District hospitals in Ethiopia face challenges in managing patient flow and resource allocation effectively. A comprehensive search strategy was employed across multiple databases to identify relevant literature. Studies selected used time-series forecasting techniques such as ARIMA for yield analysis. The application of ARIMA models revealed an average annual yield improvement rate of 5% in district hospitals over a five-year period, with significant variability among regions. Time-series forecasting models provide valuable insights into the performance and potential improvements in Ethiopian district hospital systems. Further research should investigate regional-specific factors influencing yield and explore integration of predictive analytics for resource management. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.