Methodological Evaluation of District Hospitals Systems in Kenya: A Randomized Field Trial on Cost-Effectiveness Assessment

District hospitals in Kenya play a crucial role in healthcare delivery but often face challenges in cost-effectiveness due to inadequate funding and resource allocation. A randomized controlled trial was conducted across ten districts with baseline data collected on patient flow, treatment outcomes, and resource utilization. A cost-effectiveness analysis (CEA) model was used to assess the financial impact of different management strategies. The trial revealed that implementing a tiered referral system significantly reduced emergency room wait times by 40% while maintaining comparable treatment efficacy. This study provides evidence for cost-effective healthcare interventions in district hospitals, highlighting the importance of strategic resource allocation and patient flow management. District health authorities should prioritise the adoption of a tiered referral system to enhance service delivery efficiency and financial sustainability. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.