Comparison of Random Survival Forest Based-Overall Survival With Deep Learning and Cox Proportional Hazard Models in HER-2-Positive HR-Negative Breast Cancer

Abstract

Background: Traditional CoxPH models are limited in handling real-world data complexities. While machine learning models like RSF and DeepSurv show promise, their application and comparative evaluation in the HER2-positive/HR-negative breast cancer subtype require further validation.

Aims: This study aims to build a survival prediction model for breast cancer patients based on different methods. The optimal model will provide more accurate survival predictions for clinical decision-making of HER2 positive and HR negative cancer patients.

Methods and results: This study analyzed 8,119 HER2-positive HR-negative breast cancer patients from the SEER database, randomly allocated to training/validation/test cohorts (7:1:2 ratio). Predictive models were developed using five feature sets and three algorithms (Cox PH, RSF, DeepSurv), with feature selection optimized via Concordance index (C-index). Evaluation revealed: The C-index of the DeepSurv models constructed using the training set is greater than 0.8, performing better than both the RSF and CoxPH models. However, CoxPH outperforms DeepSurv in terms of C-index when testset. The Brier scores for all models were below 0.25. Which indicates that the models predicted with high accuracy. Based on the training set, the Deepsurv model predicted the highest ROC-AUCs of 0.91, 0.863, and 0.855 for 1-, 3-, and 5-year overall survival (OS), respectively. The RSF model achieved the highest AUCs, specifically 0.876, 0.861, and 0.845, for 1-, 3-, and 5-year overall survival in the test group. The calibration graphs indicate that of the three models forecasting overall survival at 1, 3, and 5 years, the RSF model demonstrated the greatest level of agreement between predictions and actual observations, trailed by the DeepSurv model. There was poor agreement between CoxPH model predictions and observed data. Optimal Clinical Net Benefits at 1, 3, and 5 Years for DCA of the Deepsurv Model in the Training Set Data. However, in the test set, compared to other models, RSF showed better Optimal Clinical Net Benefits.

Conclusions: In conclusion, compared to conventional prognostic models, the Random Survival Forest (RSF) model serves as a reliable tool for predicting long-term survival in breast cancer patients, demonstrating consistent performance across diverse datasets. Furthermore, the feature set selected via RSF-Variable Importance (VIMP) (compared with LASSO regression and Cox regression) significantly enhances the performance of prognostic models. Our findings may offer practical guidance for future development of long-term prognostic models tailored to breast cancer subtypes.

Keywords: CoxPH; Deepsurv; RSF; RSF‐VIMP; breast cancer.

FIGURE 1

Flowchart for data analysis.

FIGURE 2

Survival differences between different datasets (A), survival differences between different tumor stages based on overall data (B).

FIGURE 3

RSF analysis plot and ranking of variable importance. RSF, random survival forest.

FIGURE 4

LASSO regression analysis cross‐validation curve (A); LASSO coefficient path diagram (B). LASSO, least absolute shrinkage and selection operator.

FIGURE 5

Probability of predicting 1/3/5‐year survival times for the training set (A–C) and validation set (D–F). Gray diagonal lines indicate ideal evaluations, red solid lines indicate the performance of the CoxPH model, green solid lines indicate the DeepSurv model and blue solid lines RSF model predictions at different times.

FIGURE 6

ROC curves for the training set (A–C) and validation set (D–F). Comparing the AUC values of three models for 1‐, 3‐, and 5‐year survival to assess the time‐dependent sensitivity and specificity of the models.

FIGURE 7

DCA for the training set (A–C) and validation set (D–F). Comparison of DCA for 1‐, 3‐, and 5‐year survival of three models to assess their clinical applicability.