Development and validation of machine learning models for esophagogastric variceal bleeding risk in hepatocellular carcinoma patients

Abstract

BACKGROUND

Esophagogastric variceal bleeding (EGVB) is a common and highly fatal complication in patients with hepatocellular carcinoma (HCC). In this study, our aim was to develop a predictive model to assess the risk of EGVB in patients with HCC.

AIM

To construct and internally validate a machine learning model to predict the risk of EGVB in patients with HCC.

METHODS

This study included 188 patients with HCC, who were randomly assigned to the training set and validation set in a 7:3 ratio. Using LASSO regression and multivariate Logistic regression, the variables significantly associated with EGVB were identified, and six machine learning models were constructed using these variables. The predictive performance of different models was compared using metrics such as the area under the curve (AUC). The optimal model was further evaluated, and the SHapley Additive exPlanation (SHAP) interpretability analysis was performed.

RESULTS

In the end, four characteristic variables, namely albumin, splenic vein diameter, tumor burden score, and ascites, were selected. These four variables were used to build six machine learning models. Among these, the support vector machine (SVM) achieved the highest AUC (0.931), F1 score (0.889), Youden index (0.785), and sensitivity (0.889) across all six models. Based on the overall performance, SVM was identified as the optimal model. Internal validation demonstrated that the SVM model had good calibration performance and clinical applicability. SHAP interpretability analysis further visualized the contribution pathways of each variable through a feature importance bar chart, a swarm plot, dependence plots, and a waterfall plot, providing interpretable evidence for clinical decision-making.

CONCLUSION

The successful development of a predictive model for EGVB in HCC patients, along with SHAP analysis, can help clinicians identify high-risk individuals at an early stage and implement personalized interventions.

Key Words: Hepatocellular carcinoma; Esophagogastric variceal bleeding; Machine learning; Prediction model; SHapley Additive exPlanation

Core Tip: This study developed and validated six machine learning models for the early identification of the risk of early-stage esophagogastric variceal bleeding in patients with hepatocellular carcinoma. Albumin, splenic vein diameter, tumor burden score, and ascites were identified as feature variables through LASSO and multivariate Logistic regression. Based on these variables, six machine learning models were constructed, and the support vector machine model was selected as the optimal model. This model demonstrated satisfactory predictive performance, calibration, and clinical applicability.

INTRODUCTION

Esophagogastric variceal bleeding (EGVB) is a common and life-threatening complication of portal hypertension (PHT). It progresses rapidly and often leads to severe complications such as hemorrhagic shock, hepatic encephalopathy, and acute kidney injury with a high mortality rate and rebleeding rate[1]. PHT is mostly caused by chronic liver inflammation and vascular endothelial growth factor-related angiogenesis. These same two pathophysiological mechanisms also promote the development of liver cancer. Since hepatocellular carcinoma (HCC) accounts for approximately 85%-90% of all liver cancers, EGVB is also a common complication of HCC[2,3]. Studies have found that among HCC patients screened by endoscopy, approximately 50% have esophagogastric varices (EGV), and approximately 15%-35% of HCC patients will experience variceal bleeding[4,5]. Endoscopy is recommended to assess the status of EGV[6]. However, its implementation is limited by factors such as invasiveness, patient tolerance, anesthesia risks, and the rapid progression of HCC itself, making it difficult to achieve dynamic monitoring of the risk of EGVB. Furthermore, for low-risk patients, excessive endoscopic examinations may not be necessary. Therefore, there is an urgent need to establish a non-invasive predictive model for the risk of EGVB in patients with HCC to identify high-risk individuals as early as possible, optimize the schedule of endoscopy, and implement intervention measures for preventing EGVB in this population.

Several potential risk factors for EGVB have been identified, including tumor diameter ≥ 5 cm, Child-Pugh classification, history of bleeding, portal vein tumor thrombus (PVTT), and the fibrosis-4 index (FIB-4)[5,7]. However, previous studies on this topic have had certain limitations. Firstly, most studies focused on the general cirrhosis population, and there were relatively few studies specifically targeting patients with HCC, resulting in insufficient exploration of specific risk factors for HCC. Secondly, no studies have reported the use of machine learning to construct a predictive model for EGVB in HCC. As an emerging technological paradigm, machine learning is adept at handling nonlinear relationships and can construct robust risk models and improve predictive performance. These advantages have made it widely applied in various medical fields.

In this study, we retrospectively analyzed the clinical data of inpatients diagnosed with HCC at Yibin Second People’s Hospital from January 2018 to March 2025. After identifying the significant variables associated with EGVB, we developed and compared the performance and clinical utility of six machine learning models. Subsequently, we selected the optimal model for predicting EGVB risk in HCC patients, aiming to provide a practical decision support tool for clinicians.

MATERIALS AND METHODS

Data sources

Data were collected from 689 inpatients diagnosed with HCC at Yibin Second People’s Hospital from January 2018 to March 2025. After applying the inclusion and exclusion criteria, 188 patients were enrolled in the study.

Inclusion criteria: (1) Age between 18 and 80 years; (2) HCC diagnosed by non-invasive imaging or histopathological examination, according to the 2023 AASLD guidelines[8]; (3) The diagnosis of EGVB is based on endoscopic findings: (a) Active bleeding or oozing from varices; (b) No active bleeding, but signs of recent variceal rupture, such as white thrombi or blood clots; and (c) Presence of varices and blood accumulation in the stomach, with no other identifiable bleeding sites[9]; (4) All patients underwent gastroscopy. Patients in the bleeding group had no history of EGVB before the onset of the disease, and had clear clinical symptoms of upper gastrointestinal bleeding upon admission, such as hematemesis or melena, and the endoscopic examination results confirmed the diagnosis of EGVB. Patients in the non-bleeding group had no history of EGVB, no clinical symptoms of upper gastrointestinal bleeding upon admission, and no EGVB was confirmed by endoscopy; and (5) Patients must have complete clinical records.

Exclusion criteria: (1) Patients with concurrent malignant tumors in other sites or hematological diseases; (2) Patients who have not undergone gastroscopy; (3) Patients who have undergone liver resection; (4) Patients who have undergone splenectomy or splenic embolization; (5) In the bleeding group, patients with gastrointestinal bleeding caused by other factors, such as peptic ulcer bleeding, or bleeding from the mouth, pharynx, or nose, must be excluded; or (6) Cases with missing or incomplete clinical records.

Definition

The tumor burden score (TBS) is defined as the Euclidean distance between two variables on a Cartesian plane: Maximum tumor diameter (X-axis) and number of tumor lesions (Y-axis). The distance from the origin (0, 0) to any given point is calculated using the Pythagorean theorem[10]. TBS2 = (maximum tumor diameter)² + (number of tumors)². The measurement guidelines are as follows: (1) Imaging should be performed using arterial-phase contrast-enhanced computed tomography (CT) or magnetic resonance imaging; (2) For patients with a single lesion, the maximum tumor diameter should be directly measured, while for those with multiple lesions, the largest diameter (in centimeters) of all the lesions should be recorded; and (3) The number of liver tumors is determined by counting all the visible primary tumor lesions and intrahepatic metastases within the liver.

The Model for End-Stage Liver Disease (MELD) score was calculated as follows: MELD score = 3.78 × ln[total bilirubin (TBIL; µmol/L)] + 11.2 × ln[international normalised ratio] + 9.57 × ln[serum creatinine (µmol/L)] + 6.43 × etiology factor (0 for biliary or alcoholic, 1 for other).

The FIB-4 index was calculated as follows: FIB-4 = [age (year) × aspartate aminotransferase (AST; U/L)]/[PLT (10⁹/L) × alanine aminotransferase (ALT; U/L)^1/2].

Data collection

Among the 188 patients, there was no data missing, which ensured the integrity of the data. All clinical data were collected within 24 hours after admission. The data quality control measures included: (1) Establishing standardized data collection criteria and operation manuals; (2) All investigators underwent standardized training and passed evaluations before data collection; (3) Clinical data were entered independently by two researchers, and radiological parameters were independently interpreted by two radiologists; If there were differences, consensus was reached through thorough internal discussion; (4) The data entry system was equipped with logical error-checking functions to automatically identify outliers, logical inconsistencies, and missing data; and (5) Random checks were conducted daily.

The collected data included the following: (1) Demographic and medical history, comprising age, sex, smoking history, alcohol consumption history, history of hypertension, history of diabetes, presence of cirrhosis, and etiology; (2) Comorbidities, including ascites and spontaneous bacterial peritonitis; (3) Laboratory parameters, such as AST, ALT, TBIL, direct bilirubin (DBIL), indirect bilirubin (IBIL), albumin, alpha-fetoprotein (AFP), MELD score, and FIB-4; and (4) Imaging parameters, encompassing maximum tumor diameter, number of tumor, TBS, China Liver Cancer Staging, intrahepatic metastasis, extrahepatic metastasis, PVTT, portal vein diamete, anteroposterior diameter of the spleen, spleen craniocaudal length, spleen thickness, and splenic vein diameter (SVD).

Feature selection strategy

The study subjects were randomly assigned in a 7:3 ratio to the training set and the validation set. The training set was used for feature selection and model building, while the validation set was used for independent validation. In this study, feature selection was accomplished through LASSO regression combined with multivariate Logistic regression. LASSO regression helps alleviate multicollinearity and overfitting. Specifically, this method incorporates an L1 regularization term, which continuously shrinks the coefficients and effectively removes redundant variables. The optimal regularization parameter λ was determined through ten-fold cross-validation. Subsequently, the λ value with a difference of no more than one standard error from the model error was selected to identify the feature variables with non-zero regression coefficients. These variables were then included in the multivariate Logistic regression, and those with a P value < 0.05 were selected to construct the machine learning model.

Development and evaluation of predictive models

Six machine learning prediction models were built using the training set data, including decision tree (DT), random forest (RF), extreme gradient boosting (XGBoost), light gradient boosting machine (LightGBM), support vector machine (SVM), and artificial neural network (ANN).

The hyperparameters of each model were optimized through grid search and 5-fold cross-validation, with area under the curve (AUC) as the primary evaluation metric, and all combinations within the predefined hyperparameter space were exhaustively explored. The 5-fold cross-validation method splits the training set into five subsets, iteratively using four for training and one for validation. The average of the five validation AUCs estimates generalization error, thereby mitigating the influence of sampling fluctuations on model selection.

Model performance was systematically evaluated using the validation set data, with discrimination assessed via the receiver operating characteristic (ROC) curve and the AUC. Calibration was evaluated with the Brier score. Classification performance was assessed using F1 score, accuracy, precision, sensitivity, and specificity, with raw classification results presented in the confusion matrix. The selection of the optimal model was mainly based on the discriminative performance, while the calibration and classification performance were also comprehensively evaluated.

Optimal model performance evaluation

Calibration curves and the Brier score were used to assess the accuracy of the optimal model’s predicted probabilities. The Hosmer-Lemeshow goodness-of-fit test was used to evaluate the fit of the optimal model in the validation set, with P > 0.05 indicating a good fit. Decision curve analysis (DCA) was used to evaluate the clinical net benefit of the model at different decision thresholds.

SHapley Additive exPlanation interpretability analysis

Machine learning models generally outperform traditional linear models in predictive tasks, but their “black-box” nature often necessitates post-hoc interpretability tools. This study applied the SHapley Additive exPlanation (SHAP) framework to explain the selected optimal model, with its theoretical basis rooted in the Shapley value from game theory. The value quantified the marginal contribution of features to the model’s prediction through its absolute magnitude, where the larger the absolute value, the greater the importance, and the sign conveyed the effect direction. A positive sign indicated a positive driving effect on the prediction, whereas a negative sign denoted a negative inhibitory effect. At the global level, a swarm plot and a feature importance bar chart were used to display the feature attribution distribution across all samples, and dependence plots were used to illustrate the nonlinear relationships between specific features and SHAP values, as well as the interaction effects among features. At the local level, representative samples were selected, and a waterfall plot was used to visualize the specific direction and magnitude of each feature’s influence on individual prediction results.

Statistical analysis

All statistical analyses were conducted using R 4.5.1 and Python 3.10.4. The normality of continuous variables was assessed with the Kolmogorov-Smirnov test. Normally distributed quantitative data were presented as mean ± SD, and comparisons between groups were conducted using the two-sample t-test. Non-normally distributed continuous variables were reported as median (Q1, Q3), and the nonparametric Mann-Whitney U test was applied for intergroup comparisons. Categorical data were presented as n (%), and differences between groups were evaluated using the χ² test or Fisher’s exact test. All tests were two-sided. P valve < 0.05 indicated statistical significance.

RESULTS

Clinical characteristics of patients

From January 2018 to March 2025, a total of 689 patients with HCC were enrolled. After screening, 501 were excluded, and finally, 188 patients were included in the final analysis (Figure 1).

Figure 1 Technology roadmap. HCC: Hepatocellular carcinoma; SHAP: SHapley Additive exPlanation.

All HCC patients were assigned to the non-bleeding group (n = 97) or the bleeding group (n = 91). The age range of the patients was from 26 years to 82 years, with an average age of 56.90 ± 10.88 years. The cohort included 163 males and 25 females. There were several significant baseline characteristic differences between the two groups: The average age of the non-hemorrhage group was higher (58.5 years vs 55.2 years, P = 0.039). The dimensions of the spleen in the hemorrhage group were all larger, including median anteroposterior diameter (14.7 cm vs 11.9 cm), superior-inferior diameter (13.2 cm vs 11.3 cm), and splenic thickness (5.4 cm vs 4.4 cm), and all differences were statistically significant (P < 0.001). The diameters of the portal vein and SVD were also significantly greater in the bleeding group (both P < 0.001). In terms of tumor characteristics, the TBS of the hemorrhage group was higher (median 7.9 vs 5.6, P < 0.001), a greater proportion of tumors exceeded the maximum diameter threshold (69.2% vs 47.4%, P = 0.002), and the incidence of multifocal tumors, intrahepatic metastases, and PVTT was significantly elevated (all P < 0.01). In the clinical aspect, the proportion of patients with liver cirrhosis was higher in the bleeding group (98.9% vs 88.7%, P = 0.004), and the incidences of stage III-IV HCC, ascites, and spontaneous peritonitis were significantly higher (all P < 0.001). In the laboratory parameters, the median albumin level was lower in the bleeding group, while the MELD score, FIB-4, and DBIL were significantly higher (all P < 0.05). No significant differences were observed between the groups in sex, etiology, smoking, alcohol consumption, diabetes, hypertension, extrahepatic metastasis, AFP, ALT, AST, TBIL, or IBIL (all P > 0.05; Table 1).

Table 1 Clinical characteristics of patients in the entire cohort.

Variables	Total (n = 188)	Non-bleeding (n = 97)	Bleeding (n = 91)	P value
Sex (male)	163 (86.70)	81 (83.51)	82 (90.11)	0.183
Cirrhosis (yes)	176 (93.62)	86 (88.66)	90 (98.90)	0.004
Hepatitis B (yes)	171 (90.96)	89 (91.75)	82 (90.11)	0.695
Smoking (yes)	119 (63.30)	61 (62.89)	58 (63.74)	0.904
Drinking (yes)	98 (52.13)	45 (46.39)	53 (58.24)	0.104
Diabetes (yes)	25 (13.30)	10 (10.31)	15 (16.48)	0.213
Hypertension (yes)	25 (13.30)	17 (17.53)	8 (8.79)	0.078
China liver cancer staging III-IV (yes)	92 (48.94)	33 (34.02)	59 (64.84)	< 0.001
Intrahepatic metastasis (yes)	123 (65.43)	54 (55.67)	69 (75.82)	0.004
Extrahepatic metastasis (yes)	20 (10.64)	8 (8.25)	12 (13.19)	0.272
Portal vein tumor thrombus (yes)	86 (45.74)	31 (31.96)	55 (60.44)	< 0.001
Ascites (yes)	109 (57.98)	33 (34.02)	76 (83.52)	< 0.001
Spontaneous bacterial peritonitis (yes)	32 (17.02)	7 (7.22)	25 (27.47)	< 0.001
AFP < 400 µg/L	74 (39.36)	40 (41.24)	34 (37.36)	0.587
Maximum tumor diameter ≥ 5 cm	109 (57.98)	46 (47.42)	63 (69.23)	0.002
Multiple tumors	128 (68.09)	56 (57.73)	72 (79.12)	0.002
Age (year)	56.90 ± 10.88	58.48 ± 11.12	55.21 ± 10.42	0.039
Tumor burden score	13.25 ± 3.34	11.89 ± 3.10	14.69 ± 2.98	< 0.001
Portal vein diameter (mm)	6.88 (4.46, 9.35)	5.59 (3.83, 7.96)	7.87 (5.76, 10.31)	< 0.001
Spleen anteroposterior diameter (cm)	15.00 (14.00, 17.00)	14.00 (13.00, 15.00)	16.50 (15.00, 18.00)	< 0.001
Spleen craniocaudal length (cm)	12.20 (10.70, 13.91)	11.30 (9.86, 12.60)	13.20 (11.95, 14.75)	< 0.001
Spleen thickness (cm)	4.90 (4.20, 5.82)	4.40 (3.80, 5.30)	5.40 (4.69, 6.15)	< 0.001
Splenic vein diameter (mm)	8.00 (6.00, 10.00)	7.00 (6.00, 8.00)	10.00 (8.00, 12.00)	< 0.001
ALT (U/L)	41.75 (24.58, 68.82)	44.20 (27.40, 77.80)	36.60 (22.60, 59.10)	0.112
AST (U/L)	57.30 (36.77, 98.80)	56.60 (37.60, 95.00)	57.50 (36.75, 119.85)	0.532
TBIL (µmol/L)	20.14 (13.97, 32.25)	18.70 (12.90, 29.30)	22.11 (15.50, 32.80)	0.145
IBIL (µmol/L)	11.10 (8.47, 14.83)	11.20 (8.30, 15.70)	10.90 (8.50, 14.10)	0.665
DBIL (µmol/L)	7.93 (5.30, 16.29)	6.80 (4.82, 13.60)	9.50 (5.95, 18.40)	0.010
Albumin (g/L)	32.90 (28.20, 39.05)	38.10 (35.00, 41.80)	28.30 (26.45, 31.40)	< 0.001
MELD score	9.80 (8.00, 12.65)	8.47 (7.31, 10.71)	11.41 (9.32, 13.82)	< 0.001
Fibrosis-4 index	5.79 (3.45, 10.89)	4.74 (2.93, 8.51)	8.40 (4.33, 13.88)	< 0.001

Normally distributed quantitative data were presented as mean ± SD. Non-normally distributed continuous variables were reported as median (Q1, Q3). Categorical data were presented as n (%). AFP: Alpha-fetoprotein; ALT: Alanine aminotransferase; AST: Aspartate aminotransferase; TBIL: Total bilirubin; DBIL: Direct bilirubin; IBIL: Indirect bilirubin; MELD: Model for End-Stage Liver Disease.

Feature selection

The 188 patients were randomly assigned to the training set and validation set in a 7:3 ratio. All variables in the training set were included in the LASSO regression, with the λ value corresponding to the minimum mean squared error plus one standard error (λ.1se) selected as the final regularization parameter. When λ.1se = 0.07670288, the model retained four variables with non-zero coefficients: Ascites, TBS, SVD, and albumin (Figure 2). These four features selected by LASSO regression were entered into the multivariate Logistic regression. The results showed that ascites, TBS, SVD, and albumin were independent risk factors for EGVB in patients with HCC (P < 0.05; Table 2).

Figure 2 Schematic diagram of variable selection via LASSO regression analysis. A: Ten-fold cross-validation plot; B: Coefficient path diagram.

Table 2 Multivariate logistic regression analysis.

Variable	β	SE	Waldχ2	OR	95%CI	P value
Ascites	1.371	0.610	2.246	3.939	1.190-13.031	0.025
Tumor burden score	0.283	0.111	2.555	1.327	1.068-1.648	0.011
Splenic vein diameter	0.590	0.140	4.207	1.804	1.370-2.374	< 0.01
Albumin	-0.188	0.049	-3.867	0.829	0.754-0.912	< 0.01

Model performance and comparison

Six machine learning models, including DT, RF, XGBoost, LightGBM, SVM, and ANN, were constructed based on the aforementioned feature variables. Figure 3 presents the ROC curves of each model for detecting HCC combined with EGVB on the validation set. Figure 4 displays the corresponding confusion matrices. Table 3 summarizes the model evaluation metrics.

Figure 3 Receiver operating characteristic curves of six machine learning models on the validation set. ROC: Receiver operating characteristic; AUC: Area under the curve; XGBoost: Extreme gradient boosting; LightGBM: Light gradient boosting machine; SVM: Support vector machine; ANN: Artificial neural network.

Figure 4 Confusion matrices of six machine learning models on the validation set. A: Decision tree; B: Random forest; C: Extreme gradient boosting; D: Light gradient boosting machine; E: Support vector machine; F: Artificial neural network. EGVB: Esophagogastric variceal bleeding; XGBoost: Extreme gradient boosting; LightGBM: Light gradient boosting machine; SVM: Support vector machine; ANN: Artificial neural network.

Table 3 Performance evaluation metrics of six machine learning models on the validation set.

Model	Brier	Accuracy	Precision	Sensitivity	Specificity	F1 score	Youden’s index	Cut-off
DT	0.114	0.875	0.857	0.889	0.862	0.873	0.751	0.200
RF	0.106	0.893	0.920	0.852	0.931	0.885	0.783	0.590
XGBoost	0.112	0.875	0.917	0.815	0.931	0.863	0.746	0.590
LightGBM	0.136	0.839	0.909	0.741	0.931	0.816	0.672	0.670
SVM	0.105	0.893	0.889	0.889	0.897	0.889	0.785	0.550
ANN	0.104	0.893	0.957	0.815	0.966	0.880	0.780	0.650

DT: Decision tree; RF: Random forest; XGBoost: Extreme gradient boosting; LightGBM: Light gradient boosting machine; SVM: Support vector machine; ANN: Artificial neural network.

ROC curve analysis indicated that these six machine learning models achieved satisfactory discriminatory performance in the validation set. Among these, the AUC value of SVM was the highest (0.931), followed by RF (0.926), ANN (0.925), XGBoost (0.916), LightGBM (0.90), and DT (0.899). In terms of calibration, the Brier scores of each model ranged from 0.104 to 0.136. The Brier score of SVM was 0.105, second only to the ANN (0.104), with a negligible difference between the two. Both models exhibited good probability calibration. In terms of classification performance, SVM ranked first among the six models in F1 score (0.889), Youden’s index (0.785), and sensitivity (0.889), while maintaining balanced performance across accuracy (0.893), precision (0.889), and specificity (0.897). The confusion matrix further showed that SVM had the fewest false negatives, with only 3 cases, accounting for 11.11% of the actual positive samples. Considering its overall performance, SVM had the best predictive capability in the validation set and was identified as the optimal model.

Optimal model performance evaluation

The calibration curve results (Figure 5A) indicate that the observed curve in the validation set closely matches the bias-corrected curve, suggesting no marked overfitting. After Bootstrap correction (B = 1000 iterations), the bias-corrected curve aligns well with the ideal calibration line, indicating a strong consistency between the model’s predicted and observed probabilities. The Brier score of 0.105 indicated good accuracy of the model’s probabilistic predictions. The Hosmer-Lemeshow test yielded χ² (8) = 5.690, P = 0.682, suggesting an adequate model fit. The DCA (Figure 5B) indicates that the SVM model delivers higher net benefits than both the “full intervention” and “no intervention” strategies across the full range of threshold probabilities (0%-100%), suggesting broad clinical applicability.

Figure 5 The calibration curve and decision curve analysis curve of the support vector machine model in the validation set. A: Calibration curve; B: Decision curve analysis curve.

SHAP interpretability analysis

The SHAP framework was used to conduct an interpretability analysis on the optimal SVM model. The feature importance bar chart (Figure 6A) identifies albumin, SVD, TBS, and ascites as the four most important features, ranked in descending order by their mean absolute SHAP values. Among these, albumin, SVD, and TBS substantially influence EGVB prediction in HCC patients, while the impact of ascites is relatively limited.

Figure 6 support vector machine model interpretable analysis SHapley Additive exPlanation plot. A: Feature importance bar chart; B: Swarm plot. The X-axis represents SHapley Additive exPlanation values, with positive values indicating an increased probability of esophagogastric variceal bleeding and negative values indicating a decreased probability. Dot colors represent feature values, ranging from low (blue) to high (red). Albumin, splenic vein diameter, and tumor burden score are continuous variables, while ascites is a binary variable. SHAP: SHapley Additive exPlanation.

The swarm plot (Figure 6B) displays the direction and magnitude of each feature’s contribution to the prediction of EGVB. Albumin is negatively correlated with the model output because higher levels are mainly concentrated in the region with negative SHAP values, thereby reducing the predicted probability of EGVB. In contrast, SVD, TBS, and ascites are positively correlated with the model output. Higher SVD and TBS levels, as well as the presence of ascites, are mainly concentrated in the region with positive SHAP values, thereby increasing the probability of EGVB prediction.

The dependence plot (Figure 7) shows how each feature value relates to the probability of EGVB. Ascites follows a binary distribution, with negative SHAP values corresponding to negative results and positive values corresponding to positive results, reflecting the binary threshold effect. Both TBS and SVD display a nonlinear upward trend, where higher values markedly increase the risk of EGVB. Albumin exhibits a nonlinear downward trend, and low albumin levels are risk factor for EGVB.

Figure 7 Dependence plots of the support vector machine model. A-D: The X-axis represents feature values, and the Y-axis represents SHapley Additive exPlanation (SHAP) values (contribution to the predicted probability). Each dot denotes an individual sample. Positive SHAP values indicate an increased risk of esophagogastric variceal bleeding, while negative values indicate a decreased risk. SHAP: SHapley Additive exPlanation.

The waterfall plot (Figure 8) depicts the individualized prediction pathway for a representative patient. This patient has a relatively low albumin level (29.59 g/L), which increases the predicted EGVB probability from a baseline of 0.493-0.673 (contribution: +0.18). TBS (9.85) is relatively high, further increasing the probability to 0.763 (contribution: +0.09). The SVD (9 mm) is relatively high, with a positive adjustment to 0.833 (contribution: +0.07). The presence of ascites contributes an additional +0.03. Ultimately, the predicted probability of EGVB for this patient is 0.863.

Figure 8  Waterfall plot of the support vector machine model.

DISCUSSION

With the iterative development of artificial intelligence, machine learning has shifted from theoretical exploration to clinical applications. Compared with traditional methods, machine learning has obvious advantages in handling nonlinear relationships and complex pattern recognition[11]. It can also optimize treatment decisions and generate personalized recommendations based on individual patient characteristics[12].

In this study, LASSO regression and multivariate logistic regression were used to screen variables. The results showed that albumin, SVD, TBS, and ascites were closely related to the risk of EGVB in HCC patients. In the LASSO regression analysis, we selected λ.1se as the final regularization parameter. Compared with the 14 feature variables identified using λ.min, λ.1se further reduced the number of variables while maintaining acceptable predictive accuracy, ultimately resulting in four predictive variables. This choice followed the principle of parsimony, that is, when the predictive performance is similar, it is preferred to choose a model with fewer variables, thereby improving generalization and clinical applicability. After validation through multivariate logistic regression, these four variables maintained statistical significance.

The inclusion and exclusion criteria for common clinical factors in this study are as follows. Regarding the Child-Pugh classification, we included its independent components, such as albumin, ascites, and bilirubin. Including the composite score would have introduced multicollinearity. Therefore, only the individual components of the Child-Pugh classification were considered in this study. As for the history of bleeding, all patients in the bleeding group had experienced their first episode of EGVB, while those in the non-bleeding group did not have such a history. This factor did not show any change and thus was excluded from the candidate pool. Regarding PVTT, it was initially included in the candidate variable pool, but ultimately was not retained by the LASSO algorithm. This might be due to its multiple collinearity with the diameter of the splenic vein. Both variables reflect the severity of PHT. In summary, the four variables identified through preliminary LASSO screening and validated by logistic regression provide a robust and simplified model that is more suitable for clinical application.

This study developed six EGVB risk prediction models for HCC patients based on machine learning algorithms. Comprehensive evaluation showed that the SVM model outperformed the other six models in discriminatory ability, sensitivity, and overall balance, achieving the highest AUC, sensitivity, F1 score, and Youden index. In addition, its false negative rate (equivalent to the missed diagnosis rate) was only 11.11%, highlighting its potential to reduce the risk of missed diagnoses and prevent delays in intervention. The model developed in this study integrates imaging features, biochemical markers, and TBS, thereby overcoming the limitations of models based solely on a single biochemical or clinical indicator. The prevalence of EGVB was 48.40% (91/188), higher than the 15%-35% reported in other studies[4,5]. This difference may be due to the study population being limited to hospitalized patients with EGVB confirmed by endoscopy, and may also be related to regional differences and the varying inclusion and exclusion criteria of different studies.

Recently, Li et al[5] developed the BFE-HCC scoring model. In comparison, the SVM model demonstrates a significant relative advantage in both clinical applicability and predictive performance. In terms of clinical accessibility, the BFE-HCC scoring system relies on the presence of high-risk varices, which requires invasive endoscopic procedures, thereby limiting its broader clinical use. In contrast, the SVM model relies only on four easily obtainable non-invasive indicators, making it more suitable for clinical screening and dynamic monitoring. In terms of predictive performance, the BFE-HCC, which relies on traditional logistic regression, has difficulty capturing complex nonlinear relationships among features. However, the SVM model effectively addresses this issue through machine learning algorithms. Indirect comparisons based on published data show that the SVM model outperforms the BFE-HCC score in discriminative ability (AUC: 0.931 vs 0.81), calibration (Brier: 0.105 vs 0.175), and clinical benefit (DCA: 0%-100% vs approximately 17%-90%)[5]. However, due to differences in study population characteristics and validation methods, a strict direct comparison cannot be made. Nevertheless, the theoretical basis and supporting data suggest that this model may have significant advantages. Overall, the model developed in this study provides a more convenient, accurate, and non-invasive tool for stratifying the risk of EGVB in HCC patients. However, its stability and generalizability still need to be further verified through prospective, multicenter studies.

In order to further elucidate the decision-making mechanism of the SVM model, this study introduced the SHAP interpretability framework. An interpretability analysis was conducted on four selected core predictive factors, including albumin, SVD, TBS, and ascites. SHAP scores quantified each variable’s contribution and its direction of influence, while visualizations clearly demonstrated how each factor increased or decreased the risk of EGVB. This analysis provides a scientific basis for clinical risk assessment and the formulation of personalized treatment plans. The following content will provide a detailed explanation of these four factors.

This study further indicates that albumin is an independent clinical predictor of EGVB, and there is a monotonically decreasing relationship between the two[13,14]. SHAP analysis shows that as albumin levels increase, the risk of EGVB gradually decreases. When albumin levels fall below approximately 34 g/L, it promotes the development of EGVB. The biological basis of this phenomenon lies in the protective effect of albumin on the vascular endothelial barrier. First, albumin binds to the endothelial glycocalyx, enhancing the mechanical strength of the vascular wall and limiting the expansion of intercellular gaps[15]. Secondly, the cysteine-34 residue in albumin can scavenge reactive oxygen species and free radicals in the blood, thereby preventing vascular wall damage caused by oxidative stress[16]. It is noteworthy that approximately 80% of patients with HCC have low albumin levels (≤ 35 g/L)[17]. This suggests that hypoalbuminemia is a common high-risk factor driving the occurrence of EGVB in the HCC population, and clinicians should closely monitor the intravascular environment of these patients. For HCC patients with significantly reduced albumin levels (below 34 g/L, especially below 30 g/L), human serum albumin should be actively administered to improve the intravascular environment and reduce the risk of EGVB.

SVD is a key hemodynamic indicator for assessing the risk of EGVB in HCC patients. SHAP analysis shows that the relationship between SVD and the risk of EGVB is roughly an “S”-shaped curve. When SVD is below 8 mm, the risk of EGVB remains low. Within the range of 8-12 mm, the sharp increase in SHAP values indicates a rapid increase in risk. Once SVD exceeds 12 mm, the risk of EGVB will stabilize at a high level, and further vessel dilation will not significantly elevate the probability of bleeding. Wicaksono et al[18] reported that the ratio of splenic venous blood flow volume to portal venous blood flow velocity can effectively predict the severity of esophageal varices. The higher this ratio is, the more severe the PHT is, and the higher the risk of esophageal variceal rupture bleeding. Our results are consistent with these findings, and we further identified the high-risk period of EGVB when SVD exceeded 12 mm. Future studies with larger sample sizes are needed to validate the universality and stability of this threshold. Splenic vein dilation frequently occurs as a secondary manifestation of PHT, and the two conditions are mutually reinforcing, together elevating the risk of EGVB[19]. In patients with HCC, splenic vein thrombosis may be caused by tumor infiltration, compression, or local inflammation. This obstruction can impede splenic vein return, leading to blood stasis and forcing blood to flow retrogradely through the short gastric vein collateral, thereby particularly increasing the risk of EGVB[20]. Based on the above situation, we propose a stratified management strategy based on the SVD threshold. For HCC patients with an SVD < 8 mm, routine follow-up every 6 months is recommended. For those with an SVD of 8-12 mm, we recommend using an intensive monitoring window with follow-up via ultrasound or CT every 3 months. For patients with an SVD > 12 mm, the risk of EGVB reaches a high plateau. We recommend initiating routine endoscopy promptly and conducting a comprehensive assessment of albumin levels, TBS, and ascites to formulate an individualized intervention plan.

The results of this study demonstrate that TBS can predict EGVB in HCC patients and outperforms individual imaging features. TBS integrates the maximum diameter and number of tumors to provide a quantitative measure of HCC tumor burden[21]. The SHAP analysis shows that TBS has a monotonically increasing relationship with the risk of EGVB. When TBS exceeds 8, it becomes a significant risk factor for EGVB. Previous studies have reported that tumor diameter ≥ 5 cm or multifocality is significantly associated with adverse outcomes such as EGVB or rebleeding[7,22]. However, in this study, single-dimensional indicators (e.g., tumor diameter or number of lesions) did not demonstrate independent predictive value for the risk of EGVB. In contrast, TBS demonstrates significant predictive ability. This difference may reflect the heterogeneity of the causes of cirrhosis, variations in tolerance to PHT among different patient groups, and a reduction in the statistical power of individual indicators due to limited sample size. By integrating multidimensional information, TBS effectively reduces random error and maintains robust statistical performance even with a limited sample. Patients with higher TBS have tumors that occupy a larger volume of the liver, which may directly compress the portal and hepatic veins. Studies have demonstrated that tumor burden is positively correlated with the hepatic venous pressure gradient (HVPG)[23]. As HVPG increases, the risk of EGVB rises significantly[24]. An increase in TBS reflects a more active tumor microenvironment. An increase in tumor burden leads to the massive release of procoagulant and proangiogenic factors, which induce microthrombi in the portal vein, further impeding blood flow and heightening the risk of EGVB[25]. Thus, for HCC patients with TBS > 8, clinicians should initiate endoscopic screening early and combine antitumor therapy with pharmacological or endoscopic decompression to reduce the tumor burden and lower EGVB risk.

Ascites is an important manifestation of PHT. The SHAP analysis ascites has a binary threshold effect on the risk of esophageal variceal rupture, that is, its presence increases the risk of bleeding. A large-scale study of 38000 patients identified ascites as a predictive factor for esophageal variceal bleeding[26]. Ascites is mainly caused by fluid leakage due to PHT[27]. However, its presence increases the intra-abdominal pressure, compressing the inferior vena cava and portal vein and thereby impairing portal venous return. This further increases portal venous pressure, leading to blood accumulation at esophageal and gastric varices, heightened vessel wall tension, and a greater risk of EGVB[28,29]. For HCC patients with ascites, clinical management should prioritize controlling PHT. Using only beta-blockers has limited efficacy in preventing EGVB in these patients. It is recommended to adopt comprehensive interventions, including diuretics, sodium restriction, and, when necessary, transjugular intrahepatic portosystemic shunting[30].

The SVM model developed in this study, combined with SHAP interpretability analysis, can achieve relatively accurate EGVB predictions and provide clear and quantitative evidence to support clinical decision-making. In the future, we plan to develop a user-friendly visualization interface to lower the barrier to entry and promote the translation and clinical application of the model.

This study has several limitations. This model has only undergone internal validation and has not been externally validated, which may affect its generalizability and stability. Although internal rigor was enhanced through five-fold cross-validation combined with grid search for hyperparameter optimization, the use of an independent internal validation set, and multidimensional performance evaluation, these measures still cannot fully replace multicenter prospective validation. Future studies should be conducted in larger multicenter prospective cohorts. Secondly, all data in this study were collected within 24 hours of patient admission. However, EGVB itself may cause abnormalities in various hematological parameters, which could interfere with the research results. Future studies should include outpatient follow-up to obtain hematological parameters before the occurrence of EGVB, thereby mitigating the impact of this confounding factor. Third, this study did not consider the potential impact of anticancer treatments on coagulation function, as such treatments may indirectly affect the risk of EGVB by altering liver function or platelet levels. These intervention factors can be incorporated into future model development. Finally, due to the relatively small sample size, subgroup analysis based on tumor staging or liver function stratification could not be performed, which may obscure differences in model performance within these subgroups. Future large-scale multicenter studies should explore stratified modeling approaches to improve predictive accuracy in high-risk subgroups.

CONCLUSION

In summary, six machine learning models were initially developed to predict the risk of EGVB in patients with HCC, among which the SVM model was considered the optimal model. SHAP interpretability analysis showed that albumin levels, SVD, TBS, and ascites may influence the risk of EGVB. This model can stratify the risk of EGVB in patients with HCC, thereby guiding clinical monitoring and preventive interventions. This model should not be used as the final diagnostic tool. Before wide clinical application, it is necessary to conduct prospective, multi-center validation.