District hospitals in Rwanda face challenges related to resource allocation and operational efficiency. A systematic literature review employing rigorous academic databases including MEDLINE, PubMed, and Web of Science. Studies published between and were considered. Quasi-experimental designs showed a mixed impact on improving efficiency across studies, with some achieving gains in resource utilization by up to 20%. While quasi-experimental designs can be effective tools for evaluating hospital system efficiency, their application requires careful methodological consideration and robust statistical analysis. Future research should prioritise the validation of selected quasi-experimental methods through replication studies and incorporate feedback loops for continuous improvement in healthcare systems. Quasi-Experimental Design, Hospital Efficiency, District Hospitals, Rwanda Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.