District hospitals in Tanzania play a crucial role in healthcare delivery, yet their operational efficiencies are often suboptimal. A comprehensive search of peer-reviewed journals was conducted to identify studies employing panel-data estimation techniques. Studies were critically appraised based on their methodology, data sources, and statistical models. Panel data estimations revealed significant variability in hospital performance across different districts, with some showing improvements in yield by up to 20% through targeted interventions. The review highlights the importance of robust methodological approaches for improving healthcare delivery at district hospitals, particularly through panel-data analysis. District health authorities should prioritise data collection and use advanced statistical methods like panel-data estimation to enhance operational efficiencies. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.