## 3 Results
The key hyperparameter search space explored included the following:  
n_estimators (number of trees): [50, 100, 200]  
max_depth (maximum depth of trees): [3, 5, 7]  
learning_rate (step size shrinkage): [0.01, 0.1, 0.2]  
subsample (subsampling ratio of training instances): [0.7, 0.8, 0.9]  
colsample_bytree (subsampling ratio of features): [0.7, 0.8, 0.9]  
A five-fold cross-validation was employed to evaluate each hyperparameter combination, and the configuration yielding the highest AUC score was selected for the final model training. The dataset used in this study was derived from the Framingham Heart Study, consisting of 11,627 instances and 39 variables. The outcome variable was the incidence of cardiovascular disease (CVD), with an event rate of 24.93%. The Framingham study is a large-scale longitudinal cohort study initiated in 1948, and the data used in our analysis included up to 24 years (8766 days) of follow-up for each subject. It is noteworthy that the Random Forest (RF) and Support Vector Machine (SVM) models exhibited performance metrics of zero for precision, recall, F1-score, and sensitivity under the original, imbalanced dataset when evaluated using the default decision threshold (0.5). This occurred because these models, without adequate resampling or threshold adjustment, predominantly predicted the majority class (CVD = 0), completely failing to identify any positive cases (CVD = 1). Consequently, the number of true positives was zero, rendering all derived performance metrics undefined or zero. Despite this, their respective AUC scores were 0.642 (RF) and 0.500 (SVM), indicating performance at or only marginally above random chance. These results underscore the critical importance of addressing class imbalance--through methods such as resampling or using appropriate evaluation metrics--when developing models on imbalanced clinical datasets. The vertical axis shows true positive rate, and the horizontal axis shows false positive rate. The true positive rate (TPR) and false positive rate (FPR) are calculated for each cutoff point used to distinguish between survived and non-survived. These points are plotted on a graph, with the TPR on the vertical axis and the FPR on the horizontal axis, and are then connected by a line. The closer a point is to the top left corner--indicating a low false positive rate and a high true positive rate--the better the model's performance. Similarly, a larger area under the curve (AUC) reflects a more effective discriminative marker. The dataset shows a correlation matrix that has been cleaned using principal component analysis (PCA) for 15 factors in the dataset, such as gender and age. Various risk factors have been strongly associated with the onset of CVD and increased mortality. In the Framingham Heart Study (FHS), the variable \"educ\" represents years of education: 1 to \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Model** & **AUC\({}_{1}\) (95\% CI)** & **AUC\({}_{2}\) (95\% CI)** & \(\Delta\) AUC & **Z** & \(p\)**-Value** & **Adj. P** & **Effect Size** \\ \hline XGBoost vs. & 0.834 & 0.831 & & & & & \\ LightGBM & (0.814–0.854) & (0.811–0.851) & & & & & \\ \hline XGBoost vs. & & & & & & \\ Gradient & 0.834 & 0.832 & & & & & \\ Boosting & (0.814–0.854) & (0.812–0.852) & 0.0019 & 0.93 & 0.352 & 1.000 & 0.005 \\ \hline \hline \end{tabular}
\begin{tabular}{c} Asterisks (\(\uparrow\)) next to the results of statistical analysis indicate statistical significance. The number of asterisks corresponds to the \(p\)-value: \(\uparrow\); \(p<0.05\), ***; \(p<0.001\). \\ \hline \end{tabular}
\end{table} 
Table 5: _Cont._11 for elementary to high school (including dropouts), 12 for high school graduates, 13 to 15 for some college (including associate degrees), 16 for university graduates (bachelor's degree), and 17 or more for graduate or professional education. This variable is used to analyze the relationship between educational level and health or cardiovascular disease risk.