District hospitals in Nigeria face challenges in delivering efficient healthcare services. The study employed a meta-analysis approach to review existing literature and apply statistical methods for analysis. A significant proportion (35%) of hospitals showed improvement in service delivery when using the quasi-experimental design. Quasi-experimental designs can be effective tools for assessing efficiency gains in district hospital systems, with a focus on healthcare service improvements. Future research should continue to validate these findings and explore cost-effectiveness of interventions. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.