## 4 Discussion
The improvements in these models were not better than those of the RF models (+0.03815) but were better than those of the SVM models (\(-\)0.0074). Compared to our XGBoost models, the current models showed significant improvement in every aspect of the performance parameters, indicating that this optimization method works well in improving predictive performance [19]. MICE generally showed slight advantages over the SVM models in terms of mean imputation, while the pattern was less clear for the RF and XGBoost models. MICE imputation showed consistent performance across all models, but due to its complexity, it did not provide the expected advantages over simpler methods like mean imputation [19]. After cross-validation, the XGBoost models worked better than the others with kNN imputation, while RF imputation showed variable results across all models. The effectiveness of the optimization methods varied by model type. The SVM models presented minimal variation across the optimization methods, suggesting that the model's hyper-parameter space might be relatively smooth and well-behaved due to its less complex characteristics. The RF models benefited more from Bayesian Search but showed a preference for Random Search, particularly after cross-validation. XGBoost showed better results with Random Search and generally outperformed Grid Search, especially in cross-validated scenarios. These findings suggest that the choice of optimization method should be model-specific rather than follow a one-size-fits-all approach. We used cross-validation to provide a more realistic assessment of model performance and generalization capabilities [42]. This generated several important insights, including that some configurations that performed well in baseline testing showed decreased performance under cross-validation, which indicates potential overfitting in the baseline models. On the other hand, the RF and XGBoost models showed increased performance under cross-validation, which suggests they are more robust and reliable. In general, the findings of this study suggest that even though model choice is essential, the selection of an appropriate hyper-parameter optimization method and imputation technique can have significant impacts on model performance. The results also emphasize the importance of cross-validation to obtain reliable performance estimates: baseline performance metrics alone may not provide a complete picture of model generalization capability. Additionally, Bayesian Search consistently required less processing time compared to Grid and Random Search in terms of computational efficiency, with average processing times of 7, 5.3, and 4.8 min, respectively, for SVM, RF, and XGBoost. The software and hardware that were used to conduct these experimental studies have limits to their processing ability. Thus, processing times would differ with other devices. Although our study primarily focuses on comparing hyper-parameter optimization methods and used metrics such as accuracy, sensitivity, and AUC, the clinical context of heart failure prediction remains an important consideration. In practice, predictive models must not only deliver robust statistical performance but also offer interpretability and reliable decision thresholds that balance sensitivity and specificity--key aspects for clinical decision-making [4, 6]. For instance, while our SVM model achieved high-performance metrics, the slight overfitting observed during cross-validation underscores the need for future work to integrate interpretability techniques and threshold calibration to minimize misclassification risks. These enhancements would help bridge the gap between methodological optimization and practical, clinically deployable tools, ultimately supporting more informed decisions in patient management [7]. This study has limitations, including the generalizability of the dataset we used in this experiment. We only relied on a dataset from a single hospital (Zigong Fourth People's Hospital, China), which may limit the generalizability of our findings.