Machine learning models for predicting survival in patients of hepatocellular carcinoma with second primary malignancy

Introduction

Hepatocellular carcinoma (HCC) ranks as the sixth most prevalent cancer and the fourth leading cause of cancer-related deaths globally (1,2). With the advancement of medical technology and the development of various new anticancer drugs, the number of HCC survivors is gradually increasing. Due to the cancer constitution of patients with HCC, it is necessary to be alert to the occurrence of second primary cancer. Second primary malignancies (SPMs), refers to the same patient suffering from two primary malignant tumors at the same time or successively (3), each of which is malignant, and histopathologically independent, except for recurrence or metastasis. A study based on a large database showed (4) that eight types of first primary cancers including HCC have a higher risk of developing second primary cancers, so sufficient attention should be paid to the occurrence of second primary cancers of patients with HCC.

In this context, an effective prognostic model for patients with HCC and a second primary malignancy (HCC-SPM) is valuable for the clinical management of these cases. Several clinical prediction models for HCC patient survival have already been developed. Cao et al. (5) used COX proportional hazards (COXPH) regression to construct a prognostic model for patients with primary non-cirrhotic liver cancer, and the effect was better than the traditional American Joint Committee on Cancer (AJCC) staging system. Liu et al. (6) used COXPH regression to construct a model of the prognosis of patients with primary liver cancer from previous thyroid cancer. However, there are few prognostic studies on patients with HCC-SPM and high-performance predictive models are lacking.

Random survival forest (RSF) (7) is a non-parametric algorithm for analyzing right-truncated survival data. Due to its high performance and interpretability, RSF is being widely accepted. DeepSurv, a novel method devised by Katzman and colleagues (8), employs deep learning to incorporate COXPH proportional hazards into survival analysis. This approach leverages the capabilities of deep neural networks to improve the modeling of survival data by understanding complex relationships within the data.

In this research, our objective was to utilize data from the Surveillance, Epidemiology, and End Results (SEER) database to develop the most accurate and clinically applicable prognostic model for HCC-SPM patients using COXPH regression, RSF, and DeepSurv algorithms for improving the management of HCC-SPM patients. By comparing these models, we aimed to identify the most effective one, providing a predictive tool for physicians and patients to evaluate risk stratification and individual prognosis. We present this article in accordance with the TRIPOD reporting checklist (available at https://tcr.amegroups.com/article/view/10.21037/tcr-2025-589/rc).

Methods

Data sources

Patients diagnosed with HCC-SPM from 2010 to 2021 were selected from the SEER database (https://seer.cancer.gov/), a comprehensive U.S. cancer registry that encompasses approximately 30% of the population across 17 cancer treatment centers. Since the SEER database provides publicly accessible data with anonymized patient details, neither ethical approval nor patient consent was necessary for this study. This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The methodologies employed adhered to the SEER database’s published research protocols.

Methods of identifying HCC-SPM cases

The patient’s initial diagnosis must be HCC and the HCC must be their first primary cancer. Screening for confirmatory criteria for HCC was performed using the International Classification of Diseases for Oncology, Third Edition (ICD-O-3). All selected patients with HCC were further screened to confirm the presence of an SPM. SPM is defined as an SPM of a different type that occurs in a patient on top of an HCC. The SEER database records the diagnostic information and chronological order of all primary tumors, and can therefore come to confirm the presence of an SPM.

Research variable

This study incorporated variables such as demographic details (sex, age, race, marital status), tumor attributes [grade, tumor (T) stage, node (N) stage, metastasis (M) stage, tumor size, type of second primary cancer], and treatment modalities (surgery, radiotherapy, chemotherapy), alongside survival status, cause of death, and duration of survival. Inclusion criteria: patients with HCC diagnosed in 2010–2021. Exclusion criteria: (I) HCC was not the initial primary cancer; (II) HCC is not the first primary cancer; (III) non-pathologic diagnosis confirmed; (IV) patients with deletions in each variable except grade; (V) survival time <1 month or survival time unknown. The process of data screening is illustrated in Figure 1.

Figure 1 Flowchart for data screening. SEER, Surveillance, Epidemiology, and End Results.

Methods of model construction and validation

Patients were randomly allocated into training and validation sets at a 7:3 ratio. Initially, COXPH regression models were built by selecting variables via univariate regression, followed by multivariate COXPH regression models. The other two models, RSF and DeepSurv, underwent hyperparameter tuning on the training set through a grid search technique to identify optimal hyperparameters for each model.

The efficacy of each model was assessed on the validation set using specific metrics: the concordance index (C-index) and the area under the receiver operating characteristic curve (AUROC) for 1, 2, and 3 years to evaluate their discriminative capacities. Model calibration was examined using calibration curves at 1, 2, and 3 years. Additionally, decision curve analysis (DCA) for the same time intervals was employed to determine the clinical net benefit of each model.

Risk stratification, interpretation, and individual prediction for optimal modeling

The optimal model derived from the comparison of the individual models allows for the calculation of a risk score for each patient. Patients were grouped based on their risk scores. Survival outcomes were analyzed using Kaplan-Meier curves, with differences evaluated using the log-rank test.

Shapley Additive exPlanation (SHAP) can be used for the interpretation of machine learning models (9-11), in a SHAP plot, the position of each variable along the horizontal axis reflects its impact on the outcome, while the color of the dots indicates the magnitude of the variable’s contribution.

Individual predictions include survival probability plots and local SHAP plots, which offer detailed forecasts regarding survival expectations and risk factors for each person. Survival probabilities are determined using nonparametric estimates. The local SHAP plot, a localized interpretation of SHAP, illustrates the impact of variables on an individual’s prognosis. This analysis helps establish a correlation between risk factors and individual outcomes.

Ultimately, we created a web-based calculator using the optimal model to forecast the prognosis for patients with liver cancer who have a secondary primary cancer, facilitating personalized predictions.

Statistical analysis

The R language CatPredi package (12) was used for discretization of continuous variables such as age, tumor size and risk score. Categorical variables across the training and validation sets were analyzed using the χ² test or Fisher’s exact test. A bilateral P value below 0.05 was deemed statistically significant. The mlr3proba package (13) for R (version 0.4.13) was used to construct each of the five survival machine learning models, with the DeepSurv model relying on the Pycox module. Interpretation of the survival machine learning model was done using Python’s shap module (version 0.37.0). A web-based calculator for the optimal prediction model was developed using Shiny (https://www.shinyapps.io).

Results

Clinical characteristics of patients with HCC-SPM

A total of 1,580 HCC-SPM patients were enrolled in the study. Age was divided into two categories with 65 years old as the dividing point, and tumor size is divided into three categories with 2.2 and 4.2 cm as the dividing points, respectively. The division results are detailed in Figure S1. The demographic and clinical details of the patients in the training and validation sets are presented in Table 1.

Building 5 survival machine learning models

According to the TIMER database, numerous tumor types, particularly LUAD, exhibit significantly elevated PRSS3 mRNA expression (Figure 2A). We next assessed PRSS3 expression in LUAD through the UALCAN database (Figure 2B). We analyzed the downloaded LUAD data with the R package tidyverse (version 2.0.0). Compared with those in tumor samples, PRSS3 mRNA transcript levels were lower in normal samples (Figure 2C).

Figure 2 ROC curves for 3 models in the training set: (A) the time point is 1 year; (B) the time point is 2 years; (C) the time point is 3 years. ROC curves for 3 models in the validation set: (D) the time point is 1 year; (E) the time point is 2 years; (F) the time point is 3 years. AUC, area under the curve; CI, confidence interval; ROC, receiver operating characteristic; RSF, random survival forest.

RSF model: modeling was performed directly using all variables, using grid search, and 10-fold cross-validation was used to determine the optimal combination of hyperparameters for the model, including a ntree of 500, a mtry of 2, a nodesize of 4, a nodedepth of 4, and the rest of the hyperparameters at their default values.

COXPH model: univariate COXPH regression analysis identified significant variables such as SPM, sex, age, marital status, race, grade, tumor size, T stage, N stage, M stage, surgery, chemotherapy, and radiation. The multivariate COXPH regression analysis highlighted SPM, sex, age, marital status, grade, tumor size, T stage, N stage, and surgery as key prognostic factors for HCC-SPM patients. Details from both univariate and multivariate analyses are displayed in Table 2.

DeepSurv model: the modeling was performed directly using all variables, using a grid search with 10-fold cross-validation to determine the optimal combination of hyperparameters for the model, including an alpha of 0.6, a learning rate of 0.02, and the remaining hyperparameters at their default values.

Evaluation and interpretation of models

Comparing the differentiation performance C-index of each model in the training set, the RSF model had the highest C-index of 0.746, followed by the COXPH model (0.738), and the worst was the DeepSurv model (0.681). While, in the validation set, the RSF model had the highest C-index of 0.730, followed by the COXPH model (0.713), and the worst was the DeepSurv model (0.685).

Comparing the ROC curves for 1, 2, and 3 years predictions of each model in the training set (Figure 2A-2C), the RSF model demonstrated the best differentiation among the three models and the same was observed in the validation set (Figure 2D-2F).

Comparing the calibration curves for 1, 2, and 3 years predictions of each model in the training set (Figure 3A-3C), the RSF model performed the best among the three models in terms of prediction consistency, While in the validation set, the consistency of the RSF model also performs well (Figure 3D-3F).

Figure 3 Calibration curves for 3 models in the training set: (A) the time point is 1 year; (B) the time point is 2 years; (C) the time point is 3 years. Calibration curves for 3 models in the validation set: (D) the time point is 1 year; (E) the time point is 2 years; (F) the time point is 3 years. RSF, random survival forest.

Comparing the DCA curves for 1, 2, and 3 years predictions of each model in the training set (Figure 4A-4C), the RSF model showed better clinical net benefit among the three models and the same was observed in the validation set (Figure 4D-4F).

Figure 4 DCA curves for 3 models in the training set: (A) the time point is 1 year; (B) the time point is 2 years; (C) the time point is 3 years. DCA curves for 3 models in the validation set: (D) the time point is 1 year; (E) the time point is 2 years; (F) the time point is 3 years. DCA, decision curve analysis; RSF, random survival forest.

Additionally, the RSF model was visualized and interpreted using a SHAP plot (Figure 5), where variables were ranked by importance. Surgery emerged as the most significant variable, followed by age, T stage, tumor size, and SPM, among others.

Figure 5 SHAP diagram of the RSF model. M, metastasis; N, node; RSF, random survival forest; SHAP, Shapley Additive exPlanation; SPM, second primary malignancy; T, tumor.

Risk of RSF stratification in HCC-SPM patients

Patients in the training and validation sets were divided into high-risk (risk score >86.17), intermediate-risk (56.32≤ risk score ≤86.17), and low-risk (risk score <56.32) groups. Kaplan-Meier analysis and log-rank tests for these groups are depicted in Figure 6A,6B, showing statistically significant differences among them.

Figure 6 Risk stratification of RSF models in training set (A) and validation set (B). RSF, random survival forest.

Prediction of individual prognosis for HCC-SPM

Three patients were randomly selected and sequentially numbered for individual prognostic prediction arguments. Figure 7A shows the individual predicted survival rates. It can be seen that the 3rd patient has a relatively good survival rate, while the 1st patient has a poor survival rate. The local SHAP plot elucidates each patient’s prognosis by detailing the impact of various variables, where red bars indicate risk factors associated with a poorer prognosis, and blue bars represent protective factors.

• Patient 1: the local SHAP plot (Figure 7B) showed that of the first five most important variables, age, T stage, and chemotherapy were prognostic protective factors, while surgery and SPM were a risk factor for promoting a poor prognosis.
• Patient 2: the local SHAP plot (Figure 7C) showed that of the first 5 most important variables, surgery, SPM, and age were prognostic protective factors, while tumor size and grade were a risk factor for promoting a poor prognosis.
• Patient 3: the local SHAP plot (Figure 7D) showed that of the first 5 most important variables, surgery, age, sex, T stage, and race were all prognostic protective factors.

Figure 7 Prediction of individual HCC-SPM patients. (A) Survival curves of individual patients. (B) Localized SHAP plot of patient 1. (C) Localized SHAP plot of patient 2. (D) Localized SHAP plot for patient 3. HCC-SPM, hepatocellular carcinoma and a second primary malignancy; M, metastasis; N, node; SHAP, Shapley Additive exPlanation; SPM, second primary malignancy; T, tumor.

Web application for predicting the prognosis of HCC-SPM patients

This study established and validated 3 models, concluding that the RSF model is the best for HCC-SPM patients. To further disseminate our findings, we developed a web application (https://pre-model.shinyapps.io/RSF-Model/) based on Shiny to predict the prognosis risk of HCC-SPM patients, aiming to assist doctors in clinical prognosis evaluation.

Discussion

In this study, prognostic models for HCC-SPM patients were developed based on SEER database using 3 machine learning methods. RSF model had better discrimination, calibration and clinical applicability in predicting OS at 1, 2 and 3 years in HCC-SPM patients, followed by COXPH model and the worst was the DeepSurv model. Interpretation of the RSF model based on SHAP showed that surgery was the most important risk factor, followed by age, T stage, tumor size, and SPM, etc. In addition, patient risk stratification was performed based on the RSF model, and there was a significant difference in survival among different stratified populations. For the prediction of individual prognosis, localized SHAP maps showed potential in clinical practice.

The traditional COXPH model is widely used in the field of survival analysis, however, there are some limitations of this model. First, the effect of covariates on survival cannot vary over time (14). Second, the sample size for positive outcomes is greater than 10 times the number of variables in the COXPH model (15). Third, the impact of nonlinear factors on patient survival outcomes cannot be considered. Because of their nonparametric structure, machine learning methods do not suffer from these limitations and are increasingly used in clinical research. The RSF model (16,17) proposed in 2008 and characterized by a balance between model fitting and interpretation, is increasingly being used in prognostic prediction models, as evidenced by the construction of the RSF model and the SHAP-based interpretation in this study. In addition, the DeepSurv model has performed well in previous studies, especially those related to imaging data (18,19), however, this study does not reflect the advantages of the DeepSurv model, which may be related to the low data complexity of this study.

The RSF model of this study ranked the importance of the influential factors affecting the prognosis of patients with HCC-SPM in order to help clinicians to identify the important factors affecting the prognosis. Surgery was considered to be the most important variable in terms of prognosis, i.e., the adoption of surgical treatments significantly improved the prognostic outcomes of patients with HCC-SPM. Previous studies (20-22) related to HCC have also demonstrated more clinical benefit in HCC patients who underwent surgery. Ge et al. (23) constructed a prognostic model for risk factors of HCC using COXPH regression model and RSF model, respectively, where the importance of the variables in the RSF model showed that surgery was the most important variable, which is consistent with the findings of this study. The traditional T stage and N stage can provide a rough assessment of the prognosis of patients with HCC, and a number of studies (24-26) have confirmed the importance of these AJCC staging. The significance of the variables in this study also suggests that T stage, N stage and M stage are factors that have a greater impact on prognosis. This study shows that tumor size has a significant impact on the prognosis of HCC. However, Zhang et al. (27) conducted age-stratified COXPH regression on patients with isolated HCC without vascular infiltration and found that, after the age of 65 years, tumor size was no longer an independent risk factor for the prognosis of isolated HCC without vascular invasion. Xie et al. (28) used PSM to confirm that there was no significant difference between tumor size and prognosis in patients with distant metastatic HCC. This study also showed that different types of SPM are also more important influences on the prognosis of HCC. According to our knowledge, this has not been reported in previous studies. In addition, the prognostic impact of marital, sex, chemotherapy, race, and radiation sequentially appeared to be less important in patients with HCC-SPM.

The classification of patients into high, intermediate and low risk groups based on the risk scores of the predictive nomogram is one of the more popular methods used in a large number of COXPH regression models (29-32) and has been widely applied. For the RSF model, risk scores can be obtained directly, and therefore patients can also be categorized into high, medium, and low risk groups. This study has modeled survival differences between high, intermediate, and low risk populations classified based on the RSF model, which can help clinicians identify those at high risk of death among HCC-SPM patients in a timely manner and take timely interventions. More surprisingly, the RSF model also outputs survival curves for individual HCC-SPM patients, which enable more accurate prediction of individual prognosis. This compensates for the fact that nomogram based on COXPH regression can only predict prognosis at certain specified time points. More importantly, the local SHAP plot of the RSF model visually explains the impact of risk factors on individual survival outcomes, which may be a new trend for future clinical prediction models.

There are some limitations in this study. First, the retrospective study data may have some selection bias. Second, both the training and validation sets are homologous data from the SEER database, which lacks external validation to confirm the generalization ability of the model. Third, limited by the SEER database, some clinical indicators and treatment protocols could not be included in the study.

Conclusions

This study developed a prediction model for the prognosis prediction of HCC-SPM patients using the RSF model. Patients were categorized into high-, intermediate-, and low-risk groups, aiding clinicians in identifying those at higher risk. Additionally, the RSF model enables accurate prediction of individual patient survival, supporting personalized medicine.

Acknowledgments

None.

Footnote

Reporting Checklist: The authors have completed the TRIPOD reporting checklist. Available at https://tcr.amegroups.com/article/view/10.21037/tcr-2025-589/rc

Peer Review File: Available at https://tcr.amegroups.com/article/view/10.21037/tcr-2025-589/prf

Funding: None.

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://tcr.amegroups.com/article/view/10.21037/tcr-2025-589/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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