Risk prediction for long-term cardiovascular events in patients with concurrent hypertension, HFpEF, and unstable angina: a multicenter machine learning-assisted cohort study

Figures

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  Figure 1. Feature selection using the LASSO regression model. (A) LASSO coefficient profiles of the candidate variables. Each curve represents a variable’s coefficient trajectory as the regularization parameter (λ) changes. (B) Tuning parameter (λ) selection in the LASSO model via 10-fold cross-validation, and the optimal λ was selected to balance the model complexity and predictive performance.

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  Figure 2. Feature selection using the Boruta algorithm. (A) Importance scores of all variables after Boruta selection. The Boruta algorithm selected important features (green), rejected unimportant ones (red), and marked uncertain features as tentative (yellow) using shadow features (blue) as a reference. (B) Variation in feature importance over 100 iterations illustrates the consistency of the selected variables.

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  Figure 3. Feature importance ranking and model performance of the random forest classifier. (A) The average classification accuracy of the random forest model across different numbers of decision trees illustrating model performance stabilization as tree quantity increases. (B) Variable importance ranking based on the mean decrease in accuracy, illustrating the relative contribution of each feature to the classifier’s predictive performance.

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  Figure 4. Forest plot of multivariable Cox regression analysis of independent predictors of MACEs.

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  Figure 5. Clinically validated nomogram for predicting the 2-, 3-, and 4-year risk of MACEs in patients with concurrent hypertension, HFpEF, and UAP. The model incorporates five independent prognostic variables identified through machine learning feature selection algorithms: diabetes mellitus (binary), previous myocardial infarction, SII, triglyceride levels, and NT-proBNP (continuous, pg/mL). Risk calculation was performed by drawing a vertical line from each variable value to the corresponding point on the axis, summing the points, and identifying the predicted MACEs probability on the risk axis.

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  Figure 6. ROC curves of the nomogram for predicting 2-, 3-, and 4-year MACEs in (A) development, (B) validation, and (C) test cohorts. The x-axis represents 1- specificity and the y-axis represents sensitivity.

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  Figure 7. Calibration curves for the nomogram in (A) development, (B) validation, and (C) test cohorts at 2-, 3-, and 4-years. The x-axis represents the nomogram-predicted probability of MACEs, and the y-axis represents the observed MACE proportion. The red, green, and blue symbols correspond to 2-year, 3-year, and 4-year predictions, respectively. Solid lines represent the fitted calibration trends, while the gray dashed line indicates perfect calibration (predicted probability = observed event risk). Points are plotted with vertical error bars denoting 95% confidence intervals. The closer the calibration curves are to the 45° reference line, the better the agreement between predicted and observed risks.

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  Figure 8. DCA evaluating the clinical utility of the nomogram for predicting 2-, 3-, and 4-year MACEs across different cohorts. DCA for predicting 2-year MACEs in (A) development, (B) validation, and (C) test cohorts. DCA for predicting 3-year MACEs in (D) development, (E) validation, and (F) test cohorts. DCA for predicting 4-year MACEs in the (G) development, (H) validation, and (I) test cohorts. The net benefit of using the nomogram (red line) is plotted against a range of threshold probabilities (x-axis). For comparison, the net benefit of two reference strategies is also shown: treat all (green line) and treat none (blue line). The width and position of the curves indicate the clinical usefulness of the nomogram across different threshold probability ranges; a higher net benefit relative to the treat-all and treat-none strategies suggests better clinical value for decision-making.

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  Figure 9. Kaplan–Meier curves illustrating MACEs-free survival stratification based on the machine learning-derived nomogram in patients with concurrent hypertension, HFpEF, and UAP. We divided patients into high-risk and low-risk groups across development (A) and validation (B) and test (C) cohorts.