District hospitals in South Africa play a crucial role in primary healthcare delivery. However, their operational efficiency varies significantly, necessitating methodological evaluation to improve service quality and resource allocation. A Bayesian hierarchical model was employed to analyse data from multiple district hospitals. The model accounts for heterogeneity in hospital performance and incorporates robust uncertainty estimates through credible intervals. The analysis revealed that the efficiency gains across districts varied, with some hospitals achieving substantial improvements in their operational effectiveness. This study demonstrates the utility of Bayesian hierarchical models in assessing district hospital systems' efficiency. The findings provide actionable insights for policymakers aiming to enhance healthcare service delivery. Policymakers should prioritise interventions targeting specific areas identified as needing improvement, such as resource allocation and staff training, based on this analysis. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.