District hospitals in Kenya play a crucial role in healthcare delivery, but their operational efficiency varies significantly. A comprehensive search of relevant databases identified studies focusing on efficiency measurement methods. A meta-analysis was conducted to synthesize findings from multiple studies, employing robust standard errors for statistical inference. The analysis revealed a clear trend towards improvements in operational efficiency when using time-series panel data techniques over cross-sectional approaches. Panel data methodologies offer substantial potential for enhancing the understanding of district hospital performance and identifying areas for improvement. Future research should focus on replicating studies with larger sample sizes to validate findings across different contexts. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.