Methodological Evaluation of District Hospitals Systems in Kenya: A Meta-Analysis Evaluating Efficiency Gains Through Randomized Field Trials

District hospitals in Kenya face challenges in efficiently managing healthcare resources. Randomized controlled trials (RCTs) were conducted at multiple district hospitals across Kenya. Data collection included patient wait times, resource utilization, and operational costs. The analysis revealed that implementing a structured appointment scheduling system reduced average patient wait times by 40% in the trial sites compared to baseline conditions. Randomized field trials demonstrated significant efficiency gains through targeted interventions, particularly in reducing patient wait time variability. District hospital managers should consider adopting evidence-based scheduling and resource allocation strategies. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.