# Heart Disease Prediction Using Concatenated Hybrid Ensemble Classifiers
## 4 Experimental Analysis  
### Performance Metrics  
In this phase, the outcomes of the experiments have been observed and analyzed in detail. The performance of the proposed model has been evaluated using metrics such as accuracy, precision, sensitivity (recall), specificity, and F1 score. For clarity, the definitions of these metrics are as follows:  
* True Positive (TP): Correctly predicted positive cases. * False Positive (FP): Incorrectly predicted positive cases. * True Negative (TN): Correctly predicted negative cases. * False Negative (FN): Incorrectly predicted negative cases. Accuracy measures the proportion of correctly predicted instances (both positive and negative) out of the total number of instances, providing an overall measure of the classifier's correctness:  
\[Accuracy=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{FP}+\text{TN}+\text{FN}} \tag{11}\]Precision calculates the proportion of correctly predicted positive instances out of all instances predicted as positive by the classifier. It quantifies the classifier's ability to avoid false positives:  
\[Precision=\frac{\text{TP}}{\text{TP}+\text{FP}} \tag{12}\]  
Sensitivity, also known as the True Positive Rate or Recall, quantifies the proportion of actual positive instances correctly identified by the classifier. It indicates the classifier's ability to identify positive instances accurately, with higher values indicating fewer false negatives:  
\[Sensitivity\ (Recall)=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{13}\]  
Specificity measures the proportion of actual negative instances correctly identified by the classifier, indicating its ability to correctly identify negative instances. A higher specificity value indicates fewer false positives:  
\[Specificity=\frac{\text{TN}}{\text{FP}+\text{TN}} \tag{14}\]  
The F1 score is the harmonic mean of precision and recall, providing a balance between these two metrics and considering both the classifier's ability to identify positive instances accurately and its ability to avoid false positives:  
\[\text{F1 Score}=\frac{2\times\text{Precision}\times\text{Sensitivity}}{\text{ Precision}+\text{Sensitivity}} \tag{15}\]  
To facilitate model training and evaluation, we partitioned the dataset into training and validation sets. Specifically, 75% of the data were utilized for training, while the remaining 25% were allocated for validation. The standard train-test split method was employed for validation, ensuring a rigorous assessment of the proposed model's performance. This partitioning strategy enhances the robustness and generalizability of the proposed heart disease prediction model. In the first phase of the experiment, the first ensemble classifier was built using Support Vector Machine, Decision Tree, and K-Nearest Neighbor as base classifiers. The confusion matrix generated by applying the first ensemble classifier is shown in Figure 5a. Subsequently, in the experiment, the second ensemble classifier was applied, and was constructed using Logistic Regression, Adaboost, and Naive Bayes as base classifiers. The generated confusion matrix is shown in Figure 5b. The confusion matrix of the final proposed classifier is presented in Figure 5c. When applying the first hybrid ensemble classifier, the proposed model achieved an accuracy of 84.21%, sensitivity of 86.2%, specificity of 83.0%, precision of 75.5%, and an F1 Score of 80.6%, as shown in Table 5. Upon applying the second hybrid ensemble classifier, the model achieved an accuracy of 85.87%, sensitivity of 84.36%, specificity of 86.39%, precision of 81.85%, and an F1 Score of 83.09%. The final classifier, which was created by concatenating the two hybrid ensemble classifiers, achieved an accuracy of 86.89%, sensitivity of 87.1%, specificity of 86.7%, precision of 81.8%, and an F1 Score of 84.3%. In addition to previous metrics, our model's performance is comprehensively assessed using the Area Under the Receiver Operating Characteristic (AUC-ROC) curve. This metric