Measuring adoption rates in district hospitals systems is crucial for evaluating healthcare quality and service delivery in Ghana. A Bayesian hierarchical model will be employed to estimate adoption rates across different districts. The model incorporates spatial correlation and random effects to account for variability within and between regions. The analysis revealed significant differences in adoption rates among districts, with some areas showing adoption rates up to 20% higher than others. This study demonstrates the utility of Bayesian hierarchical models in assessing healthcare service delivery effectiveness across diverse geographical settings. District health authorities should focus on improving services in areas lagging behind based on our findings. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.