Comparison of Cox proportional hazards models and random survival forests for long-term cardiovascular risk prediction incorporating coronary artery calcium score
G Abreu, A Cardoso, M Mendonca, M Ferreira, F Sousa, F Escorcio Silva, E Henriques, S Freitas, M Rodrigues, S Borges, I Ornelas, A Drumond, A C Sousa, R Palma dos ReisAbstract
Background
Coronary artery calcium (CAC) score is a strong marker of atherosclerotic burden and cardiovascular risk. Although Cox proportional hazards models remain the standard approach for survival analysis, machine learning–based methods such as Random Survival Forests (RSF) may better capture complex and non-linear associations between CAC and clinical risk factors. Direct comparisons of these approaches for long-term cardiovascular risk prediction are still limited.
Objectives
To compare discrimination, calibration, and variable importance of Cox regression models and Random Survival Forests incorporating CAC score and clinical variables for long-term cardiovascular risk prediction.
Methods
We performed a survival analysis in a cohort of patients with available CAC score and clinical data. Three models were developed: (1) a Cox model using clinical variables only (Cox1), (2) a Cox model combining clinical variables and CAC score (Cox2), and (3) a Random Survival Forest model including the same predictors. Model discrimination was assessed using the concordance index (c-index) with cross-validation and in an independent test set, as well as time-dependent area under the curve (AUC) at multiple follow-up times. Calibration at 10 years was evaluated using LOWESS-smoothed calibration plots. Variable importance was assessed using 5-fold cross-validation.
Results
In cross-validation, discrimination improved with the inclusion of CAC score, with mean c-index values of 0.687 for Cox1, 0.763 for Cox2, and 0.781 for RSF. In the independent test set, c-index values were 0.766 for Cox1, 0.762 for Cox2, and 0.757 for RSF. Time-dependent AUC analysis showed that Cox2 maintained the most stable performance over long-term follow-up. At the same time, RSF demonstrated competitive discrimination at earlier time points with a modest decline at later horizons. Calibration analysis at 10 years demonstrated good agreement between predicted and observed risks for both CAC-based models, with RSF closely tracking the line of perfect calibration, particularly in the low- to intermediate-risk range. Variable importance analysis consistently identified CAC score as the strongest predictor, followed by hypertension, diabetes, smoking, and age, with RSF capturing additional non-linear interactions among clinical variables.
Conclusions
The addition of the CAC score significantly enhances cardiovascular risk prediction. Cox models incorporating CAC demonstrated robust and stable discrimination and calibration, while Random Survival Forests achieved high cross-validated performance and provided complementary insights into complex predictor relationships. These findings support integrating CAC into survival-based risk models and suggest a potential role for machine learning in cardiovascular risk assessment.Cox vs RSF 1Cox vs RSF 2