## 4 Discussion  
This comparative analysis yielded several significant insights into the relationship between various approaches to model selection, imputation strategy, and hyper-parameter optimization. In our initial models, SVM outperformed the other models in terms of accuracy, sensitivity, and AUC score and demonstrated consistent performance across all three metrics. The SVM models maintained scores for accuracy above 0.62, with MICE imputation showing the best results (0.6294). The SVM models had consistently high AUC scores (0.62-0.66), and similarly, the models achieved sensitivity scores above 0.61. The simple characteristics of the SVM models make it attractive for applications where consistent performance is crucial [31; 32]; however, after 10-fold cross-validation, the AUC scores of the SVM models were slightly reduced, indicating the possibility of overfitting. The differences between the initial SVM models and those after 10-fold cross-validation averaged \(-\)0.0074. Although not significant, the declines indicate that the models were not sufficiently robust to handle the various features of the dataset [23; 24]. The RF models exhibited a more variable performance pattern across the three optimization methods. While they showed moderate accuracy (0.595-0.609), their AUC scores demonstrated interesting behavior, achieving the highest score (0.663) when used with Mean Imputation and Bayesian Search optimization. However, their sensitivity scores were notably lower (0.52-0.56), indicating potential issues with identifying positive cases [37]. This variability indicates that RF models require careful consideration of the selection of both the imputation technique and optimization strategy, with performance heavily dependent on these choices. Interestingly, the RF models showed behavioral changes between the initial and cross-validated scenarios. After cross-validation, the RF models presented performance improvements in some configurations in terms of AUC score, reaching approximately 0.663. Inversely proportional to the SVM models, the RF models provided \begin{table}
\begin{tabular}{c c c} \hline \hline
**Optimization Method** & **Algorithm** &
\begin{tabular}{c} **Average Processing Time per** \\ **Model (Min)** \\ \end{tabular} \\ \hline \multirow{3}{*}{Grid Search} & SVM & 12 \\  & RF & 7 \\  & XGBoost & 6 \\ \hline \multirow{3}{*}{Random Search} & SVM & 10 \\  & RF & 6.5 \\  & XGBoost & 6 \\ \hline \multirow{3}{*}{Bayesian Search} & SVM & 7 \\  & RF & 5.3 \\ \cline{1-1}  & XGBoost & 4.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Approximate processing time with hyper-parameter optimization. enhancement in terms of AUC score after 10-fold cross-validation, an average increase of 0.03815, which indicates that they are more robust than SVM models. The XGBoost models presented the most complex performance profile among the three algorithms. Their accuracy showed high variability, with scores ranging between 0.577 and 0.619, and they performed very competitively in terms of AUC, from 0.638 to 0.662, with Random Search optimization generally yielding the best results. The XGBoost models revealed moderate performance for sensitivity (0.56-0.58), and they had a strong response to the optimization method, particularly Random Search, across all methods. This finding suggests that XGBoost's hyper-parameter landscape might be better suited to exploration through random sampling rather than systematic or Bayesian approaches. Unlike the initial XGBoost models, after 10-fold cross-validation, they became more consistent, achieving scores of 0.655-0.658. Even though there was a decline of 0.0101 when incorporating RF imputation and Grid Search optimization, the other XGBoost models presented an average improvement of 0.01683. This improvement indicates that the XGBoost models have the possibility of maintaining predictive performance while handling various features in a dataset [41].