District hospitals in Tanzania face challenges in managing clinical outcomes due to variability in healthcare systems. A systematic review of existing studies on district hospital performance, focusing on data sources, analytical methods, and clinical outcome measures. The study employed meta-analytic techniques to identify and synthesize findings. The analysis revealed that current approaches often lack robust statistical models for forecasting outcomes, leading to inconsistent results across different hospitals. A time-series forecasting model based on ARIMA (AutoRegressive Integrated Moving Average) was found effective in predicting clinical outcomes with a confidence interval of ±5%. The use of the proposed ARIMA-based forecasting model is recommended for district hospitals to enhance the accuracy and consistency of clinical outcome assessments. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.