Bayesian Hierarchical Model Evaluation of District Hospital Systems in Kenya, 2004

District hospitals in Kenya play a crucial role in healthcare delivery, but their performance varies significantly across different regions. A Bayesian hierarchical model was developed to analyse data from multiple districts, incorporating spatial dependencies and heterogeneity among hospitals. Uncertainty quantification is achieved through posterior predictive checks on simulated datasets. The model identified a systematic underperformance in diagnostic accuracy across several district hospitals, with proportions of incorrect diagnoses ranging between 15% and 20%. This study highlights significant disparities in healthcare quality among Kenyan district hospitals and underscores the need for targeted interventions to improve diagnostic reliability. Immediate attention should be given to upgrading diagnostic equipment and training, with a focus on high-risk areas identified by the model. Monitoring systems should also be strengthened to ensure continuous improvement. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.