## 5 Results
### Model Accuracy  
The accuracy of the models was one of the major criteria used in measuring the predictive capability of the proposed HFL model. The models were created to forecast healthcare results, including patient risk and disease development, solely based on local data from several institutions while the raw patient data were not transferred. The application of the hierarchical aggregation mechanism of HFL showed its improved accuracy over the baseline models as represented by the red bar below. The accuracy of FLBM and PPFLB are represented by the green and blue bars, respectively, in Figure 3. From Table 3, the proposed HFL model can be seen to have attained an average accuracy of 97.69%, which is higher than that of FLBM-IoT and PPFLB, which recorded accuracies of 91.67% and 89.27%, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & **HFL (Proposed)** & **FLBM-IoT** & **PPFLB** \\ \hline Accuracy (\%) & 97.8 \(\pm\) 0.9 & 91.7 \(\pm\) 1.2 & 89.2 \(\pm\) 1.8 \\ Privacy Leakage & 0.015 \(\pm\) 0.001 & 0.038 \(\pm\) 0.002 & 0.045 \(\pm\) 0.003 \\ Training Time Reduction & 15\% (vs. FLBM-IoT) & Baseline & Low improvement \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparative analysis of models. The model updates were aggregated at the regional level before global aggregation helped manage heterogeneity in data across the various institutions, thereby enhancing the generalizability and predictive accuracy of the model. The model accuracy of the three different approaches is shown in Figure 3. The accuracy of the proposed HFL (Hierarchical Federated Learning) model, the highest accuracy, is more than 97.8%. It can be seen that the accuracy of the FLBM-IoT model is moderate at about 91.7%, while the accuracy for the PPFLB model is the lowest at about 89.2%. The superior accuracy of the HFL model highlights the effectiveness of the hierarchical structure in capturing diverse healthcare data patterns while maintaining the privacy of patient information. The training time and the communication overhead were measured as computational costs of the proposed HFL framework. The introduction of the regional aggregation hubs in the HFL model greatly decreased the data exchange traffic between the local nodes and the central server, which enabled the training cycles to be faster and more scalable. As compared with the baseline models, the HFL framework saved 15% of the total training time, as indicated in Figure 3. Another algorithm that was employed to enhance the local training stability while at the same time preventing deviations from the global model was the FedProx algorithm, which enhanced the convergence of the models, particularly when working with heterogeneous data. To support our argument that the suggested HFL framework saves overall training time by 15% and minimizes communication overhead, we examined the computational cost of the privacy-preserving technologies incorporated into the system (Table 4). Local Differential Privacy (LDP) caused a small overhead (-3-5%) since the noise was added on the  
Figure 3: Model accuracy comparison. client side without any communication between parties. Global Differential Privacy (GDP) introduced a moderate overhead (~5-7%) due to its use of centralized gradient clipping and noise injection processes. A more pronounced overhead (~10-12%) was observed in Secure Multi-Party Computation (SMPC) due to the necessity of encrypted data sharing and multi-round communication during the aggregation process. The heaviest overhead was presented by Homomorphic Encryption (HE) (~18-20%), primarily due to the complexity of encrypted gradient operations. These outcomes were comparable when applied to other healthcare datasets, demonstrating the trade-off between the strength of privacy and system efficiency. By balancing these mechanisms with a hierarchical structure, we achieved a significant improvement in training efficiency without compromising privacy guidelines. Figure 4 presents a comparison of training time for the models.