Establish and validate an artificial neural networks model used for predicting portal vein thrombosis risk in hepatitis B-related cirrhosis patients

Abstract

BACKGROUND

The portal vein thrombosis (PVT) can exacerbate portal hypertension and lead to complications, increasing the risk of mortality.

AIM

To evaluate the predictive capacity of artificial neural networks (ANNs) in quantifying the likelihood of developing PVT in individuals afflicted with hepatitis B-induced cirrhosis.

METHODS

A retrospective study was conducted at Beijing Ditan Hospital, affiliated with Capital Medical University, including 986 hospitalized patients. Patients admitted between January 2011 and December 2014 were assigned to the training set (685 cases), while those hospitalized from January 2015 to December 2016 were divided into the validation cohort (301 cases). Independent risk factors for PVT were identified using COX univariate analysis and used to construct an ANN model. Model performance was evaluated through metrics such as the area under the receiver operating characteristic curve (AUC) and concordance index.

RESULTS

In the training set, PVT occurred in 19.0% of patients within three years and 23.7% within five years. In the validation cohort, PVT developed in 16.7% of patients within three years and 24.0% within five years. The ANN model incorporated nine independent risk factors: Age, ascites, hepatic encephalopathy, gastrointestinal varices with bleeding, Child-Pugh classification, alanine aminotransferase levels, albumin levels, neutrophil-to-lymphocyte ratio, and platelet. The model achieved an AUC of 0.967 (95%CI: 0.960–0.974) at three years and 0.975 (95%CI: 0.955–0.992) at five years, significantly outperforming existing models such as model for end-stage liver disease and Child-Pugh-Turcotte (all P < 0.001).

CONCLUSION

The ANN model demonstrated effective stratification of patients into high- and low-risk groups for PVT development over three and five years. Validation in an independent cohort confirmed the model's predictive accuracy.

Key Words: Machine learning; Portal vein thrombosis; Risk; Hepatitis B-related cirrhosis

Core Tip: An artificial neural network was developed to predict portal vein thrombosis (PVT) risk in hepatitis B-induced cirrhosis. The model outperformed existing scoring systems in predicting PVT incidence at three and five years intervals. Decision curve analysis and calibration curves highlighted superior clinical utility and benefits.

INTRODUCTION

Chronic hepatitis B virus infection remains a significant global public health issue and is the leading cause of liver cirrhosis in the Chinese population[1]. Among patients with cirrhosis, the risk of developing portal vein thrombosis (PVT) reaches approximately 40%, contributing to increased healthcare costs and reduced life expectancy[2]. PVT involves thrombosis in the main portal vein and its branches, causing partial or complete vascular obstruction. Traditionally, cirrhosis has been associated with clotting factor synthesis disorders and thrombocytopenia, predisposing patients to bleeding. However, recent studies indicate that the anticoagulant and procoagulant systems in cirrhotic livers are highly dynamic and unstable. This imbalance, combined with blood flow stagnation in the portal vein and endothelial dysfunction, increases the risk of bleeding and thrombosis. Non-tumoral PVT is particularly prevalent among patients with cirrhosis, with an annual incidence estimated between 4.6% and 26%[2,3], and occurs more frequently in advanced stages of liver disease. In hepatitis B-related cirrhosis, PVT is a common complication, further aggravating conditions such as refractory ascites and upper gastrointestinal bleeding by reducing hepatic blood flow and increasing portal pressure. Early detection and management of PVT remain challenging due to the absence of specific clinical symptoms in its initial stages.

Most studies on PVT rely on retrospective analyses of influencing factors, and no reliable model currently exists for predicting its occurrence at an early stage. As a result, identifying high-risk individuals for early prevention is challenging in clinical practice[4-8]. A portal blood flow velocity below 15 cm/sec has been identified as a significant risk factor for PVT development[4,9]. Other risk factors include the severity of liver disease and the presence of portal hypertension, such as low platelet count (PLT)[4,6,10], low albumin levels[11], large esophageal varices[3,7,12], previous sclerotherapy[13], previous liver decompensation[14], and the presence of extensive portosystemic collaterals[15]. Recent studies have suggested that the model for end-stage liver disease (MELD) and Child-Pugh-Turcotte (CTP) scores could assist in predicting PVT development[7,12,16]. However, these studies have not fully accounted for the influence of other well-recognized risk factors, limiting their clinical utility.

Machine learning (ML) is increasingly utilized in liver disease research. Some studies have applied ML methods to predict PVT occurrence in patients with cirrhosis and those undergoing splenectomy and cardia devascularization surgeries[17,18]. However, these studies had limitations, such as a relatively small number of baseline indicators, insufficient cohort size, and limited population. Artificial neural networks (ANNs), a form of ML, simulate the information-processing mechanisms of brain neurons[19-22]. These mathematical models have been widely applied in medical decision-making by analyzing linear, logistic, and nonlinear complex relationships[23]. ANNs improve prediction accuracy by optimizing factors associated with outcomes through iterative training processes. Therefore, this study aims to employ ANNs to develop an advanced warning model for the accurate identification of high-risk individuals, particularly for predicting PVT development.

MATERIALS AND METHODS

Patients

A total of 1505 patients diagnosed with hepatitis B cirrhosis (HBC) were retrospectively enrolled at the Beijing Ditan Hospital of Capital Medical University in Beijing, China, from January 2011 to December 2016. Eligibility criteria required patients to have a first-time diagnosis of HBC. Inclusion criteria included: (1) Age between 18 and 75 years; (2) Diagnosis consistent with chronic hepatitis B, as defined by Asian Pacific Association for the Study of the Liver guidelines[24], with treatment involving entecavir or tenofovir; (3) Absence of prior hepatocellular carcinoma (HCC) or organ transplantation; and (4) No history of decompensated cirrhosis. Exclusion criteria were: (1) Age below 18 or above 75 years; (2) Co-infection with other hepatitis types (A, C, D, or E), human immunodeficiency virus, or other liver diseases such as autoimmune hepatitis, alcoholic hepatitis, drug-induced liver disease, fatty liver disease, idiopathic noncirrhotic portal hypertension, or genetic metabolic liver diseases; (3) Prior decompensated cirrhosis, HCC, other malignant tumors, or liver transplantation; (4) Development of HCC within the first six months of follow-up; and (5) Loss to follow-up within five years. To ensure a representative sample, 685 patients from January 2011 to December 2014 were assigned to the training cohort, and 301 patients from January 2015 to December 2016 were assigned to the validation cohort (Figure 1). This study received ethical approval from the Ethics Committee of Beijing Ditan Hospital.

Figure 1 Study flow diagram. HBV: Hepatitis B virus; HCC: Hepatocellular carcinoma; ANN: Artificial neural networks.

Clinical definition and follow-up

Chronic hepatitis B was defined as the presence of hepatitis B surface antigen for more than six months. Compensatory cirrhosis was diagnosed using the following criteria: (1) Pathological findings of F4 stage cirrhosis on biopsy; (2) Detection of esophageal varices during endoscopy, with noncirrhotic portal hypertension excluded; and (3) In the absence of histological and endoscopic evidence, at least two of the following three criteria: (1) Imaging findings [ultrasonography, computed tomography (CT), or magnetic resonance imaging (MRI)] showing liver morphology changes such as nodules and an irregular surface; (2) PLT below 100 × 10⁹ cells/L without other identifiable causes; and (3) Serum albumin (ALB) < 35.0 g/L, international normalized ratio (INR) > 1.3, or prothrombin time prolonged by more than three seconds. Decompensated cirrhosis was diagnosed based on the presence of cirrhosis accompanied by complications related to portal hypertension and/or liver dysfunction. The diagnostic criteria included: (1) Evidence of cirrhosis; and (2) Complications such as ascites, bleeding from esophageal or gastric varices, or hepatic encephalopathy (HE)[25]. PVT is diagnosed through a meticulous process that involves the detection of non-malignant thrombosis within the portal vein or its tributaries. The diagnostic procedure relies on the utilization of advanced imaging techniques, specifically CT Angiography or MRI, which provide high-resolution cross-sectional views of the venous system. PVT was classified as occlusive if blood flow was completely absent in the vein and partial if the vein's lumen was partially occluded with residual blood flow.

The starting point of this research was the initial cirrhosis diagnosis at the hospital. The conclusion of this study focused on the recent identification of PVT within the first year and subsequent follow-up over five years. Clinical data collection included several categories: Demographics (age and gender), complications (gastrointestinal variceal bleeding, ascites, and HE, and biochemical indicators such as alanine aminotransferase (ALT), aspartate aminotransferase, total bilirubin, ALB, gamma-glutamyl transpeptidase, white blood cell count, neutrophil count, lymphocyte count, PLT, creatinine, prothrombin time, INR, and alpha-fetoprotein. Additional parameters included hepatitis B e-antigen status, HBV-DNA levels, and routine laboratory assessments. Radiological evaluations, including CT and MRI, were conducted every 3–6 months.

Construction of ANN

An ANN is a sophisticated computational system composed of a modular structure, featuring interconnected neuronal units. This architecture organizes units into three fundamental compartments: An input layer, an output layer, and one or more hidden layers[26,27]. These neurons are linked through weighted connections, which are adjusted during the learning process. ANNs offer advantages such as self-learning, self-adaptation, and inference capabilities. The learning process involves analyzing examples and adjusting connection weights to establish relationships between inputs and outputs. Input data flows through the network layers, producing an output. An error signal is generated if the output differs from the desired result. The backpropagation (BP) method uses this error to adjust connection weights to minimize overall network error. Through iterative adjustments, the error between predicted and desired outputs gradually decreases until reaching a minimum, indicating convergence of the network. After convergence, the ANN applies its trained knowledge to new input data, generating accurate predictions or outputs across various datasets[28-30].

In this study, the 5-year progression of PVT in HBC was analyzed using an ANN model. The input layer comprised 637 neurons that imported clinical, demographic, and laboratory data. The output layer comprised neurons that generated the corresponding predictive results. Hidden layers facilitated complex interactions between the input and output neurons. A novel ANN was meticulously designed to unravel the pivotal predictors of PVT in cirrhosis. Mathematica 11.1.1 for Microsoft Windows (64-bit), a powerful software platform designed specifically for the efficient and interactive construction of neural networks. The BP algorithm guided the learning process by calculating errors between predicted and desired outputs. Neuron connections were adjusted by modifying weights to minimize overall network errors. Learning was terminated when the sum of squared errors reached a minimum against the cross-validation dataset. The final model provided individualized PVT risk predictions over the years for each patient.

Statistical analysis

Quantitative variables that follow a normal distribution were expressed as the mean and SD, while those not following a normal distribution were presented as quartiles. As appropriate, continuous data were compared using either the Student's t-test (for normally distributed data) or the non-parametric Mann-Whitney U test (for non-normal distributions). Categorical variables were analyzed using either the χ²-distribution goodness-of-fit test (χ²-d) for ample sample sizes or Fisher's exact test. Variables showing statistically significant differences or clinical relevance were selected as input layers for constructing ANN models to predict PVT development over 3 and 5 years. Hazard ratios (HR) with 95%CI and P-values were reported. Discriminative prowess of models was systematically assessed through the computation of receiver operating characteristic (ROC) curves, which visually portrayed the trade-off between true positive and false positive rates. The diagnostic accuracy was quantified by calculating the area under the ROC curve (AUC), commonly referred to as Harrell's c-index, serving as a robust measure of predictive discriminatory power. The performance of the ANN model was compared to the MELD score using ROC curves[31,32]. MELD scores were calculated based on the established scoring formula. Calibration plots were employed to visually assess the agreement between predicted and observed probabilities of PVT over 3 and 5 years. Utilizing decision curve analysis (DCA), we conducted a comparative assessment of the clinical net benefits between the innovative ANN model and conventional methodologies. A stringent significance criterion of p < 0.05 was adopted to determine statistical relevance across all assessments. Data analyses were performed employing the software packages, specifically IBM SPSS Statistics, version 22 (IBM Corporation, Armonk, NY, United States), and the open-source environment R, release 3.3.2 (R Core Team, 2010).

RESULTS

Baseline characteristics

Between 2008 and 2016, a study involving 986 patients was conducted. A total of 685 patients admitted from January 2011 to December 2014 were assigned to the training cohort, while 301 patients admitted from January 2015 to December 2016 were assigned to the validation cohort. In the training cohort, the majority of participants were male (439, 69.0%), with a median age of 52.8 years (range: 40.0–74.0). In the validation cohort, 62.5% were male, with a median age of 52.9 years (43.0–75.0). No significant differences in baseline characteristics were observed between the two cohorts (Table 1). Within three years, 121 patients (19.0%) in the training group developed PVT, increasing to 151 patients (23.7%) within five years. In the validation group, 46 patients (16.7%) developed PVT within three years, and 66 patients (24.0%) within five years. The characteristics of the two cohorts were comparable, as detailed in Table 1.

Table 1 Basic clinical characteristics of patients with hepatitis B virus-related cirrhosis, n (%)/mean (25^th-75^th percentiles).

Variables	All patients (n = 912)	Training cohort (n = 637)	Validation cohort (n = 275)	P value
Age, years	53.0 (41.0-73.0)	52.8.0 (40.0-74.0)	52.9 (43.0-75.0)	0.436
Male sex	611 (67.0)	439 (69.0)	172 (62.5)	0.320
Smoking	210 (23.0)	149 (23.4)	61 (22.2)	0.846
Alcohol consumption	195(21.4)	123 (19.3)	62 (22.5)	0.579
Diabetes	152 (16.7)	103 (16.2)	49 (17.8)	0.174
Hypertension	129 (14.1)	95 (14.9)	34 (12.4)	0.835
Ascites	197 (21.6)	134 (21.0)	63 (22.9)	0.485
Encephalopathy	41 (4.5)	30 (4.7)	11 (4.0)	0.458
Gastrointestinal varices with bleeding	134 (14.7)	88 (13.8)	46 (16.7)	0.348
HBeAg positivity	365 (40.0)	253 (39.9)	112 (40.7)	0.115
CTP score	7.0 (5.0-10.0)	7.0 (6.0-9.0)	7.0 (5.0-10.0)	0.626
MELD score	10.1 (7.8-12.9)	10.1 (8.0-12.6)	10.1 (7.7-13.6)	0.851
Alanine aminotransferase (U/L)	41.3 (26.5-105.8)	43.6 (27.1-112.4)	37.5 (25.1-95.5)	0.164
Aspartate aminotransferase (U/L)	47.9 (30.8-106.1)	48.6 (32.1-107.9)	46.7 (29.7-98.1)	0.282
Total bilirubin (μmol/L)	22.4 (14.2-39.2)	22.7 (14.1-38.5)	22.3 (14.5-40.7)	0.805
Albumin (g/L)	33.6 (30.3-39.2)	33.8 (30.4-40.1)	33.2 (30.1-38.4)	0.258
Gamma-glutamyl transpeptidase (U/L)	56.3 (37.2-97.8)	55.3 (36.1-99.7)	57.3 (40.4-95.6)	0.497
White blood cell count (× 109/L)	3.9 (2.8-5.3)	3.9 (2.8-5.3)	3.8 (2.7-5.3)	0.451
Neutrophil count (× 109/L)	2.2 (1.5-3.1)	2.2 (1.5-3.2)	2.2 (1.5-3.0)	0.434
Lymphocyte count (× 109/L)	1.1 (0.8-1.6)	1.1 (0.8-1.6)	1.1 (0.7-1.6)	0.921
Neutrophil-lymphocyte ratio	2.0 (1.4-2.7)	2.0 (1.4-2.8)	1.9 (1.4-2.6)	0.598
Platelets (× 109/L)	87.0 (65.8-118.6)	87.0 (65.0-116.0)	89.0 (67.0-121.0)	0.199
Creatinine (μmol/L)	66.0 (56.0-76.0)	66.1 (56.1-76.2)	65.0 (56.0-73.9)	0.602
Blood urea nitrogen (mmol/L)	5.1 (4.0-6.7)	5.1 (4.0-6.7)	5.2 (4.1-6.7)	0.717
Prothrombin time (s)	14.3 (12.7-16.3)	14.3 (12.8-16.1)	14.1 (12.5-16.7)	0.801
Prothrombin activity (%)	67.0 (54.0-80.0)	67.0 (54.0-80.0)	67.0 (53.0-81.0)	0.944
International normalized ratio	1.2 (1.1-1.3)	1.2 (1.1-1.3)	1.2 (1.1-1.4)	0.865
Width of portal vein, mm	7.1 (3.4-30.1)	7.2 (3.4-30.5)	6.7 (3.3-26.0)	0.375
HBV DNA (log 10IU/mL)	2.7(1.2-5.9)	2.7(1.2-5.8)	2.7(1.2-6.0)	0.340
NA(s) ETV/TDF	614/298	421/216	193/82	0.783
3-year PVT	167(18.3)	121(19.0)	46(16.7)	0.202
5-year PVT	217(23.8)	151(23.7)	66(24.0)	0.172

MELD: Model for end-stage liver disease; CTP: Child-Turcotte-Pugh; ALT: Alanine aminotransferase; AST: Aspartate aminotransferase; TBIL: Total bilirubin; ALB: Albumin; WBC: White blood cells; NLR: Neutrophil–lymphocyte ratio; PLT: Platelet count; Cr: Creatinine; INR: International normalized ratio; NA(s): Nucleos(t)ide analogues; ETV: Entecavir; TDF: Tenofovir.

Construction of the ANN model

Table 2 shows the results of the Cox regression analysis, highlighting significant associations between various factors and PVT occurrence. Age (HR = 1.045, 95%CI: 1.029–1.061, P < 0.001), gastrointestinal varices with bleeding (HR = 0.767, 95%CI: 1.420–3.265, P < 0.001), ALT (HR = 0.998 95%CI: 0.996–0.999, P = 0.004), ALB (HR = 0.972, 95%CI: 0.947–0.997, P = 0.028), NLR (HR = 1.331, 95%CI: 1.262–1.403, P < 0.001), PLT (HR = 0.979, 95%CI: 0.972–0.985, P < 0.001), INR (HR = 1.749, 95%CI: 0.936–3.628, P = 0.008), and portal vein width (HR = 0.998, 95%CI: 0.996–1.000, P = 0.003) were all identified as significant predictors of PVT in the training group.

Table 2 Factors associated with prediction incidence of portal vein thrombosis.

Variables	Univariate analysis		P value
	β	HR (95%CI)
Age (year)	0.044	1.045 (1.029-1.061)	< 0.001
Sex (male)	0.267	1.306 (0.873-1.954)	0.194
Smoking	0.081	0.922 (0.605-1.405)	0.706
Alcohol consumption	0.161	1,175 (0.767-1.800)	0.458
Diabetes	0.255	1.291 (0.807-2.064)	0.287
Ascites	0.660	1.935 (1.354-2.766)	< 0.001
Hepatic encephalopathy	0.255	1.291 (0.807-2.064)	0.287
Gastrointestinal varices with bleeding	0.767	2.153 (1.420-3.265)	< 0.001
Alanine aminotransferase (U/L)	-0.002	0.998 (0.996-0.999)	0.004
Aspartate aminotransferase (U/L)	-0.002	0.998 (0.996-0.999)	0.323
Total bilirubin (mg/dL)	-0.003	0.997 (0.992-1.001)	0.114
Albumin (g/L)	-0.029	0.972 (0.947-0.997)	0.028
gamma-glutamyl transpeptidase (U/L)	0.001	1.001 (0.998-1.003)	0.637
White blood cell count (× 109/L)	-0.007	0.993 (0.913-1.079)	0.861
NLR	0.286	1.331 (1.262-1.403)	< 0.001
Platelets (× 109/L)	-0.022	0.979 (0.972-0.985)	< 0.001
Creatinine (μmol/L)	0.001	1.001 (0.995-1.007)	0.758
International normalized ratio	0.559	1.749 (0.936-3.268)	0.080
Width of portal vein	-0.002	0.998 (0.996-1.000)	0.063
HBeAg positivity	0.726	1.242 (0.681–2.267)	0.487
HBV DNA (log 10IU/mL)	0.828	1.237 (0.677–2.244)	0.567
NA(s) ETV/TDF	0.925	1.245 (0.755–1.956)	0.789

ALT: Alanine aminotransferase; AST: Aspartate aminotransferase; TBIL: Total bilirubin; ALB: Albumin; WBC: White blood cells; HBeAg: Hepatitis B e-antigen; NLR: Neutrophil–lymphocyte ratio; PLT: Platelet count; Cr: Creatinine; INR: International normalized ratio; NA(s): Nucleos(t)ide analogues; ETV: Entecavir; TDF: Tenofovir.

The identified factors were incorporated into the construction of an ANN model, available at https://Lixuan.me/annmodel/myg-v4/. The ANN deployed a sophisticated architecture known as a Multi-Layer Perceptron (MLP). This network was composed of three fundamental layers: An input layer, an intermediate hidden layer, and an output layer. The input layer served as a bridge, taking clinical and biochemical parameters as input variables, reflecting patient characteristics. The hidden layer, characterized by its non-linear processing capabilities, extracted intricate features from these inputs. Finally, the output layer delivered precise predictions for the prognosis, effectively translating the processed information into actionable insights[25]. The predictive model for 3- and 5-year PVT risk in cirrhotics is available at https://houyixin.math.ink/PVTR/index.html. Employing a deep-learning architecture, the model featured weighted synapses connecting 8 input and 2 output neurons. Four intricately designed hidden layers were systematically integrated post-thorough debugging and optimization, significantly boosting the multilayer perceptron's (MLP) predictive prowess (Figure 2).

Figure 2 Artificial neural network model page design according to different conditions of patients. INR: International normalized ratio; NLR: Neutrophil–lymphocyte ratio; PLT: platelet count; ALB: Albumin; ALT: Alanine aminotransferase.

Application of the ANN model for risk stratification

Patient information was input into the ANN model to estimate the 3- to 5-year risk of developing PVT, allowing for risk classification into high- and low-risk groups. In the training cohort, the incidence of PVT was significantly higher in the high-risk group compared to the low-risk group (P < 0.0001) (Figure 3A-B). Similarly, in the validation cohort, a marked difference in PVT incidence was observed between the two groups (P < 0.0001) (Figure 3C-D). The ANN model effectively distinguished patients based on their risk levels in training and validation cohorts. For the validation cohort, the positive predictive value (PPV) for low-risk classification was 26.2% (95%CI: 25.0–27.4), with a negative predictive value (NPV) of 98.7% (95%CI: 95.2–99.7). For high-risk classification, the PPV was 54.7% (95%CI: 48.6–60.7), and the NPV was 91.6% (95%CI: 89.4–93.4). In another subset of the validation cohort, the PPV for low-risk classification was 20.9% (95%CI: 19.6–22.2), with an NPV of 100% (no events observed). For high-risk classification, the PPV was 41.5% (95%CI: 32.8–50.8), and the NPV was 91.9% (95%CI: 88.6–94.3) (Table 3).

Figure 3 According to the artificial neural network model, the patient training and validation sets are divided into two risk layers as follows: High and low through Kaplan–Meier method. A: The Kaplan–Meier (KM) curve for the risk of the occurrence of portal vein thrombosis (PVT) through the artificial neural network (ANN) model within three years in the training group; B: The KM curve for the risk of the occurrence of PVT through the ANN model within five years in the training group; C: The KM curve for the risk of the occurrence of PVT through the ANN model within three years in the validation group; D: The KM curve for the risk of the occurrence of PVT through the ANN model within five years in the validation group.

Table 3 Positive predictive and negative predictive values, 95%CI.

Cohort	Models	3-year risk of PVT		5-year risk of PVT
		Positive (%)	Negative (%)	Positive (%)	Negative (%)
Training cohort	ANN (low risk)	26.2 (25.0-27.4)	98.7 (95.2-99.7)	23.2 (21.0-28.4)	97.7 (95.2-99.7)
	ANN (high risk)	54.7 (48.6-60.7)	98.6 (89.4-99.4)	52.7 (49.6-60.7)	98.6 (88.4-99.5)
Validation cohort	ANN (low risk)	20.9 (19.6-22.2)	100 (-)	19.9 (19.6-24.2)	97.9 (89.6-98.3)
	ANN (high risk)	41.5 (32.8-50.8)	91.9 (88.6-94.3)	31.5 (28.8-51.8)	98.9 (88.6-99.3)

PVT: Portal vein thrombosis; ANN: Artificial neural network.

Comparison of ANN model with CTP and MELD scores

In the training cohort, the ANN model achieved outstanding performance in predicting PVT occurrence over 3 and 5 years, with area under the receiver operating characteristic curve (AUROC) values of 0.967 (95%CI: 0.960–0.974) and 0.975 (95%CI: 0.955–0.992), respectively, and corresponding C-index values of 0.954 and 0.958 (Table 4). These results demonstrated significantly superior predictive accuracy compared to the MELD and CTP models (P < 0.001). Similarly, in the validation cohort, the ANN model maintained excellent predictive capability for PVT over 3 and 5 years, with AUROC values of 0.958 (95%CI: 0.944–0.973) and 0.973 (95%CI: 0.958–0.987), respectively, and C-index values of 0.941 and 0.948 (Table 4). The predictive performance of the ANN model was significantly better than that of the MELD and CTP models (P < 0.001) (Table 4).

Table 4 Comparison of performance and discriminative ability among the current model and other models, 95%CI.

Cohort	Models	3-year risk of PVT			5-year risk of PVT
		AUROC	C-index	P value	AUROC	C-index	P value
Training cohort	ANN	0.967 (0.960-0.974)	0.954		0.975 (0.955–0.992)	0.958
	CTP	0.593 (0.568-0.618)	0.591	< 0.001	0.602 (0.579-0.625)	0.592	< 0.001
	MELD	0.530 (0.550-0.560)	0.535	< 0.001	0.555 (0.528-0.581)	0.544	< 0.001
Validation cohort	ANN	0.958 (0.944–0.973)	0.941		0.973 (0.958–0.987)
	CTP	0.541 (0.497-0.585)	0.552	< 0.001	0.547 (0.508-0.585)	0.541	< 0.001
	MELD	0.539 (0.492-0.586)	0.544	< 0.001	0.553 (0.512-0.594)	0.546	< 0.001

PVT: Portal vein thrombosis; AUROC: Area under the receiver operating characteristic curve; CTP: Child-Pugh-Turcotte; MELD: Model for end-stage liver disease; ANN: Artificial neural network.

Discrimination and calibration of the ANN model

DCA further demonstrated the superior performance of the ANN model compared to the MELD and CTP models in both the training (Figure 4A and B) and validation cohorts (Figure 4C and D). Calibration curves further confirmed the strong agreement between the predicted probability of being PVT-free and the observed probability over 3 and 5 years in both the training (Figure 5A and B) and validation cohorts (Figure 5C and D). These results highlight the clinical practicability and reliability of the ANN model, making it a more effective tool for predicting PVT risk than the MELD and CTP models.

Figure 4 Predicted vs observed cumulative incidence of portal vein thrombosis based on the predictive model. A: The decision curve analysis (DCA) curve comparing the artificial neural network (ANN) model with other models for predicting the occurrence of portal vein thrombosis (PVT) within three years in the training group; B: The DCA curve comparing the ANN model with other models for predicting the occurrence of PVT within five years in the training group; C: The DCA curve comparing the ANN model with other models for predicting the occurrence of PVT within three years in the validation group; D: The DCA curve comparing the ANN model with other models for predicting the occurrence of PVT within five years in the validation group.

Figure 5 The cumulative probabilities of portal vein thrombosis of our model at 3/5 years in the training and validation data sets. A: The cumulative curve for predicting the occurrence of portal vein thrombosis (PVT) using the artificial neural network (ANN) model within three years in the training group; B: The cumulative curve for predicting the occurrence of PVT using the ANN model within five years in the training group; C: The cumulative curve for predicting the occurrence of PVT using the ANN model within three years in the validation group; D: The cumulative curve for predicting the occurrence of PVT using the ANN model within five years in the validation group.

DISCUSSION

Our research identifies several factors closely associated with PVT development, including gastrointestinal varices with bleeding, ALB levels, PLT levels, INR, and portal vein width. Previous studies have similarly suggested that decompensation and low PLT are significant risk factors for PVT[33]. However, some controversy exists regarding the reproducibility of portal vein width as a predictive factor for PVT development[34]. In clinical practice, common biochemical indicators, the presence of esophageal-gastric variceal bleeding, and abdominal ultrasound findings are sufficient to evaluate a patient's 3-year and 5-year PVT risk using our online platform. These readily available indicators facilitate risk assessment, particularly in regions with limited healthcare resources, allowing for the identification of high-risk populations and the efficient allocation of medical resources.

The ANN model demonstrated exceptional performance in predicting the occurrence of PVT at 3 and 5 years, as reflected by a significantly high AUC of 0.956 in both training and calibration curves. In comparison, conventional models such as MELD and CTP exhibited lower AUC, indicating the better predictive ability of the ANN model, particularly in cirrhosis patients. ANN models are able to learn from data and optimize prediction accuracy by iteratively adjusting the connections among variables. Unlike traditional logistic or Cox regression models, ANN models are non-linear, allowing them to train factors relevant to the outcome through repeated iterations. This non-linear framework enables ANN models to achieve higher prediction accuracy[35,36].

The study had some limitations which should be acknowledged. First, the retrospective design introduces potential selection bias. Key indicators, such as portal vein blood flow velocity, splenic vein diameter, spleen thickness, and thromboelastographic parameters, were incomplete in the dataset. Incorporating these variables in future studies could further enhance the accuracy of the prediction model. Prospective studies that systematically collect these indicators at admission are necessary to address this limitation. Second, baseline data for an external validation group were unavailable for comparison, highlighting the need for additional studies to validate the model externally. Despite these limitations, the deep neural network model demonstrated robust predictive capability for PVT in patients with cirrhosis.

This model provides a user-friendly and easily implementable tool for clinical use. Regular evaluation of relevant indicators during the management of cirrhosis patients is essential. This approach enables the early identification of high-risk PVT patients and supports timely clinical decision-making to improve patient prognosis.

CONCLUSION

We utilized an ANN model to develop a predictive tool for estimating the 3- and 5-year risk of PVT in patients with HBC. The ANN model exhibited excellent performance in individualized risk prediction, providing a valuable tool for assessing PVT risk in clinical practice and facilitating improved management of patients with HBC.

ACKNOWLEDGEMENTS

We gratefully recognize the patients who participated in this study. We thank for Li-Hua Yu helping with the data collection.