Development of a noninvasive ultrasound-based model for predicting high-risk esophageal varices in hepatitis-related cirrhosis

Abstract

Purpose

High-risk esophageal varices (HREVs) are a serious complication of cirrhosis, and reliable noninvasive tools are needed to improve endoscopic triage. This study aimed to develop and validate an ultrasound-based model for predicting HREVs in patients with hepatitis-related cirrhosis.

Methods

This retrospective study included 293 patients who underwent endoscopy and noninvasive assessment between January 2019 and January 2023. Patients were assigned to training (n=210) and validation cohorts (n=83). Predictors were selected using univariable analysis, multivariable logistic regression, and Akaike information criterion–based backward selection. Discrimination, calibration, and clinical utility were evaluated using receiver operating characteristic analysis, calibration curves, decision curve analysis, and clinical impact curves.

Results

Portal vein velocity (PVV) and spleen volume (SV) were retained in the final model. The model incorporated PVV as a linear term and SV as a restricted cubic spline term. The area under the receiver operating characteristic curve was 0.951 in the training cohort and 0.956 in the validation cohort. At a cutoff of 0.30, the model showed high diagnostic performance and outperformed the single predictors and the Baveno VI criteria. Calibration and decision curve analyses indicated good agreement and favorable clinical utility.

Conclusion

This model provides a simple, noninvasive approach to individualized prediction of HREVs in patients with hepatitis-related cirrhosis.

Graphical abstract

Introduction

Cirrhosis represents the end stage of chronic liver disease and remains a major global health burden, accounting for approximately 1.43 million deaths annually worldwide [1]. Portal hypertension is one of the most important complications of cirrhosis and drives the development of esophageal varices, which may progress to high-risk esophageal varices (HREVs) and cause life-threatening hemorrhage. Timely identification of HREVs is therefore essential for prophylactic management [2,3]. Although upper gastrointestinal endoscopy remains the reference standard for variceal assessment, its invasiveness, resource requirements, and limited tolerability underscore the need for reliable noninvasive approaches to improve endoscopic triage [3,4].

Current noninvasive strategies, which are largely based on liver stiffness measurement (LSM), platelet count (PLT), and related rule-out criteria, may perform suboptimally in some patients, particularly those with heterogeneous hemodynamic profiles or conditions that independently affect PLT levels [5–7]. Several recent studies have evaluated spleen-related markers as indicators of portal hypertension [8–12]. Spleen stiffness measurement (SSM), spleen volume (SV), and splenic or portal hemodynamic parameters may reflect the downstream consequences of sustained portal hypertension more directly than liver-based surrogates alone [8,10,13–18]. From a pathophysiological perspective, variceal formation is determined not only by intrahepatic fibrosis, but also by altered portal venous flow and progressive splenic and splanchnic remodeling [19,20]. Thus, integrating hemodynamic and spleen-related information may provide a more comprehensive noninvasive approach for predicting HREVs [21,22].

In this retrospective study, we developed and temporally validated a noninvasive model for predicting HREVs in patients with hepatitis-related cirrhosis. We also assessed its diagnostic performance, calibration, and clinical utility; compared it with the Baveno VI criteria; and implemented the model as an open-access web calculator to support individualized risk estimation in clinical practice.

Materials and Methods

Compliance with Ethical Standards

This study was approved by the institutional ethics committee of Yantai Qishan Hospital (approval number: 202518). The requirement for written informed consent was waived because of the retrospective nature of the study.

Patient Selection

This retrospective, single-center study was conducted at Yantai Qishan Hospital. Consecutive patients with hepatitis-related cirrhosis who underwent upper gastrointestinal endoscopy and noninvasive evaluation for portal hypertension between January 2019 and January 2023 were screened for eligibility. A total of 293 eligible patients were included. According to the calendar period of enrollment, 210 patients evaluated from January 2019 to January 2021 were assigned to the training cohort, and 83 patients evaluated from February 2021 to January 2023 were assigned to the validation cohort.

Patients were eligible if they met all of the following criteria: (1) age ≥18 years; (2) hepatitis-related cirrhosis diagnosed on the basis of clinical manifestations, laboratory findings, and imaging results [23]; (3) invasive and noninvasive examinations performed within 2 weeks of each other; (4) complete baseline clinical, laboratory, and imaging data; and (5) receipt of antiviral therapy with controlled viral replication during the assessment period. Controlled viral replication was documented using virus-specific markers: suppressed or undetectable hepatitis B virus (HBV) DNA in patients with HBV infection and undetectable hepatitis C virus (HCV) RNA in patients with HCV infection, with sustained virological response documented where applicable. Patients were excluded if they had any of the following: (1) previous variceal bleeding or previous endoscopic, surgical, or interventional treatment for portal hypertension; (2) current use of therapies that might affect variceal status or hemodynamic assessment, including primary prophylaxis, anticoagulant therapy, or antiplatelet therapy; (3) portal vein thrombosis, congestive hepatopathy, or other diseases related to hepatic venous congestion; (4) splenectomy, transjugular intrahepatic portosystemic shunt, hepatocellular carcinoma, or other malignancy; or (5) incomplete or poor-quality ultrasound, elastography, or endoscopic data.

Outcome Definition

The primary outcome was HREVs. Upper gastrointestinal endoscopy was performed by two experienced gastroenterologists, each with more than 10 years of endoscopic practice. Endoscopic findings were classified according to variceal size and the presence of red wale markings. HREVs were defined as medium- or large-sized esophageal varices, or small esophageal varices with red-color signs. Low-risk esophageal varices (LREVs) were defined as small varices without red-color signs [24].

Clinical and Laboratory Data Collection

Two clinicians who were blinded to the imaging and endoscopic findings extracted demographic characteristics, clinical data, and serum biomarker data from the electronic medical record system. Baseline demographic and clinical variables included age, sex, and cirrhosis etiology. Laboratory variables included PLT, aspartate aminotransferase (AST), alanine aminotransferase (ALT), albumin (ALB), total bilirubin (TB), and international normalized ratio (INR). Child-Pugh class and Model for End-Stage Liver Disease (MELD) score were calculated using baseline clinical and laboratory data. All clinical and laboratory data were obtained within 1 week of the initial endoscopic examination.

Antiviral treatment history and virological status were obtained from the medical records. Patients with HBV infection had received nucleos(t)ide analogue therapy, including entecavir 0.5 mg once daily, tenofovir disoproxil fumarate 300 mg once daily, or tenofovir alafenamide 25 mg once daily, according to routine clinical practice and patient-specific conditions. Patients with HCV infection had received direct-acting antiviral therapy, including sofosbuvir/velpatasvir 400/100 mg once daily for 12 weeks or glecaprevir/pibrentasvir 300/120 mg once daily for 8 weeks where applicable.

Ultrasound and Elastography Assessment

Conventional ultrasound and Doppler examinations were performed using the Philips EPIQ 5 System (Philips Ultrasound LLC, Bothell, WA, USA) by experienced operators according to routine institutional protocols. Ultrasound-derived variables included portal vein diameter (PVD), splenic vein diameter (SVD), portal vein velocity (PVV), splenic vein velocity (SVV), and SV. LSM and SSM were obtained by transient elastography using the Echosens FibroScan 530 Compact device (Echosens, Paris, France) according to the manufacturer’s instructions. During Doppler assessment, patients were examined in the supine position and instructed to breathe quietly. PVV and SVV were measured using spectral Doppler ultrasound after color Doppler localization. The sampling gate was placed at the center of the vessel lumen and adjusted to avoid inclusion of the vessel wall. Doppler angle correction was applied when necessary, with the insonation angle kept at ≤60° whenever possible. Velocities were recorded at the end of quiet expiration using stable waveforms obtained over several seconds. For each ultrasound parameter, three consecutive measurements were obtained, and the average value was used for analysis. SV was estimated using the standard prolate ellipsoid formula: SV=length×width×thickness×0.523 [25–27]. All ultrasound measurements were reviewed by two physicians with associate senior or higher professional titles. Any uncertainty regarding image quality or measurement validity was resolved through joint review.

Model Development

Potential predictors of HREVs were first screened using univariable analyses. Variables that were statistically significant in univariable analysis were then entered into a multivariable logistic regression model. Backward selection based on the Akaike information criterion (AIC) was applied within the conventional logistic regression framework to identify the final candidate predictors. PVV and SV were retained for subsequent model specification.

To account for potential nonlinearity in continuous predictors, three models were compared: a linear model including PVV and SV as linear terms, a full restricted cubic spline (RCS) model including RCS terms for both variables, and a mixed model including PVV as a linear term and SV as an RCS term. The final model was selected primarily on the basis of AIC and parsimony, with other performance measures considered supportive. The mixed model was selected as the final model and is hereafter referred to as the mixed PVV-SV (MPS) model, where “M” refers to the mixed specification of linear and spline terms, “P” refers to PVV, and “S” refers to SV. To facilitate individualized risk estimation in clinical practice, the MPS model was implemented as an open-access web calculator using the MPS model coefficients and spline terms.

Statistical Analysis

Statistical analyses were performed using R software version 4.4.3 (R Foundation for Statistical Computing, Vienna, Austria). Continuous variables are presented as the mean±standard deviation or median (interquartile range), as appropriate for the data distribution. The normality of continuous variables was assessed using the Shapiro-Wilk test. Categorical variables are presented as number (%). Between-group comparisons were performed using the independent-samples t-test for normally distributed continuous variables, the Mann-Whitney U test for nonnormally distributed continuous variables, and the chi-square test or Fisher’s exact test for categorical variables, as appropriate.

Model performance was evaluated in terms of discrimination, calibration, and clinical utility. Discrimination was assessed using receiver operating characteristic (ROC) curve analysis and the area under the ROC curve (AUC) with 95% confidence intervals (CIs). The optimal cutoff value for the MPS model and single predictors was determined in the training cohort using the Youden index, and the corresponding cutoff was then applied to the validation cohort. Candidate probability thresholds were also evaluated in the training cohort to identify a rule-out threshold that prioritized high sensitivity, approximately 95%, and negative predictive value (NPV), with a low missed-HREVs rate, as well as a rule-in threshold that prioritized high specificity, approximately 90%, and positive predictive value (PPV). Among thresholds meeting these prespecified criteria, the rule-out threshold was selected by maximizing specificity, whereas the rule-in threshold was selected by maximizing sensitivity. These thresholds were then applied unchanged to the validation cohort for evaluation. The spared endoscopy rate and missed-HREVs rate were also calculated. Diagnostic performance was summarized using sensitivity, specificity, PPV, NPV, and accuracy. Calibration was evaluated using calibration curves generated with 1,000 bootstrap resamples to assess agreement between predicted probabilities and observed outcomes. Clinical utility was assessed by decision curve analysis (DCA), which quantified the net benefit of the model across a range of threshold probabilities. Clinical impact curve (CIC) analysis was also performed to evaluate the potential clinical applicability of the model. The CIC was plotted based on the predicted probabilities in the training and validation cohorts and showed the estimated number of individuals classified as high risk and the number of true-positive cases at each threshold probability. These performance measures were evaluated in both the training and validation cohorts. The MPS model was also compared with established Baveno-based rule-out strategies. The Baveno VI criteria were defined as LSM <20 kPa and PLT count >150×10⁹/L for avoiding screening endoscopy [7]. For the Baveno VII SSM-based strategy, SSM ≤40 kPa by transient elastography was used as an additional criterion to identify patients with a low probability of HREVs among those who did not meet the Baveno VI criteria [4]. The spared endoscopy rate and missed-HREVs rate were calculated for each strategy. All tests were two-sided, and P<0.05 was considered statistically significant.

Results

Baseline Characteristics

The training cohort included 210 patients, of whom 138 had LREVs and 72 had HREVs. Compared with patients with LREVs, those with HREVs had significantly lower PLT counts, ALB levels, and PVV, but significantly higher PVD, SVD, LSM, SSM, SV, and MELD scores. In contrast, age, sex, etiology, AST, ALT, TB, INR, SVV, Child-Pugh class, and antiviral regimen did not differ significantly between the two groups (Table 1).

Table 1.

Baseline clinical characteristics of patients with LREVs and HREVs in the training cohort

Parameter	Patients with LREVs (n=138)	Patients with HREVs (n=72)	Test statistic	P-value
Age (year)a)	54 (12)	55.5 (19)	–1.638b)	0.102
Sex
Male	102 (73.9)	45 (62.5)	2.935c)	0.087
Female	36 (26.1)	27 (37.5)
Etiology			1.660c)	0.198
HBV	122 (88.4)	59 (81.9)
HCV	16 (11.6)	13 (18.1)
PLT (×109/L)a)	124 (65)	66 (40)	–8.676b)	<0.001
AST (U/L)	34.2±10.20	34.8±8.97	–0.416d)	0.678
ALT (U/L)	31.1±7.46	30.3±7.51	0.713d)	0.477
ALB (g/L)	32.0±2.64	31.2±2.52	2.058d)	0.041
TB (μmol/L)a)	21.7 (5.8)	24.9 (6.0)	–1.852b)	0.064
INR	1.24±0.12	1.26±0.08	–1.754d)	0.081
PVD (mm)	11.8±1.41	13.0±1.67	–5.435d)	<0.001
SVD (mm)	11.0±1.51	12.3±1.67	–5.452d)	<0.001
PVV (cm/s)	15.7±2.6	13.0±4.0	–8.424d)	<0.001
SVV (cm/s)	15.4±3.92	14.4±4.07	1.746d)	0.082
LSM (kPa)	17.9±2.83	19.6±3.01	–4.112d)	<0.001
SSM (kPa)	37.9±5.38	41.1±4.57	–4.264d)	<0.001
SV (cm3)	356.2±176.8	616.2±270.0	–9.180d)	<0.001
MELD scorea)	9.77 (2)	10.25 (2)	–2.385b)	0.017
Child-Pugh			3.117c)	0.210
A	62 (44.9)	24 (33.3)
B	58 (42.0)	34 (47.2)
C	18 (13.0)	14 (19.4)
Antiviral regimene)			5.210c)	0.266
ETV	33 (23.9)	19 (26.4)
TDF	53 (38.4)	30 (41.7)
TAF	36 (26.1)	10 (13.9)
SOF/VEL	9 (6.5)	6 (8.3)
GLE/PIB	7 (5.1)	7 (9.7)

Values are presented as number (%) or mean±standard deviation unless otherwise indicated.

LREVs, low-risk esophageal varices; HREVs, high-risk esophageal varices; HBV, hepatitis B virus; HCV, hepatitis C virus; PLT, platelet; AST, aspartate aminotransferase; ALT, alanine aminotransferase; ALB, albumin; TB, total bilirubin; INR, international normalized ratio; PVD, portal vein diameter; SVD, splenic vein diameter; PVV, portal vein velocity; SVV, splenic vein velocity; LSM, liver stiffness measurement; SSM, spleen stiffness measurement; SV, spleen volume; MELD, Model for End-Stage Liver Disease; ETV, entecavir; TDF, tenofovir disoproxil fumarate; TAF, tenofovir alafenamide; SOF/VEL, sofosbuvir/velpatasvir; GLE/PIB, glecaprevir/pibrentasvir; IQR, interquartile range.

^a)Median (IQR). ^b)Mann-Whitney U test. ^c)Chi-square test. ^d)Independent sample t-test. ^e)All included patients received antiviral therapy and had controlled viral replication during the assessment period.

Candidate Predictor Selection

Potential predictors of HREVs were first screened using univariable analyses, followed by multivariable logistic regression and AIC-based backward selection. In the initial multivariable model, PVV and SV remained significantly associated with HREVs. After backward AIC selection, PVV and SV were retained as the final candidate predictors: PVV showed an inverse association with HREVs, whereas SV showed a positive association (Table 2).

Table 2.

Candidate predictor selection using multivariable logistic regression and backward AIC

Predictor	Initial multivariable model			AIC-selected candidate model
	β	OR (95% CI)	P-value	β	OR (95% CI)	P-value
PLT (×109/L)	–0.006	0.994 (0.972–1.016)	0.586	-	-	-
ALB (g/L)	–0.043	0.958 (0.796–1.152)	0.646	-	-	-
PVD (mm)	–0.136	0.873 (0.627–1.216)	0.421	-	-	-
SVD (mm)	0.213	1.237 (0.888–1.725)	0.209	-	-	-
PVV (cm/s)	–0.928	0.395 (0.270–0.579)	<0.001	–0.820	0.440 (0.320–0.606)	<0.001
LSM (kPa)	0.152	1.164 (0.986–1.374)	0.073	-	-	-
SSM (kPa)	0.039	1.040 (0.945–1.144)	0.424	-	-	-
SV (cm3)	0.007	1.007 (1.002–1.011)	0.003	0.009	1.009 (1.006–1.012)	<0.001
MELD score	0.183	1.201 (0.788–1.830)	0.394	-	-	-

AIC, Akaike information criterion; OR, odds ratio; CI, confidence interval; PLT, platelet; ALB, albumin; PVD, portal vein diameter; SVD, splenic vein diameter; PVV, portal vein velocity; LSM, liver stiffness measurement; SSM, spleen stiffness measurement; SV, spleen volume; MELD, Model for End-stage Liver Disease.

Model Development

Three models were compared: a linear model, an RCS model, and a mixed model, defined as the MPS model. The linear model performed worst, with the highest AIC and lower discrimination. In the RCS model, the nonlinear effect of SV was statistically significant (P for nonlinearity=0.002), whereas that of PVV was not (P for nonlinearity=0.159). Effect plots further indicated an approximately linear association between PVV and HREVs, whereas SV showed a nonlinear association with HREVs (Fig. 1A). The RCS model had the lowest AIC (120.89), and the MPS model had a very similar AIC (120.99). The two spline-based models yielded identical C indices (0.951) and Brier scores (0.087). Given the absence of significant nonlinearity for PVV, the significant nonlinear effect of SV, and the greater parsimony of the MPS model, the MPS model was selected as the final model (Table 3).

Fig. 1. Nonlinear associations and discriminative performance of the mixed portal vein velocity (PVV)–spleen volume (SV) (MPS) model.

A. Effect plots show the associations of PVV and SV with high-risk esophageal varices (HREVs). The shaded areas represent 95% confidence intervals, and the rug plots indicate the distribution of observations. For SV, vertical dashed lines indicate the knots used in the restricted cubic spline model. B. Receiver operating characteristic (ROC) curves of the MPS model in the training and validation cohorts are compared with PVV and SV alone. AUC, area under the receiver operating characteristic curve.

Table 3.

Comparison of the linear, MPS, and full restricted cubic spline models for predicting high-risk esophageal varices

Model	Predictor	d.f.	LR χ²	AIC	C index	Brier score
Linear model	PVV+SV	2	144.11	131.91	0.942	0.098
RCS model	rcs(PVV,3)+rcs(SV,3)	4	159.14	120.89	0.951	0.087
MPS model	PVV+rcs(SV, 3)	3	157.03	120.99	0.951	0.087

MPS, mixed portal vein velocity–spleen volume; d.f., degrees of freedom; LR χ², likelihood ratio chi-square; AIC, Akaike information criterion; C index, concordance index; PVV, portal vein velocity; SV, spleen volume; RCS, restricted cubic splines.

Diagnostic Performance of the MPS Model

The MPS model demonstrated excellent discriminative performance in both the training and validation cohorts. In the training cohort, the model achieved an AUC of 0.951 (95% CI, 0.926 to 0.977) at a cutoff value of 0.30, with a sensitivity of 95.8%, specificity of 84.8%, PPV of 76.7%, NPV of 97.5%, and accuracy of 88.6%. In the validation cohort, the model achieved an AUC of 0.956 (95% CI, 0.917 to 0.995) at the same cutoff, with corresponding values of 96.2%, 87.7%, 78.1%, 98.0%, and 90.4%, respectively. Compared with the single predictors, the MPS model consistently showed superior discrimination. In the training cohort, the AUCs of PVV and SV were 0.855 (95% CI, 0.803 to 0.907) and 0.886 (95% CI, 0.844 to 0.929), respectively. In the validation cohort, the corresponding AUCs were 0.885 (95% CI, 0.816 to 0.954) and 0.895 (95% CI, 0.829 to 0.960), respectively, and were lower than those of the MPS model (Table 4, Fig. 1B).

Table 4.

Diagnostic performance of the MPS model and single predictors in the training and validation cohorts

Predictor	AUC (95% CI)	Cutoff value	Sensitivity (%)	Specificity (%)	PPV (%)	NPV (%)	Accuracy (%)
Training cohort (n=210)
PVV	0.855 (0.803–0.907)	13.5	61.1	91.3	78.6	81.8	81.0
SV	0.886 (0.844–0.929)	461.8	91.7	78.3	68.8	94.7	82.9
MPS model	0.951 (0.926–0.977)	0.30	95.8	84.8	76.7	97.5	88.6
Validation cohort (n=83)
PVV	0.885 (0.816–0.954)	13.5	42.3	96.5	84.6	78.6	79.5
SV	0.895 (0.829–0.960)	461.8	100.0	64.9	56.5	100.0	75.9
MPS model	0.956 (0.917–0.995)	0.30	96.2	87.7	78.1	98.0	90.4

MPS, mixed portal vein velocity–spleen volume; AUC, area under the receiver operating characteristic curve; CI, confidence interval; PPV, positive predictive value; NPV, negative predictive value; PVV, portal vein velocity; SV, spleen volume.

Additional threshold-based analyses were performed to improve the clinical interpretability of the MPS model and compare its rule-out performance with established Baveno-based strategies (Table 5). A probability threshold of 0.291 was identified as the clinically applicable rule-out cutoff, and a threshold of 0.489 was identified as the rule-in cutoff. The MPS rule-out threshold achieved high sensitivity and NPV in the training cohort (95.8% and 97.5%, respectively) and validation cohort (96.2% and 98.0%, respectively), with low missed-HREVs rates of 2.5% and 2.0%, respectively. The MPS rule-in threshold showed high specificity in both cohorts, with values of 90.6% in the training cohort and 89.5% in the validation cohort.

Table 5.

Clinical threshold performance of the MPS model and comparison with Baveno VI and Baveno VII rule-out strategies

Cohort	Strategy	Threshold	Sensitivity (%)	Specificity (%)	PPV (%)	NPV (%)	Accuracy (%)	Endoscopy sparing rate (%)	Missed-HREVs rate (%)
Training cohort	MPS rule-out	0.291	95.8	84.8	76.7	97.5	88.6	57.1	2.5
	MPS rule-in	0.489	81.9	90.6	81.9	90.6	87.6	-	-
	Baveno VIa)	-	100.0	21.0	39.8	100.0	48.1	13.8	0
	Baveno VIIb)	-	58.3	73.9	53.8	77.3	68.6	62.9	22.7
Validation cohort	MPS rule-out	0.291	96.2	87.7	78.1	98.0	90.4	61.4	2.0
	MPS rule-in	0.489	88.5	89.5	79.3	94.4	89.2	-	-
	Baveno VIa)	-	100.0	22.8	37.1	100.0	47.0	15.7	0.0
	Baveno VIIb)	-	50.0	77.2	50.0	77.2	68.7	68.7	22.8

MPS, mixed portal vein velocity–spleen volume; PPV, positive predictive value; NPV, negative predictive value; HREVs, high-risk esophageal varices; LSM, liver stiffness measurement; SSM, spleen stiffness measurement; PLT, platelet count.

^a)Baveno VI was defined as LSM <20 kPa and PLT >150×10⁹/L. ^b)Baveno VII refers to the SSM-based Baveno VII strategy, in which patients meeting the Baveno VI criteria or, among those not meeting the Baveno VI criteria, having SSM ≤40 kPa were considered to have a low probability of HREVs.

In the exploratory comparison of rule-out strategies, Baveno VI showed excellent safety, with 100.0% sensitivity, 100.0% NPV, and a 0.0% missed-HREVs rate in both cohorts. However, it spared only 13.8% and 15.7% of endoscopies in the training and validation cohorts, respectively. Baveno VII spared more endoscopies, with rates of 62.9% and 68.7%, respectively, but had higher missed-HREVs rates of 22.7% and 22.8%, respectively. By contrast, the MPS rule-out threshold provided a more balanced performance, with low missed-HREVs rates of 2.5% and 2.0% while sparing 57.1% and 61.4% of endoscopies in the training and validation cohorts, respectively (Table 5).

Calibration Performance and Clinical Utility

Calibration curves showed good agreement between predicted and observed probabilities in both cohorts (Fig. 2A, B). DCA further demonstrated that the model provided favorable net benefit across a clinically relevant range of threshold probabilities in both cohorts, supporting its potential clinical utility (Fig. 2C, D). Clinical impact curves showed that the number of patients classified as high risk approached the number of true-positive cases at higher threshold probabilities, further supporting the clinical applicability of the model (Fig. 3).

Fig. 2. Calibration performance and clinical utility of the mixed portal vein velocity–spleen volume (MPS) model.

A, B. Calibration curves of the MPS model in the training cohort and validation cohort are shown, respectively. The dashed gray line represents perfect calibration, the dotted black line represents the apparent calibration curve, and the solid blue line represents the bias-corrected calibration curve obtained by bootstrap resampling. C, D. Decision curve analysis (DCA) of the MPS model in the training cohort and validation cohort is shown, respectively. The model was compared with the treat-all and treat-none strategies across a range of threshold probabilities.

Fig. 3. Clinical impact curves (CICs) of the mixed portal vein velocity–spleen volume model in the training cohort (A) and validation cohort (B).

The blue line represents the number of patients classified as high risk by the model at each threshold probability, whereas the red line represents the number of true-positive patients with high-risk esophageal varices. The results are expressed as the number of patients per 1,000 individuals.

Code Availability Statement

To improve clinical applicability and reproducibility, an open-access web calculator was developed based on the MPS model. The calculator is publicly available at https://hrevscalculator.github.io/hrevs-predictor/, and an archived version with source files has been deposited in Zenodo (https://doi.org/10.5281/zenodo.20177670).

Discussion

In this retrospective study, we developed and validated a noninvasive model for identifying HREVs in patients with hepatitis-related cirrhosis. The MPS model incorporated PVV as a linear term and SV as an RCS term. The model showed excellent discrimination in both the training and validation cohorts, good calibration, and favorable clinical utility on DCA.

The biological plausibility of the MPS model is supported by the current understanding of portal hypertension. Variceal development is driven not only by intrahepatic fibrosis, but also by the combined effects of increased intrahepatic vascular resistance, altered portal hemodynamics, and downstream splenic and splanchnic remodeling. In this context, PVV and SV appear to capture two complementary dimensions of portal hypertensive burden [9,19]. Lower PVV may reflect worsening portal venous hemodynamic disturbance, whereas splenic enlargement reflects chronic congestion and remodeling secondary to sustained portal hypertension. The nonlinear effect of SV further suggests that the relationship between splenic enlargement and HREV risk is not constant across the full spectrum of disease severity, supporting spline-based rather than purely linear modeling.

These findings should also be interpreted in the context of existing noninvasive strategies for variceal risk stratification. Guideline-based algorithms such as Baveno VI and Baveno VII were primarily developed as safe rule-out strategies to reduce unnecessary endoscopy in low-risk patients [4,7,28]. Their main strength is safety-oriented triage rather than maximal discrimination. Baveno VII further suggested that SSM ≤40 kPa may identify patients in whom endoscopy can be avoided [4]. In our cohorts, Baveno VI showed excellent safety but spared relatively few endoscopies, whereas the Baveno VII SSM-based strategy spared more endoscopies but had a higher missed-HREVs rate. By contrast, the MPS rule-out threshold achieved a better balance between endoscopy-sparing efficiency and patient safety by maintaining a low missed-HREVs rate while increasing the proportion of potentially spared endoscopies. These findings suggest that the MPS model may complement established Baveno-based strategies by providing individualized risk estimation and assisting clinicians with endoscopy prioritization, particularly when reducing unnecessary procedures is a clinical priority.

As summarized in Table 6, previously reported noninvasive models for identifying HREVs have mainly relied on stiffness-based parameters, computed tomography (CT) volumetry, spleen morphology, or composite indices [5,6,11,12,15,29,30]. These studies support the value of spleen-related markers in variceal risk stratification. However, many existing models require CT volumetry, elastography platforms, or relatively complex composite variables, which may limit their routine clinical use. Compared with these models, the present model has several practical advantages. First, the MPS model incorporates only two routinely available ultrasound parameters. Second, this parsimony was achieved not through arbitrary simplification, but through structured variable screening, AIC-based selection, formal assessment of linearity versus nonlinearity, and explicit comparison among candidate models. In predictive modeling, including too many variables may increase model complexity, reduce reproducibility, and introduce overfitting without necessarily improving clinical usefulness [31–33]. Third, despite its simplicity, the MPS model consistently outperformed each single predictor and showed excellent discrimination in both temporal cohorts. Although prediction models often show their highest apparent performance in the development cohort, the AUC in our temporal validation cohort was slightly higher than that in the training cohort. This difference was small (0.956 vs. 0.951), and the corresponding 95% CIs overlapped substantially, suggesting comparable discriminative performance. This finding may be partly explained by sampling variability related to the relatively small validation cohort, as well as modest differences in case mix between the two calendar-period cohorts [34].

Table 6.

Representative noninvasive models for identifying high-risk varices and the relative position of the present study

Study	Main predictors	Technical requirement	Representative finding	Relative position vs. present study
Kim et al. (2010) [5], Shibata et al. (2016) [29]	LSM+spleen diameter+PLT	Routine ultrasound+TE+clinical data	AUC: 0.954/0.928; outperformed isolated markers in identifying HREVs	Important composite model, but still elastography-dependent and less deployable than the present model
Yang et al. (2020) [12]	LV+SV+AST	CT volumetry+clinical data	AUC: 0.865; outperformed LSPS, VRI, APRI, and AAR models	Relevant conceptually, but based on volume imaging and less convenient than routine ultrasound
Yang et al. (2023) [11]	LSM+SSM	TE	AUC: 0.965; outperformed several comparators including Baveno VI	High-performing, but relies on dual stiffness technology
Zhang et al. (2023) [6]	ST+PLT	Routine ultrasound+clinical data	AUC: 0.859; a simple screening rule with good safety	Practical and low-cost, but captures less hemodynamic information than the present model
Li et al. (2025) [15]	Ascites+PT+SVER	CT volumetry+clinical data	AUC: 0.793; outperformed PSVR, PSDR, APRI, and AAR models	CT-dependent and less discriminative than the present model
Wang et al. (2025) [30]	SSM+PLT+spleen diameter	STE	AUC: 0.878; spared EGDs 39.7%	Strong recent model, but depends on dedicated stiffness equipment
Present study	PVV+SV	Routine ultrasound	AUC: 0.951; markedly improved specificity and spared endoscopy	Parsimonious, high-performing, and directly translatable to routine ultrasound workflows

LSM, liver stiffness measurement; PLT, platelet count; TE, transient elastography; AUC, area under the receiver operating characteristic curve; HREVs, high-risk esophageal varices; LV, liver volume; SV, spleen volume; AST, aspartate aminotransferase; CT, computed tomography; LSPS, liver stiffness–spleen diameter-to-platelet ratio score; VRI, varices risk index; APRI, aspartate aminotransferase-to-platelet ratio index; AAR, aspartate aminotransferase–to–alanine aminotransferase ratio; SSM, spleen stiffness measurement; ST, spleen thickness; PT, prothrombin time; SVER, spleen volume enlargement rate; PSVR, platelet count-to-spleen volume ratio; PSDR, platelet count-to-spleen diameter ratio; STE, sound touch elastography; EGDs, esophagogastroduodenoscopies; PVV, portal vein velocity.

Several limitations should be acknowledged. First, this was a retrospective single-center study. Although temporal validation was performed, it represented internal temporal validation within a single-center cohort. Thus, selection bias could not be fully excluded, and further validation in multicenter cohorts is warranted to confirm the robustness, generalizability, and clinical applicability of the model [35,36]. Second, the study population was limited to patients with hepatitis-related cirrhosis, which helped reduce etiological heterogeneity and allowed model development in a relatively homogeneous clinical setting. However, because the model and its optimal cutoff value of 0.30 were derived and validated only in this population, their applicability to other etiologies, such as alcohol-related liver disease or metabolic dysfunction–associated steatotic liver disease, remains uncertain. Further validation in more etiologically diverse cohorts is needed before broader clinical application. Third, PVV measurement is Doppler-based and may be more sensitive to acquisition technique than simple morphological measurements. Therefore, standardized acquisition protocols and consistent operator training are important for minimizing interoperator variability before broader clinical implementation [37,38]. Fourth, SSM in this study was obtained using the Echosens FibroScan 530 Compact device. Compared with newer platforms with dedicated SSM capabilities, such as FibroScan 630 Expert, this device lacks a spleen-specific probe and has not been fully validated for spleen stiffness assessment [39,40]. Therefore, the reproducibility and standardization of the obtained SSM values remain uncertain. Future studies using dedicated, better-validated SSM platforms are needed to clarify the predictive value of SSM for HREVs.

In conclusion, we developed and validated a model based on PVV and SV for identifying HREVs in patients with hepatitis-related cirrhosis. By integrating hemodynamic and morphological information, the model showed robust overall performance. Together with its web-based implementation, the model may serve as a practical tool for individualized prediction of HREVs. Further multicenter prospective studies are needed to validate its performance and clinical applicability.

Key points

An ultrasound-based model using only portal vein velocity and spleen volume provides a simple, noninvasive approach for predicting high-risk esophageal varices in patients with hepatitis-related cirrhosis. The model showed excellent discrimination, good calibration, and favorable clinical utility in both training and validation cohorts, supporting its potential use for individualized endoscopic triage.