Community health centres (CHCs) play a crucial role in healthcare delivery in Nigeria, but their efficiency and effectiveness are often under scrutiny. A Bayesian hierarchical model was employed to analyse data from Nigerian CHCs, aiming to quantify yield improvements over time. The analysis revealed that yield in one-third (30%) of CHCs showed significant growth, indicating potential for systemic enhancement through targeted interventions. The use of the Bayesian hierarchical model provided nuanced insights into CHC performance, facilitating evidence-based policy recommendations. Policy makers should prioritise investment and training programmes to capitalize on identified yield improvement areas in CHCs. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.