Nigeria faces significant challenges in healthcare delivery, particularly in district hospitals where efficiency is crucial for effective resource allocation. A systematic literature review will be conducted to analyse existing studies and methodologies used in evaluating healthcare system performance in Nigerian district hospitals. The review will include econometric models such as stochastic frontier analysis (SFA) for efficiency measurement. The analysis reveals a direction towards increased efficiency gains with panel data estimation techniques, particularly when accounting for unobserved heterogeneity through robust standard errors. Panel data estimation methods offer a nuanced understanding of healthcare system performance in Nigerian district hospitals, providing insights into potential areas for improvement. District hospital managers should consider implementing SFA to enhance efficiency and resource utilization, with further research on specific interventions. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.