The Application and Comparison of Machine Learning Models for the Prediction of Breast Cancer Prognosis: Retrospective Cohort Study

Abstract

Background: Over the recent years, machine learning methods have been increasingly explored in cancer prognosis because of the appearance of improved machine learning algorithms. These algorithms can use censored data for modeling, such as support vector machines for survival analysis and random survival forest (RSF). However, it is still debated whether traditional (Cox proportional hazard regression) or machine learning-based prognostic models have better predictive performance.

Objective: This study aimed to compare the performance of breast cancer prognostic prediction models based on machine learning and Cox regression.

Methods: This retrospective cohort study included all patients diagnosed with breast cancer and subsequently hospitalized in Fudan University Shanghai Cancer Center between January 1, 2008, and December 31, 2016. After all exclusions, a total of 22,176 cases with 21 features were eligible for model development. The data set was randomly split into a training set (15,523 cases, 70%) and a test set (6653 cases, 30%) for developing 4 models and predicting the overall survival of patients diagnosed with breast cancer. The discriminative ability of models was evaluated by the concordance index (C-index), the time-dependent area under the curve, and D-index; the calibration ability of models was evaluated by the Brier score.

Results: The RSF model revealed the best discriminative performance among the 4 models with 3-year, 5-year, and 10-year time-dependent area under the curve of 0.857, 0.838, and 0.781, a D-index of 7.643 (95% CI 6.542, 8.930) and a C-index of 0.827 (95% CI 0.809, 0.845). The statistical difference of the C-index was tested, and the RSF model significantly outperformed the Cox-EN (elastic net) model (C-index 0.816, 95% CI 0.796, 0.836; P=.01), the Cox model (C-index 0.814, 95% CI 0.794, 0.835; P=.003), and the support vector machine model (C-index 0.812, 95% CI 0.793, 0.832; P<.001). The 4 models' 3-year, 5-year, and 10-year Brier scores were very close, ranging from 0.027 to 0.094 and less than 0.1, which meant all models had good calibration. In the context of feature importance, elastic net and RSF both indicated that TNM staging, neoadjuvant therapy, number of lymph node metastases, age, and tumor diameter were the top 5 important features for predicting the prognosis of breast cancer. A final online tool was developed to predict the overall survival of patients with breast cancer.

Conclusions: The RSF model slightly outperformed the other models on discriminative ability, revealing the potential of the RSF method as an effective approach to building prognostic prediction models in the context of survival analysis.

Keywords: breast cancer; machine learning; medical informatics; prediction models; random survival forest; support vector machine; survival analysis.

Figure 1

The coefficients of features change for varying α.

Figure 2

The important coefficient of each feature corresponding to the optimal α by elastic net. Ln: lymph node; PR: progesterone receptors.

Figure 3

The important coefficient of each feature by random survival forest. Ln: lymph node; PR: progesterone receptors.

Figure 4

Time-dependent receiver operating characteristic curves of models at 3 years, 5 years, and 10 years. EN: elastic net; RSF: random survival forest; SVM: support vector machine.

Figure 5

Time-dependent AUC of models over time. AUC: area under the curve; EN: elastic net; RSF: random survival forest; SVM: support vector machine.

Figure 6

Survival curves of high-risk and low-risk groups divided according to the risk score from (A) Cox, (B) Cox-EN (elastic net), (C) SVM (support vector machine), and (D) RSF (random survival forest).