Development of prognostic models for advanced multiple hepatocellular carcinoma based on Cox regression, deep learning and machine learning algorithms

Abstract

Background: Most patients with multiple hepatocellular carcinoma (MHCC) are at advanced stage once diagnosed, so that clinical treatment and decision-making are quite tricky. The AJCC-TNM system cannot accurately determine prognosis, our study aimed to identify prognostic factors for MHCC and to develop a prognostic model to quantify the risk and survival probability of patients.

Methods: Eligible patients with HCC were obtained from the Surveillance, Epidemiology, and End Results (SEER) database, and then prognostic models were built using Cox regression, machine learning (ML), and deep learning (DL) algorithms. The model's performance was evaluated using C-index, receiver operating characteristic curve, Brier score and decision curve analysis, respectively, and the best model was interpreted using SHapley additive explanations (SHAP) interpretability technique.

Results: A total of eight variables were included in the follow-up study, our analysis identified that the gradient boosted machine (GBM) model was the best prognostic model for advanced MHCC. In particular, the GBM model in the training cohort had a C-index of 0.73, a Brier score of 0.124, with area under the curve (AUC) values above 0.78 at the first, third, and fifth year. Importantly, the model also performed well in test cohort. The Kaplan-Meier (K-M) survival analysis demonstrated that the newly developed risk stratification system could well differentiate the prognosis of patients.

Conclusion: Of the ML models, GBM model could predict the prognosis of advanced MHCC patients most accurately.

Keywords: advanced multiple hepatocellular carcinoma; deep learning; gradient boosted machine; machine learning; prognosis.

Figure 1

Flow chart of patients’ selection in the training and test cohorts from the SEER database.

Figure 2

Demonstration of multivariate Cox regression analysis and analysis of patients in different months from diagnosis to treatment. (A) Forest plot based on multivariate Cox regression analysis. (B) Bar plot of important features of advanced MHCC patients in different months from diagnosis to treatment. The vertical coordinate is the percentage of the feature subgroup in the group.

Figure 3

Nomogram of patients with advanced MHCC and evaluation of the performance of the five models. (A) Nomogram of patients with advanced MHCC. (B–D) ROC curves for prognostic models predicting 1-, 3-, and 5-year OS in the training cohort. (E–G) DCA curves of prognostic models for 1-year, 3-year, and 5-year OS prediction in the training cohort.

Figure 4

Validation of the GBM model and development of new risk stratification system. (A, B) Time-dependent AUC for the GBM model in internal test cohort (A) and external test cohort (B). (C-E) Calibration curves of first (C), third (D) and fifth (E) year in the internal test cohort. (F) Survival curves based on AJCC-TNM stage. (G) Cut off values for optimal grouping determined using X-tile. (H) K-M survival curves based on new risk stratification system. (I) K-M survival curves of external test cohort based on new risk stratification system (Only one of these patients was high risk and was merged into the intermediate risk group).

Figure 5

The SHAP plot of the GBM model. (A) SHAP beeswarm summary plot on the impact of input variables on the GBM model’s prediction. (B) The local SHAP plot of patient #1. Patient #1: 74-year-old male, survival time was 96 months, alive. AJCC TNM stage was IIIA, Histological grade was II, tumor size = 6.0 cm, AFP was positive. She was treated 2 months after diagnosis, underwent partial hepatectomy and regional lymph surgery, only had HCC in his life. (C) The local SHAP plot of patient #2. Patient #2: 42-year-old male, survival time was 2 months, died. AJCC TNM stage was IV, Histological grade was III, tumor size = 13.0 cm, AFP was negative. She was treated 2 months after diagnosis, no tumor site and regional lymph surgery, only had HCC in his life. (D) The local SHAP plot of patient #3. Patient #3: 82-year-old male, survival time was 7 months, died. AJCC TNM stage was IIIA, Histological grade was II, tumor size = 5.9 cm, AFP was negative. She was treated 1 month after diagnosis, no tumor site and regional lymph surgery. Only had HCC in his life. The red ribbons in the local SHAP plot represent risk factors that lead to a poor prognosis, whereas the blue ribbons are the relatively protective factors.