Development and validation of a postoperative prediction model for residual stones after hepatectomy in patients with hepatolithiasis

Abstract

BACKGROUND

Residual stones after hepatectomy for hepatolithiasis are associated with recurrent cholangitis, repeat interventions, and long-term biliary morbidity. Current classification systems assist in disease characterization and operative planning but fail to provide individualized risk estimates in the early postoperative period.

AIM

To develop and internally validate an early postoperative model for predicting residual stones in patients with hepatolithiasis after hepatectomy.

METHODS

This study included 300 consecutive patients who underwent hepatectomy between January 2019 and December 2022. Residual stones were identified by postoperative imaging within 1 year and classified as incomplete clearance rather than recurrence. The cohort was randomly split into a development dataset (70%) and a held-out internal validation dataset (30%), and 12 candidate prediction models were developed and compared. Within the development dataset, preprocessing, feature shrinkage, hyperparameter tuning, and algorithm selection were performed using repeated nested cross-validation (outer 5-fold cross-validation repeated three times; inner 5-fold cross-validation). The final model was then locked and evaluated in the held-out validation cohort. Model performance was evaluated based on discrimination, prediction error, calibration, threshold-based classification, and decision-curve analysis.

RESULTS

Residual stones were identified in 82 of 300 patients (27.3%). The development cohort included 211 patients (58 events), and the validation cohort included 89 patients (24 events). Based solely on the out-of-fold performance within the development cohort, least absolute shrinkage and selection operator-penalized logistic regression (LASSO-LR) was selected as the final model. This model achieved a patient-level out-of-fold area under the receiver operating characteristic curve (AUC) of 0.849 [95% confidence interval (CI): 0.794-0.904] and a Brier score of 0.138. In the validation cohort, the AUC was 0.877 (95%CI: 0.807-0.947) with a Brier score of 0.134, confirming stable discrimination and predictive accuracy. Using the development-derived cutoff of 0.270, the validation sensitivity, specificity, and negative predictive value were 0.875, 0.785, and 0.944, respectively. The final model retained four predictors: Operative time, bilateral stone distribution, T-tube drainage, and postoperative biliary stricture before outcome ascertainment. Calibration intercepts neared zero in both cohorts, and decision-curve analysis showed net benefit across threshold probabilities from 0.05 to 0.40.

CONCLUSION

The LASSO-LR model demonstrated favorable internally validated performance for early postoperative residual-stone risk stratification and may facilitate individualized surveillance after hepatectomy for hepatolithiasis.

Key Words: Hepatolithiasis; Hepatectomy; Residual stones; Least absolute shrinkage and selection operator-penalized logistic regression; Prediction model

Core Tip: Residual stones remain an important and clinically consequential challenge after hepatectomy for hepatolithiasis, yet individualized tools for early postoperative risk stratification remain limited. In this retrospective cohort of 300 consecutive patients, 12 complete prediction pipelines were rigorously compared using repeated nested cross-validation within the development cohort, and least absolute shrinkage and selection operator-penalized logistic regression was selected before evaluation in a strictly held-out internal validation cohort. The final model retained only four routinely available perioperative predictors: Operative time, bilateral stone distribution, T-tube drainage, and postoperative biliary stricture documented before outcome ascertainment, and achieved an internally validated area under the receiver operating characteristic curve of 0.877 with a Brier score of 0.134 and a negative predictive value of 0.944. Its combination of parsimony, interpretability, low data-acquisition burden, and stable internally validated performance represents a practical strength for postoperative risk stratification. The model may help identify patients who warrant intensified surveillance and earlier imaging assessment, while independent external validation remains necessary before routine clinical implementation.

INTRODUCTION

Hepatolithiasis is a complex biliary disorder characterized by stones located proximal to the confluence of the right and left hepatic ducts. It is particularly prevalent in East and Southeast Asia and remains challenging because of recurrent cholangitis, biliary strictures, liver atrophy, repeated interventions, and the risk of malignant transformation[1-3]. Hepatolithiasis is characterized by an insidious onset, a complex and variable clinical course, distinct geographical patterns, and an as-yet unclear etiology[4]. Although hepatolithiasis is histologically benign, it is associated with considerable long-term morbidity, primarily resulting from persistent biliary inflammation, recurrent cholangitis, biliary obstruction, repeated surgical interventions, and the potential progression to biliary cirrhosis or cholangiocarcinoma[5,6].

Management of hepatolithiasis should follow the principles of lesion removal, complete stone clearance, correction of biliary strictures, adequate biliary drainage, and recurrence prevention[7]. Among available treatment options, hepatectomy is widely regarded as a definitive and effective approach for selected patients, particularly those with multiple intrahepatic stones, irreversible biliary strictures, segmental hepatic atrophy, severe fibrosis or liver abscess, atrophy-hypertrophy complex, or suspected concomitant cholangiocarcinoma. By removing the affected liver segments and diseased bile ducts, hepatectomy may eliminate the inflammatory nidus of stone formation, restore biliary drainage, reduce recurrence, and prevent further disease progression[2,8,9]. Compared with non-resectional treatments, hepatectomy may reduce residual stone burden and recurrence[10]. Nevertheless, residual stones remain a major postoperative challenge, occurring in approximately 10%-30% of patients after surgery. This risk is particularly high in patients with anatomical or structural biliary abnormalities[3,11]. In addition, because the extent of resection is constrained by the distribution of stones and the need to preserve an adequate future liver remnant, some patients can undergo only limited hepatectomy, leaving affected liver segments or stones in situ[3]. Repeated surgical interventions further impose substantial physical, psychological, and financial burdens on patients and their families. These considerations highlight the need for accurate perioperative and postoperative risk stratification of patients at high risk of residual stones after hepatectomy.

Conventional anatomical classifications remain qualitative and fail to estimate individual probabilities of residual stones. Although several clinical factors have been linked to incomplete clearance, prior analyses have largely focused on prognostic associations rather than prediction models anchored to a defined post-procedural landmark[11-16]. Furthermore, applying machine learning to modest surgical cohorts carries a high risk of optimism unless variable selection, preprocessing, and hyperparameter tuning are strictly isolated within cross-validation loops[17,18]. To address these clinical and methodological limitations, we engineered a data-partitioned predictive pipeline that strictly separates model development from internal validation. The primary objective of this study was to develop and validate an interpretable model for predicting early post-hepatectomy residual stones in hepatolithiasis, evaluated on an untouched held-out cohort to ensure unbiased performance estimation for post-procedural surveillance.

MATERIALS AND METHODS

Study design

This retrospective study enrolled patients with hepatolithiasis who underwent hepatectomy at the Second Affiliated Hospital of Kunming Medical University from January 1, 2019, to December 31, 2022. The study was approved by the Ethics Committee of the Second Affiliated Hospital of Kunming Medical University, and the requirement for informed consent was waived because of its retrospective design. The inclusion criteria were: (1) Hepatolithiasis diagnosed on the basis of preoperative imaging findings, intraoperative findings, and postoperative pathological examination; (2) Child-Pugh class A or B liver function; (3) Age between 18 years and 80 years; and (4) Availability of complete medical records. The exclusion criteria were: (1) No hepatectomy performed; (2) Previous gastrointestinal surgery other than biliary surgery; (3) Concomitant malignancy or postoperative pathological evidence of malignant transformation; and (4) Loss to follow-up or missing key data. The study was reported in accordance with the transparent reporting of a multivariable prediction model for individual prognosis or diagnosis + artificial intelligence and strengthening the reporting of observational studies in epidemiology reporting guidelines[19,20].

Outcome definition and prediction time point

The primary outcome was residual stones identified on postoperative imaging within 1 year after hepatectomy and adjudicated as incomplete clearance of pre-existing stones rather than de novo stone formation or recurrence. Patients with no stones detected during the 1-year follow-up period were classified as having no residual stones. The model was intended for early postoperative risk stratification before imaging had established residual-stone status. Accordingly, only predictors documented during the index hospitalization and before the first outcome-defining postoperative imaging examination were eligible. The model was not intended for preoperative prediction or intraoperative decision-making.

Clinical data collection and preprocessing

Clinical data were obtained from the electronic medical record system of the hospital and included information from the entire hospitalization period. The collected variables included demographic characteristics, disease course, comorbidities, imaging findings, laboratory parameters, and perioperative surgical variables. The cohort was stratified by outcome and randomly partitioned (7:3) into a development dataset and a held-out internal validation dataset. All preprocessing, hyperparameter tuning, threshold derivation, and algorithm selection were strictly confined to the development cohort. Variables with missing observations exceeding 30% were excluded. No missing values occurred within the final set of predictors used for model development, and data imputation was not required. Within each training resample, preprocessing included categorical encoding, removal of zero-variance predictors and exact linear combinations, and algorithm-specific standardization. No synthetic oversampling was performed. The held-out validation cohort remained completely untouched until the entire model was finalized and locked.

Model development, evaluation, and interpretation

A total of 12 candidate models were evaluated: Random forest, eXtreme Gradient Boosting (XGBoost), support vector machine with radial basis function kernel, least absolute shrinkage and selection operator-penalized logistic regression (LASSO-LR), k-nearest neighbors, partial least squares regression, gradient boosting machine (GBM), artificial neural network, naive Bayes, linear discriminant analysis, categorical boosting, and light GBM. Model comparison within the development cohort utilized 5-fold nested cross-validation repeated three times. In each outer loop, four folds served as outer-training data and the remaining fold was reserved for performance assessment. Within the outer-training data, an inner 5-fold cross-validation was implemented to estimate preprocessing parameters and optimize model-specific hyperparameters. Consequently, each patient received an out-of-fold (OOF) probability across each repeat, and these three probabilities were averaged to derive the final patient-level development-cohort OOF prediction.

For the LASSO logistic regression model, α was fixed at 1, and λ was evaluated over a logarithmic grid[21,22]. Within each inner cross-validation loop, the largest λ whose mean log loss was within 1 standard error of the minimum was selected. Shrinkage and variable selection were therefore repeated within each training resample rather than performed once before cross-validation.

Discrimination was assessed using the area under the receiver operating characteristic curve (AUC). For each candidate model, development-cohort discrimination was estimated from patient-level OOF predictions. After model selection, the selected model was evaluated once in the held-out internal validation cohort. For the prespecified performance measures, 95% confidence intervals (CIs) were estimated separately within each cohort using nonparametric patient-level bootstrap resampling. Overall probabilistic performance was assessed using the Brier score, scaled Brier score, and log loss. Calibration was evaluated using the calibration intercept, calibration slope, observed-to-expected (O/E) event ratio, and calibration plots[23].

Pairwise differences in AUC and Brier score between the selected model and each comparator model were estimated from the development-cohort OOF predictions using paired patient-level bootstrap resampling. As secondary exploratory analyses, pairwise AUC comparisons were performed using DeLong tests, and the resulting P values were adjusted for multiple comparisons using the Holm method.

For the selected model, an exploratory classification threshold was derived by maximizing the Youden index in the development-cohort OOF predictions and was applied unchanged to the held-out internal validation cohort. Sensitivity, specificity, accuracy, positive predictive value, negative predictive value, F1 score, and Youden index were estimated at this development-derived threshold, with 95%CIs obtained using patient-level bootstrap resampling. The potential clinical utility of the selected model was explored using decision-curve analysis by comparing its net benefit with the treat-all and treat-none strategies. The held-out internal validation cohort was reserved solely for final performance assessment and was not used for model selection, threshold derivation, model recalibration, or model updating.

Statistical analysis

Statistical analyses were performed using R version 4.4.1 (R Foundation for Statistical Computing, Vienna, Austria). Continuous variables displaying an approximately normal distribution, expressed as the mean ± SD, were compared using the Welch’s two-sample t-test; non-normally distributed continuous variables, expressed as median (interquartile range), were evaluated via the Mann-Whitney U test. Categorical variables, expressed as frequencies (%), were compared using the Pearson’s χ² test or Fisher’s exact test, as clinically appropriate. These baseline group comparisons were strictly exploratory and did not contribute to candidate-predictor screening, feature selection, or final model fitting. All statistical tests were two-sided, with actual P values reported. A two-sided P value < 0.05 was considered statistically significant.

RESULTS

Patient allocation and data partitioning

A total of 300 patients met the eligibility criteria, with 82 developing post-hepatectomy residual stones (overall incidence: 27.3%). Outcome-stratified sampling allocated 211 patients (58 events; 27.5%) to the development cohort and 89 (24 events; 27.0%) to the strictly isolated internal validation cohort. Within the development cohort, all 12 candidate models successfully completed the 15 outer loops of the repeated nested cross-validation, generating complete OOF predictions without data leakage. Cohort roles and event distributions are summarized in Table 1 and Figure 1; covariate balance is shown in Supplementary Figure 1.

Figure 1 Study population, predictive timeline, and zero-leakage model development workflow. The flow chart illustrates the selection process for the final analytic cohort (n = 300) from hepatolithiasis patients undergoing hepatectomy. The predictive timeline defines the eligible predictor window prior to the prediction landmark (first postoperative imaging) to prevent look-ahead bias. The methodological framework summarizes the steps for model development and internal validation. An outcome-stratified split (7:3) yielded a development cohort (n = 211; 58 events) and a held-out validation cohort (n = 89; 24 events). Candidate predictors were evaluated across 12 candidate modeling pipelines using repeated nested cross-validation (5-fold × 3 repeats) within the development cohort. The locked least absolute shrinkage and selection operator-logistic regression model was refit on the full development cohort and subsequently evaluated once in the strictly isolated validation cohort. AUC: Area under the receiver operating characteristic curve; CV: Cross-validation; DCA: Decision curve analysis; LASSO-LR: Least absolute shrinkage and selection operator-logistic regression.

Table 1 Cohort partition and analytical role.

Cohort	Patients (n)	Events (n)	Non-events (n)	Event rate (%)	Analytical role
Overall analytic cohort	300	82	218	27.3	Source population for development and internal validation
Development cohort	211	58	153	27.5	Repeated nested-CV pipeline comparison and selection; full-development fitting of the selected pipeline; OOF threshold derivation
Validation cohort	89	24	65	27.0	Untouched until one-time evaluation of the locked model and threshold

OOF: Out-of-fold; CV: Cross-validation.

Clinical characteristics according to residual-stone status

In the overall cohort, a bilateral stone distribution was significantly more prevalent among patients with residual stones than those without (48.8% vs 16.1%; P < 0.001). Patients with residual stones exhibited a prolonged median operative duration [335.0 minutes (305.5 minutes to 404.0 minutes) vs 280.0 minutes (219.3 minutes to 322.8 minutes); P < 0.001], a lower rate of T-tube drainage (51.2% vs 77.1%; P < 0.001), and a higher incidence of postoperative biliary strictures documented prior to outcome ascertainment (43.9% vs 9.2%; P < 0.001) (Table 2). These between-group comparisons were strictly exploratory and did not dictate candidate-predictor screening or final model inclusion. The comprehensive laboratory profiles of the study population are detailed in Supplementary Table 1.

Table 2 Clinically relevant characteristics according to residual-stone status, n (%)/median (interquartile range).

Item	Overall (n = 300)	Non-residual stone group (n = 218)	Residual stone group (n = 82)	P value
Baseline characteristics
Age (years)	58.00 (51.00-66.00)	58.00 (52.00-66.00)	56.50 (50.00-65.00)	0.401
Sex				0.428
Male	101 (33.67)	70 (32.11)	31 (37.80)
Female	199 (66.33)	148 (67.89)	51 (62.20)
BMI	22.04 (19.94-24.22)	22.22 (19.98-24.41)	21.34 (19.55-23.56)	0.195
Symptoms
Abdominal pain	229 (76.33)	161 (73.85)	68 (82.93)	0.135
Nausea and vomiting	71 (23.67)	46 (21.10)	25 (30.49)	0.121
Fever	72 (24.00)	46 (21.10)	26 (31.71)	0.078
Jaundice	27 (9.00)	19 (8.72)	8 (9.76)	0.957
HBV infection	34 (11.33)	23 (10.55)	11 (13.41)	0.622
Diabetes	43 (14.33)	24 (11.01)	19 (23.17)	0.013
Hypertension	49 (16.33)	39 (17.89)	10 (12.20)	0.311
Previous surgical history
Cholecystectomy	114 (38.00)	77 (35.32)	37 (45.12)	0.154
Choledochoscopy	64 (21.33)	45 (20.64)	19 (23.17)	0.750
Cholangioenterostomy	19 (6.33)	14 (6.42)	5 (6.10)	1.000
Partial hepatectomy	14 (4.67)	8 (3.67)	6 (7.32)	0.304
Stone classification1				0.289
Type I	34 (11.33)	28 (12.84)	6 (7.32)
Type IIa	54 (18.00)	39 (17.89)	15 (18.29)
Type IIb	48 (16.00)	39 (17.89)	9 (10.98)
Type IIc	10 (3.33)	7 (3.21)	3 (3.66)
Type E	154 (51.33)	105 (48.17)	49 (59.76)
Disease duration (months)	1.50 (0.50-12.00)	1.50 (0.50-12.00)	1.50 (0.50-21.00)	0.625
Imaging
Gallstones	77 (25.67)	58 (26.61)	19 (23.17)	0.646
Cholangitis	117 (39.00)	79 (36.24)	38 (46.34)	0.143
Liver abscess	44 (14.67)	27 (12.39)	17 (20.73)	0.101
Liver atrophy	104 (34.67)	74 (33.94)	30 (36.59)	0.770
Liver cirrhosis	23 (7.67)	12 (5.50)	11 (13.41)	0.040
Biliary stricture	79 (26.33)	33 (23.24)	46 (29.11)	0.307
Biliary dilation	282 (94.00)	205 (94.04)	77 (93.90)	1.000
Stone location				< 0.001
Unilateral	225 (75.00)	183 (83.94)	42 (51.22)
Bilateral	75 (25.00)	35 (16.06)	40 (48.78)
Intraoperative characteristics
Surgical method				0.486
OH	142 (47.33)	100 (45.87)	42 (51.22)
LH	158 (52.67)	118 (54.13)	40 (48.78)
Operative time (minutes)	295.00 (230.75-335.00)	280.00 (219.25-322.75)	335.00 (305.50-404.00)	< 0.001
Intraoperative blood loss (mL)	300.00 (200.00-500.00)	300.00 (200.00-500.00)	400.00 (200.00-600.00)	0.009
Intraoperative blood transfusion	26 (8.67)	17 (7.80)	9 (10.98)	0.521
ASA classification				0.505
I	205 (68.33)	146 (66.97)	59 (71.95)
II	93 (31.00)	71 (32.57)	22 (26.83)
III	2 (0.67)	1 (0.46)	1 (1.22)
Number of pringle maneuvers				0.220
≤ 3	215 (71.67)	161 (73.85)	54 (65.85)
> 3	85 (28.33)	57 (26.15)	28 (34.15)
Liver resection extent				0.202
Left	158 (52.67)	118 (54.13)	40 (48.78)
Left lateral	71 (23.67)	55 (25.23)	16 (19.51)
Right	34 (11.33)	20 (9.17)	14 (17.07)
Right posterior	15 (5.00)	8 (3.67)	7 (8.54)
Left medial lobe + right anterior	5 (1.67)	4 (1.83)	1 (1.22)
Right anterior	3 (1.00)	3 (1.38)	0 (0.00)
Others2	14 (4.67)	10 (4.59)	4 (4.88)
Other related procedures
Cholecystectomy	136 (45.33)	97 (44.50)	39 (47.56)	0.730
Choledochoenterostomy	90 (30.00)	61 (27.98)	29 (35.37)	0.270
T-tube drainage	210 (70.00)	168 (77.06)	42 (51.22)	< 0.001
Postoperative complications
Anastomotic stenosis	30 (10.00)	16 (7.34)	14 (17.07)	0.022
Postoperative biliary stricture	56 (18.67)	20 (9.17)	36 (43.90)	< 0.001
Abdominal infection	23 (7.67)	17 (7.80)	6 (7.32)	1.000
Pulmonary infection	93 (31.00)	71 (32.57)	22 (26.83)	0.413
Incision infection	12 (4.00)	7 (3.21)	5 (6.10)	0.420
Abdominal hemorrhage	8 (2.67)	5 (2.29)	3 (3.66)	0.801
Intestinal obstruction	6 (2.00)	3 (1.38)	3 (3.66)	0.426
Positive pathogen culture
Bile	57 (19.00)	32 (14.68)	25 (30.49)	0.003
Peritoneal drainage fluid	27 (9.00)	14 (6.42)	13 (15.85)	0.020
Blood	32 (10.67)	21 (9.63)	11 (13.41)	0.462
Bile leakage	38 (12.67)	16 (7.34)	22 (26.83)	< 0.001
Intestinal leakage	11 (3.67)	4 (1.83)	7 (8.54)	0.016

¹Stone classification was based on Dong’s classification.

²Others indicate single-segment resections grouped because of small sample sizes.

BMI: Body mass index; HBV: Hepatitis B virus; OH: Open hepatectomy; LH: Laparoscopic hepatectomy; ASA: American Society of Anesthesiologists.

Candidate-model comparison and selection

Model selection and performance in the development cohort: Across the 15 outer resampled evaluations in the development cohort, all 12 candidate pipelines successfully generated patient-level OOF predictions without data leakage. As detailed in Table 3, the candidate pipelines demonstrated a spectrum of discriminative capabilities, with OOF AUCs ranging from 0.743 (K-nearest neighbors) to 0.849 (LASSO-LR). Complex ensemble algorithms, including XGBoost (AUC = 0.817), GBM (AUC = 0.813), and random forest (AUC = 0.803), achieved solid performance but failed to surpass the regularized linear architecture. Furthermore, LASSO-LR yielded the lowest probabilistic prediction error, with a Brier score of 0.138 (range across all candidate pipelines: 0.138-0.187), a log loss of 0.432, and an optimal calibration intercept of 0.022 (Figure 2 and Supplementary Tables 2-5).

Figure 2 Candidate-model selection within the development cohort. A: Out-of-fold area under the receiver operating characteristic curve (AUC) distributions for 12 candidate algorithms within the development cohort; B: Prediction error (Brier score and log loss) and calibration metrics across candidate pipelines; C: Outer-fold AUC rank variability during nested cross-validation. The held-out validation cohort remained strictly isolated during model evaluation and pipeline locking. LASSO-LR: Least absolute shrinkage and selection operator-logistic regression; XGBoost: EXtreme Gradient Boosting; GBM: Gradient boosting machine; RF: Random forest; CatBoost: Categorical boosting; LDA: Linear discriminant analysis; NB: Naive Bayes; RBF-SVM: Support vector machine with radial basis function kernel; PLSR: Partial least squares regression; LightGBM: Light gradient boosting machine; ANN: Artificial neural network; k-NN: K-nearest neighbors; AUC: Area under the receiver operating characteristic curve.

Table 3 Comparative performance of the 12 candidate models based on development-cohort out-of-fold predictions.

Candidate algorithm	AUC	Brier score	Log loss	Calibration intercept	Calibration slope
LASSO-LR	0.849	0.138	0.432	0.022	1.748
XGBoost	0.817	0.153	0.469	0.227	0.705
GBM	0.813	0.150	0.457	0.076	0.938
RF	0.803	0.154	0.472	0.016	1.085
CatBoost	0.801	0.167	0.518	0.510	0.589
LDA	0.796	0.171	0.565	0.122	0.434
NB	0.788	0.187	0.689	0.937	0.334
RBF-SVM	0.785	0.158	0.481	-0.055	0.939
PLSR	0.784	0.175	0.535	-0.581	2.237
LightGBM	0.780	0.183	0.679	0.855	0.338
ANN	0.757	0.172	0.568	0.047	0.475
k-NN	0.743	0.180	0.596	0.723	0.709

Values were derived from patient-level out-of-fold predictions generated via 15 outer resampled iterations within the development cohort (n = 211). Bold formatting highlights the pre-specified primary model. LASSO-LR: Least absolute shrinkage and selection operator-logistic regression; XGBoost: EXtreme Gradient Boosting; GBM: Gradient boosting machine; RF: Random forest; CatBoost: Categorical boosting; LDA: Linear discriminant analysis; NB: Naive Bayes; RBF-SVM: Support vector machine with radial basis function kernel; PLSR: Partial least squares regression; LightGBM: Light gradient boosting machine; ANN: Artificial neural network; k-NN: K-nearest neighbors; AUC: Area under the receiver operating characteristic curve.

Adhering to the a priori development-only selection hierarchy, LASSO-LR was designated as the primary model prior to inspecting any held-out validation data. In 1000 non-parametric bootstrap evaluations of ranking stability, LASSO-LR ranked first in 920 iterations (92.0%), demonstrating a mean outer-fold AUC rank of 2.233 and achieving top performance in 6 of the 15 outer folds. Ultimately, complete OOF prediction coverage, minimal probabilistic error, and strict model parsimony jointly substantiated the definitive selection of the LASSO-LR model.

Final model specification and nomogram construction: Following algorithm selection, refitting the definitive LASSO-LR pipeline on the entire development cohort (n = 211) under the 1-standard-error (1-SE) rule yielded an optimal regularization parameter of λ = 0.0579. Compared with the minimum-error parameter (λ_min = 0.03625), the 1-SE criterion effectively eliminated redundant clinical variables to achieve strict model parsimony. Four non-zero predictors were retained: Operative time, bilateral stone distribution, T-tube drainage, and postoperative biliary stricture documented prior to outcome ascertainment. The fitted logit equation was formulated as follows with binary features dummy-coded as 1 (present) and 0 (absent):

Postoperative biliary stricture, bilateral location, and prolonged operative time served as positive risk factors, whereas T-tube drainage exerted a protective effect. To preserve the intrinsic shrinkage properties of the penalized coefficients, no unpenalized ordinary logistic regression refit was conducted. The resulting model was mapped into a clinical nomogram, translating individual predictor values into point scores (0-100 points) to calculate a cumulative total score (0-143.6) corresponding to personalized predicted residual stone risks ranging from 5% to 95% (Figure 3).

Figure 3 Selection, specification, and clinical presentation of the final least absolute shrinkage and selection operator-logistic regression model. A: Coefficient profiles of candidate predictors across the log (λ) penalty path. The vertical green line indicates the selected 1-SE parameter (λ = 0.0579); B: Cross-validated log loss vs log (λ), contrasting the minimum-error (lambda = 0.03625; orange) and the selected 1-SE (λ = 0.0579; green) thresholds; C: Exact non-zero penalized coefficients for retained predictors: Postoperative biliary stricture, bilateral stone location, prolonged operative time (positive coefficients), and T-tube drainage (negative coefficient); D: Nomogram derived directly from the locked penalized model, mapping individual predictor values to total points and predicted residual-stone probability without unpenalized refitting. CV: Cross-validation.

Model discrimination across development and validation cohorts: The LASSO-LR model displayed robust and cross-cohort discriminative stability in estimating residual stone risk. In the development cohort, the model achieved an OOF AUC of 0.849 (95%CI: 0.794-0.904; Figure 4A). Upon direct extrapolation to the independent validation cohort without model recalibration, it maintained a comparable discriminative efficiency with an AUC of 0.877 (95%CI: 0.807-0.947; Figure 4B). Across both cohorts, the parsimonious linear architecture of the LASSO-LR achieved discrimination on par with or superior to complex ensemble machine learning algorithms, such as GBM (development OOF AUC = 0.813; validation AUC = 0.868) and XGBoost (development OOF AUC = 0.817; validation AUC = 0.854; Figure 4A and B; Table 4).

Figure 4 Discriminative performance and calibration curves of the least absolute shrinkage and selection operator-logistic regression model. A: Receiver operating characteristic curves in the development cohort evaluated via out-of-fold (OOF) cross-validation; B: Receiver operating characteristic curves in the independent held-out validation cohort (n = 89). Shaded regions represent 95% confidence intervals (CIs) for the least absolute shrinkage and selection operator-logistic regression model, with comparator models (gradient boosting machine, eXtreme Gradient Boosting, and support vector machine with radial basis function kernel) shown for reference; C: Calibration plot in the development cohort based on OOF predictions; D: Calibration plot in the held-out validation cohort. The dashed 45-degree line represents perfect calibration. Solid colored lines and scatter points indicate observed vs predicted residual stone probabilities with bootstrap-derived 95%CIs. LASSO-LR: Least absolute shrinkage and selection operator-logistic regression; ROC: Receiver operating characteristic; XGBoost: EXtreme Gradient Boosting; GBM: Gradient boosting machine; AUC: Area under the receiver operating characteristic curve.

Table 4 Performance of the least absolute shrinkage and selection operator-logistic regression model in development and held-out validation cohorts.

Metric	Development OOF estimate (95%CI)	Held-out validation estimate (95%CI)
AUC	0.849 (0.794-0.904)	0.877 (0.807-0.947)
Brier score	0.138 (0.113-0.163)	0.134 (0.098-0.171)
Log loss	0.432 (0.375-0.492)	0.417 (0.335-0.499)
Calibration intercept	0.022 (-0.288 to 0.318)	0.006 (-0.543 to 0.467)
Calibration slope	1.748 (1.365-2.315)	1.939 (1.353-3.107)

Development estimates were calculated from patient-level out-of-fold predictions across 15 outer resampled iterations in the development cohort (n = 211). Held-out validation estimates were evaluated in a single pass on the frozen model using the independent validation cohort (n = 89). 95% confidence interval was derived via 1000 patient-level non-parametric bootstrap iterations. AUC: Area under the receiver operating characteristic curve; CI: Confidence interval; OOF: Out-of-fold.

Calibration and risk shrinkage properties

Calibration analysis revealed strong alignment between predicted probabilities and observed residual stone rates across the full risk spectrum (Figure 4C and D). Near-zero calibration intercepts in both the development OOF estimations (0.022; 95%CI: -0.288 to 0.318; Figure 4C) and the validation cohort (0.006; 95%CI: -0.543 to 0.467; Figure 4D) confirmed the absence of systematic risk overestimation or underestimation. The corresponding calibration slopes (1.748 in development and 1.939 in validation; Figure 4C and D) exceeded 1.0, reflecting a moderate shrinkage of risk predictions toward the population mean that effectively moderates overconfident extreme probability estimates.

Clinical decision-curve and threshold performance

Decision-curve analysis established that the LASSO-LR model offers superior standardized net clinical benefit over default management strategies across the clinically relevant threshold range of 0.10-0.30 in both the development (Figure 5A) and validation cohorts (Figure 5B). Application of the pre-specified optimal cutoff of 0.270 (derived from the development maximum Youden index; Figure 5C) to the validation cohort yielded balanced operating metrics, achieving a sensitivity of 0.875 (21/24) and a specificity of 0.785 (51/65; Figure 5D). Most importantly for risk stratification, this decision cutoff provided a high negative predictive value of 0.944 (51/54; Table 5), confirming the model’s primary utility in reliably identifying low-risk patients while minimizing false-negative classifications.

Figure 5 Decision curves and classification performance across decision thresholds. A: Decision-curve analysis displaying the standardized net clinical benefit of the least absolute shrinkage and selection operator-logistic regression model compared with “treat-all” and “treat-none” strategies across risk thresholds in the development cohort; B: Decision-curve analysis in the held-out validation cohort; C: Classification performance metrics (sensitivity, specificity, positive predictive value, and negative predictive value) as a function of decision thresholds in the development cohort. The vertical dashed line indicates the pre-specified optimal cutoff of 0.270 derived from the maximum Youden index; D: Classification performance profiles across decision thresholds in the held-out validation cohort at the locked 0.270 cutoff. LASSO-LR: Least absolute shrinkage and selection operator-logistic regression; NPV: Negative predictive value; PPV: Positive predictive value.

Table 5 Classification performance at the locked threshold of 0.270.

Metric	Development OOF (95%CI)	Held-out validation (95%CI)
Sensitivity	0.776 (0.661-0.882)	0.875 (0.727-1.000)
Specificity	0.784 (0.715-0.845)	0.785 (0.677-0.879)
PPV	0.577 (0.468-0.688)	0.600 (0.440-0.759)
NPV	0.902 (0.846-0.951)	0.944 (0.873-1.000)
Accuracy	0.782 (0.725-0.839)	0.809 (0.719-0.888)
F1 score	0.662 (0.563-0.750)	0.712 (0.571-0.833)
Youden index	0.560 (0.433-0.683)	0.660 (0.470-0.820)

Data are presented as point estimates with 95% confidence intervals in parentheses. The locked threshold of 0.270 was derived from the maximum Youden index in the development cohort via 10-fold cross-validation. CI: Confidence interval; OOF: Out-of-fold; NPV: Negative predictive value; PPV: Positive predictive value.

DISCUSSION

In this retrospective cohort of 300 adults undergoing hepatectomy for hepatolithiasis, 82 patients (27.3%) had postoperative residual stones. A parsimonious model based on operative time, bilateral stone distribution, T-tube drainage, and postoperative biliary stricture retained promising discrimination in the untouched internal validation cohort (AUC = 0.877; Brier score = 0.134).

Hepatolithiasis is not merely a localized stone disorder but a chronic, anatomically complex hepatobiliary disease. Although its prevalence is highest in East and Southeast Asia, population migration and wider use of cross-sectional imaging have increased its recognition outside endemic regions[2,8,24]. Repeated obstruction and infection can lead to recurrent cholangitis, liver abscess, fixed biliary stricture, segmental atrophy, secondary biliary cirrhosis, and intrahepatic cholangiocarcinoma[2,24]. The long-term implications of incomplete clearance are particularly important. In an 18-year Japanese national cohort, residual stones at the end of treatment and biliary stricture during follow-up were independently associated with subsequent intrahepatic cholangiocarcinoma[25]. Residual stones should therefore be regarded as a clinically meaningful disease state that may sustain inflammation, impair drainage, and increase the need for repeated biliary procedures, rather than as a purely technical imperfection of surgery.

The primary therapeutic goals in hepatolithiasis encompass complete stone clearance, relief of pathologic strictures, resection of severely infected or atrophic hepatic segments, preservation of functional liver parenchyma, and establishment of durable biliary drainage[2,24,26]. Achieving these objectives frequently necessitates a multimodal approach combining hepatectomy, intraoperative or postoperative choledochoscopy, percutaneous transhepatic cholangioscopic lithotripsy, endoscopic interventions, and selective biliary reconstruction[5,25]. Hepatectomy is particularly definitive for localized disease as it addresses both the stone burden and the diseased duct-bearing parenchyma; however, complete clearance remains challenging in patients with diffuse or bilateral involvement[13,14,27]. Although hepatectomy achieves higher initial clearance rates compared with percutaneous or peroral cholangioscopic therapies, recurrent stones and late biliary complications remain substantial clinical concerns[14]. Consequently, contemporary clinical management has shifted beyond mere operative safety to optimizing stone clearance while preserving maximal functional liver volume, highlighting the need for early identification of patients at risk for incomplete clearance.

Differentiating residual from recurrent stones is critical when evaluating both clinical outcomes and predictive performance. Residual stones represent incomplete clearance of the stone burden present during the index procedure, whereas recurrent stones reflect de novo stone formation following documented complete clearance. These two entities differ fundamentally in their timing, underlying mechanisms, and clinical management. The observed residual stone rate of 27.3% in our cohort aligns with the wide range reported in surgical literature, which varies according to disease distribution, ductal architecture, surgical strategy, and the utilization of postoperative choledochoscopy[13,14,27]. Uchiyama et al[13] identified residual stones in approximately one-fifth of patients, while Cheon et al[14] demonstrated that biliary strictures and bilateral disease independently increased the risk of incomplete clearance, which subsequently predisposed patients to late recurrence and cholangitis. By focusing specifically on early residual stones following hepatectomy, this study targets a distinct and actionable landmark in the postoperative care pathway, contrasting with models aimed at long-term stone recurrence.

Bilateral stone distribution emerged as one of the most clinically coherent predictors. In our cohort, bilateral disease was present in 48.8% of patients with residual stones compared with 16.1% of those without. Bilateral hepatolithiasis inherently involves multiple ductal territories and frequently coexists with biliary strictures, segmental liver atrophy, prior biliary interventions, and asymmetric disease severity. While complete clearance may necessitate extensive or staged resections, the extent of hepatectomy is ultimately constrained by the future liver remnant and the critical imperative to preserve functional parenchyma. Comparative surgical series have consistently demonstrated lower immediate and final clearance rates, alongside less favorable long-term outcomes, in bilateral vs unilateral disease[11,12,28]. Modern cohorts further suggest that meticulous intrahepatic duct exploration combined with postoperative choledochoscopic lithotripsy can enhance final clearance in select complex bilateral cases[29]. Collectively, these findings validate bilateral distribution as a comprehensive anatomical marker of disease burden and surgical clearance difficulty, rather than a mere binary location variable.

Prolonged operative time was likewise retained in the finalized model, being substantially longer among patients with residual stones (median: 335.0 minutes vs 280.0 minutes). Operative time should not be interpreted as a direct etiology of residual stones. Rather, it serves as a composite surrogate integrating perioperative factors that may evade individual quantification, including dense adhesions from prior interventions, distorted hilar architecture, extensive stone burden, multiple strictures, bilateral ductal exploration, challenging parenchymal transection, and repeated choledochoscopic clearance maneuvers. Surgical series focusing on bilateral hepatolithiasis have similarly documented longer operative time in patients with higher disease extent[11,12,28], while large contemporary hepatectomy cohorts demonstrate that prolonged operative time correlates with an increased risk of postoperative infectious morbidity[30]. Within this analytical framework, operative duration functions as a pragmatic surrogate marker of technical and anatomical complexity. While its inclusion enhances model risk stratification, shortening operative time at the expense of thorough exploration or stone clearance must not be inferred as a valid clinical objective.

T-tube drainage is not randomly assigned; rather, its placement is dictated by ductal architecture, concomitant choledocholithiasis, intraoperative clearance assessment, anticipated need for postoperative access, and institutional practice. Consequently, the observed protective directionality may reflect treatment selection bias and residual confounding rather than a true biological effect. Historically, T-tube placement has established a track to facilitate postoperative cholangiography and choledochoscopic clearance of retained stones, with comparative evidence indicating that such postoperative access can reduce the final stone burden in select patients[31]. Conversely, primary common bile duct closure following hepatectomy has been validated as safe and feasible in carefully selected cohorts, circumventing T-tube-related morbidity[16]. Therefore, our model should neither be construed to endorse routine T-tube drainage nor be applied intraoperatively to guide T-tube decision-making, as drainage status represents a post-decision variable.

Postoperative biliary stricture demonstrated a strong positive association with predicted residual stone risk, a finding fully aligned with clinical rationale provided that the stricture was documented prior to the outcome-defining imaging assessment. Anatomically, a biliary stricture compromises bile flow, promotes cholestasis and bacterial colonization, obstructs endoscopic or choledochoscopic passage, and obscures retained stones within inadequately drained peripheral segments. Persistent strictures and residual stones are well-documented independent predictors of secondary intrahepatic cholangiocarcinoma following hepatectomy for hepatolithiasis[25,32]. Nevertheless, this variable represents the most temporally vulnerable feature in the model. If a postoperative stricture was diagnosed concurrently with or subsequent to the imaging workup establishing residual stone status, it risks incorporating post-outcome information, thereby introducing reverse causality or label leakage. Consequently, the clinical definition, diagnostic timestamp, and chronological relationship of stricture diagnosis relative to stone ascertainment require careful consideration in the interpretation of these findings. Furthermore, a sensitivity analysis excluding post-procedure variables would clarify whether a model constrained strictly to preoperative and intraoperative features maintains clinically robust performance.

Existing prediction tools in hepatolithiasis address distinct clinical endpoints and operational windows. Pu et al[15] developed a multicenter nomogram to predict clinical outcomes following surgery for recurrent hepatolithiasis; incorporating prior biliary interventions, bilateral stone distribution, immediate clearance status, and systemic inflammatory or nutritional markers, their model demonstrated consistent discrimination across development and external validation cohorts. Subsequently, the multicenter CARES study leveraged machine-learning algorithms to model dynamic 5-year stone recurrence risk, achieving an AUC of approximately 0.90 across sequential time horizons[33]. Parallel efforts have targeted malignant transformation or differential diagnosis rather than early residual stone risk. For instance, a multicenter machine-learning nomogram was constructed to estimate the probability of secondary intrahepatic cholangiocarcinoma in hepatolithiasis[34], whereas computed tomography- and ultrasound-based radiomics models were designed to differentiate hepatolithiasis-associated inflammatory pseudotumors from intrahepatic cholangiocarcinoma[35,36]. Although clinically impactful, these models differ fundamentally in their target outcomes, prediction timelines, study populations, and required predictors; consequently, direct head-to-head comparisons of their predictive performance would be methodologically unsound.

The principal strength of our model lies not in algorithmic novelty or incremental gains in discrimination, but in its close alignment with clinical decision-making. Specifically, the model targets early residual stones following hepatectomy, distinguishes residual burden from long-term recurrence, incorporates four routine perioperative variables, and yields an interpretable risk probability suitable for integration into postoperative surveillance pathways. Compared with radiomics or high-dimensional machine-learning architectures, it imposes a substantially lower data-acquisition burden, facilitating implementation across standard hepatobiliary centers. Conversely, unlike established multicenter recurrence models, its external transportability remains unverified given its reliance on single-center internal validation. Accordingly, this model is positioned as complementary to, rather than superior to, existing tools: It fills a distinct early-surveillance niche, whereas current models address long-term recurrence or malignant transformation along the hepatolithiasis continuum.

The model is most appropriately positioned for risk-adapted surveillance. Patients categorized with elevated predicted probabilities could be prioritized for expedited multidisciplinary review, systematic re-examination of operative and choledochoscopic findings, and earlier, definitive imaging tailored to institutional protocols. Conversely, patients identified with lower predicted risks can safely remain on routine surveillance pathways; notably, mandatory baseline imaging must not be omitted, as the model has not been prospectively validated as a rule-out screening tool. The robust negative predictive value observed in validation is encouraging, whereas the modest positive predictive value underscores that a high-risk stratification represents an actionable clinical prompt rather than a definitive diagnosis. Calibration metrics further mandate caution regarding immediate clinical deployment: Calibration slopes of approximately 1.7-1.9 indicate under-dispersion, wherein estimated probabilities are compressed toward the cohort mean[37]. Consequently, while external cohorts may preserve rank-order discrimination, local recalibration will be imperative before incorporating individual risk estimates or fixed cut-offs into routine clinical decision-making.

This study has several limitations. First, its retrospective design may have introduced selection bias and missing data. Second, this was a single-center study, and the generalizability of the findings requires external validation. Third, although 300 patients were included and cross-validation was performed, the sample size remains relatively limited for developing robust predictive models. Future prospective, multicenter studies with larger samples are needed to validate and refine the model and further assess its clinical applicability. In conclusion, this four-variable model offers an interpretable framework for identifying patients who may warrant intensified surveillance after hepatectomy for hepatolithiasis. Its principal contribution is to translate recognizable surgical and biliary features into an individualized estimate of early residual-stone risk; its clinical benefit must now be established through rigorous temporal or multicenter validation and prospective pathway testing.

CONCLUSION

The LASSO-LR model demonstrated favorable internally validated performance for early postoperative residual-stone risk stratification and may facilitate individualized surveillance after hepatectomy for hepatolithiasis.

ACKNOWLEDGEMENTS

We sincerely thank the editor and the anonymous reviewers for their thoughtful evaluation of our manuscript and for their constructive comments. Their feedback has provided valuable guidance in refining our work.