitate robust tools for evaluating their cost-effectiveness. Existing evaluations often lack longitudinal, predictive capacity. This study aimed to develop and methodologically appraise a novel time-series forecasting model designed to evaluate the cost-effectiveness of district hospital systems, providing a tool for forward-looking resource planning. We constructed a state-space model integrating historical administrative data on hospital expenditures and outcome proxies (e.g., bed-day equivalents). The core forecasting equation is yₜ = Zₜ αₜ + εₜ, where αₜ = Tₜ αₜ₋₁ + Rₜ ηₜ. Model parameters were estimated using maximum likelihood, and forecast uncertainty was quantified with 95% prediction intervals. The methodological appraisal demonstrated that the model produced stable long-term forecasts, with prediction interval coverage exceeding 93% in back-testing. A key finding was a forecasted progressive divergence between input costs and outcome gains, suggesting diminishing marginal returns on incremental expenditure under current configurations. The proposed model provides a statistically robust methodological framework for projecting cost-effectiveness trends in hospital systems, highlighting its utility for strategic planning. Health policymakers should adopt similar forecasting tools for medium-term budgetary planning. Further research should integrate more granular clinical outcome data into the model's structure. health economics, forecasting, state-space models, health systems, resource allocation This paper introduces a novel application of state-space modelling for health system cost-effectiveness forecasting, providing a methodological advance for longitudinal health policy analysis.