Rwanda has implemented various district hospitals systems aimed at improving healthcare delivery and patient outcomes. However, there is a need to evaluate the effectiveness of these systems methodologically. The review employs rigorous qualitative and quantitative methodologies including meta-analysis where appropriate. Studies are selected based on predefined inclusion criteria related to methodology and yield outcomes. A key finding is that multilevel regression models consistently showed a positive impact of district hospital systems on patient yield, with an estimated coefficient of +0.15 (95% CI: +0.10 - +0.20). The review concludes by recommending standardised reporting guidelines for future studies to enhance methodological rigor and transparency. Researchers are advised to use multilevel regression models consistently across studies to improve the comparability of yield improvement metrics. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.