Non-invasive prediction of occult peritoneal metastasis (OPM) in gastric cancer using logistic regression and random forest integrative models with CT radiomics and clinical parameters: machine learning prediction of gastric OPM

Introduction

Gastric cancer ranks as the fifth most common cancer globally, with its incidence exhibiting significant regional disparities, particularly in Asia, South America, and Eastern Europe (1,2). The peritoneal cavity is the most common site of metastasis in gastric cancer; this condition is termed gastric cancer peritoneal metastasis (GCPM). Up to 55–60% of patients develop peritoneal metastases. This type of metastasis poses a severe threat to patient survival, with a 5-year survival rate of only 2% (3,4). The standard treatment for recurrent and metastatic gastric cancer is systemic chemotherapy; however, patients with GCPM receiving palliative systemic chemotherapy have a median survival of less than 6 months (5).

Although intraperitoneal chemotherapy and cytoreductive surgery have been attempted to improve outcomes in GCPM, their efficacy remains controversial and clinical application is limited by a lack of standardized protocols (5-10). Given the limited treatment options for advanced GCPM, early and accurate preoperative prediction of peritoneal metastasis risk is critical for guiding individualized treatment strategies.

However, current diagnostic methods face substantial limitations, particularly for GCPM that is difficult to detect on computed tomography (CT). CT is the most commonly used non-invasive imaging modality, yet its sensitivity for small, early-stage, or occult peritoneal lesions remains unacceptably low. In fact, multiple studies have shown that the incidence of occult peritoneal metastasis (OPM) ranges from 8% to 22% (11-14). However, in clinical practice, these OPM lesions are often missed or misclassified by CT imaging. This diagnostic failure directly leads to significant understaging in about 30–40% of patients, who consequently still require invasive laparoscopic exploration to obtain accurate staging (15). For patients who have already developed OPM, missed diagnosis on CT not only implies unnecessary surgical trauma and impairment of performance status, but also seriously compromises subsequent comprehensive treatment decisions due to inaccurate staging. Traditionally, risk stratification for OPM has relied heavily on routine clinicopathological variables, including Borrmann type IV, diffuse histological subtype, elevated serum carcinoembryonic antigen (CEA) and carbohydrate antigen 19-9 (CA19-9), as well as deep tumor invasion with regional lymph node metastasis. Unfortunately, these factors have limited sensitivity and specificity in independently identifying genuine OPM cases (16,17). Peritoneal lavage cytology, the gold standard for detecting peritoneal micrometastases, has a sensitivity below 60%, restricting routine clinical use (18). Therefore, developing a non-invasive, accurate, and reproducible preoperative predictive biomarker—specifically for identifying patients with OPM—has become an urgent priority in GCPM management.

Multiple studies have indicated that preoperative data are feasible for predicting OPM. Zhu et al. reported that when using traditional variables alone, such as Borrmann type IV, pelvic effusion, CA125, and standardized arterial-phase CT values, the area under the curve (AUC) ranged from 0.643 to 0.696 (16). Further studies showed that a nomogram model based on multiple clinical variables achieved an AUC of 0.711 for OPM prediction (19). After incorporating CT features, the combined model’s AUC increased to 0.820 (16). Additionally, one study employing novel algorithms such as deep convolutional neural networks, integrating clinical and radiomics data, reported an AUC of 0.900 [95% confidence interval (CI): 0.851–0.953] (17). These findings suggest that radiomics features, by reflecting microscopic textural alterations of primary tumors, may provide additional value independent of clinical data. Indeed, radiomics features capture intratumoral spatial heterogeneity that is unrecognizable by clinicopathological data, reflecting microscopic architecture and vascular-perfusion dynamics invisible to the naked eye on CT (20,21). Therefore, integrated models can more comprehensively reflect the global tumor status, thereby demonstrating superior and more robust predictive performance. Although the above studies demonstrate that integrating clinical and radiomics data can effectively predict OPM, these models generally lack interpretability, and most of them adopted a single algorithmic paradigm without systematically comparing linear vs. nonlinear models in terms of feature interactions, decision boundaries, and biological interpretability. To address this gap, we extracted whole-tumor three-dimensional (3D) radiomics features from contrast-enhanced CT images, combined them with independent clinical predictors, and constructed five machine learning-based integrated models, specifically including the linear models logistic regression (LR) and support vector machine (SVM), as well as the nonlinear models random forest (RF), extreme gradient boosting (XGBoost), and light gradient boosting machine (LightGBM). Linear models serve as interpretable baselines for linearly separable patterns and clinical reference. In contrast, nonlinear tree-based ensembles capture complex feature interactions and flexible decision boundaries without strong distributional assumptions. This diversity allows us to compare paradigms on the same inputs, clarifying whether nonlinear modeling adds benefit over simpler linear approaches. We focused on a comparative SHapley Additive exPlanations (SHAP) analysis and Friedman’s H-statistic interaction assessment between the linear models and the nonlinear models. Our aim was to develop and validate a preoperative tool specifically for predicting OPM in gastric cancer patients with negative CT findings. We also sought to reveal the biological meaning of the radiomics features and the nonlinear synergistic relationships among them, thereby providing a more transparent basis for clinical decision-making. We present this article in accordance with the TRIPOD reporting checklist (available at https://jgo.amegroups.com/article/view/10.21037/jgo-2026-0509/rc) (22,23).

Methods

Collection of clinical data

This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. This clinical study was approved by the Ethics Committee of The Affiliated Hospital of Qingdao University (approval No. QYFYWZLL30180), which waived the requirement for informed consent owing to its retrospective design. Clinical data were retrospectively collected from patients diagnosed with gastric cancer at The Affiliated Hospital of Qingdao University between January 2016 and December 2022 (n=164). Among these, 100 cases were diagnosed with OPM, while the remaining 64 cases were non-metastatic (Figure 1A). The primary outcome of this study was OPM in gastric cancer patients, defined as no definite peritoneal metastasis on preoperative contrast-enhanced CT confirmed by laparoscopy, peritoneal biopsy or positive peritoneal lavage cytology. Outcome assessment was performed during staging laparoscopy or gastrectomy after baseline CT. All enrolled patients underwent baseline contrast-enhanced abdominal CT staging preoperatively, and staging laparoscopy or radical gastrectomy was performed within a median of 3 days (range, 1–6 days) after CT. OPM was confirmed using a standardized protocol: during laparoscopic exploration or open surgery, a systematic peritoneal exploration was routinely performed in all patients, covering the pouch of Douglas, bilateral diaphragmatic domes, liver surface, greater omentum, and other common sites of peritoneal metastasis. For any suspicious peritoneal nodules visible intraoperatively, intraoperative frozen biopsy was performed, and final diagnosis was confirmed by postoperative paraffin-embedded histopathological examination (reports issued 7–14 days postoperatively). For patients with no visible peritoneal lesions intraoperatively, peritoneal lavage cytology was not routinely performed at our center; it was selectively performed only in cases with high clinical suspicion of occult metastasis. Positive lavage cytology was also diagnosed as OPM. All procedures were carried out according to the standardized gastric cancer diagnosis and treatment protocol of our hospital. Inclusion criteria were: (I) diagnosed with gastric adenocarcinoma by biopsy or postoperative pathology; (II) no history of other types of malignant tumors prior to surgery; (III) complete clinical data available; (IV) abdominal contrast-enhanced CT performed at initial diagnosis; and (V) no definite peritoneal metastatic signs were reported on CT, but peritoneal metastasis was confirmed by laparoscopic exploration, peritoneal biopsy, or peritoneal lavage cytology. Exclusion criteria included: (I) local or systemic treatment received prior to baseline CT scan; (II) previous or concurrent other malignant tumors; (III) poor quality of radiological images; (IV) clinically suspected peritoneal metastasis without pathological confirmation; (V) residual stomach; and (VI) presence of other distant metastases confirmed by imaging, histopathology, or intraoperative findings. Patients were stratified by OPM status and assigned to the training and validation cohorts in a 7:3 ratio using stratified random sampling with a fixed random seed of 42 to preserve the same class distribution in both cohorts. For clinical variable missing data handling: variables with a missing rate >5% were directly excluded, and variables with a missing rate <5% were supplemented using multiple imputation. Preoperative/pretreatment data for nine demographic and clinical laboratory parameters were extracted from electronic medical records for eligible patients, including gender, age, BMI, alpha-fetoprotein (AFP), CEA, CA19-9, albumin (ALB), tumor location, and reassessment of tumor pathological tumor/node (T/N) staging according to the 8^th edition of the American Joint Committee on Cancer (AJCC) guidelines. No blinding was applied to clinical variable collection or outcome assessment.

Figure 1 Patient enrollment flowchart and representative CT images, lesion segmentation, and 3D reconstruction of gastric cancer with or without peritoneal metastasis. (A) Patient enrollment flowchart. (B) Original axial CT image of a gastric cancer patient with OPM (male, 53 years old; BMI 25.1 kg/m²). (C) Segmented annotation corresponding to (B): green area indicates primary gastric tumor tissue, red area indicates normal gastric wall tissue. (D) Original axial CT image of a gastric adenocarcinoma patient without peritoneal metastasis (male, 55 years old; BMI 24.4 kg/m²). (E) Segmented annotation corresponding to (D): green area indicates primary gastric tumor tissue; red area indicates normal gastric wall tissue. (F) 3D reconstruction model of the whole stomach and tumor from the patient with OPM [same case as (B) and (C)], illustrating the spatial relationship between the tumor and the gastric wall. (G) 3D reconstruction model of the whole stomach and tumor from the patient without peritoneal metastasis [same case as (D) and (E)]. 3D, three-dimensional; BMI, body mass index; CT, computed tomography; GC, gastric cancer; GCPM, gastric cancer peritoneal metastasis; OPM, occult peritoneal metastasis.

CT data acquisition and preprocessing

Dynamic contrast-enhanced upper abdominal CT scans were acquired using a GE Revolution 256-slice CT scanner, with the following acquisition parameters: tube voltage of 120 kV, automatic tube current modulation (GE AutomA, Waukesha, WI, USA) with a noise index of 10 yielding a tube current range from 50 to 413 mAs, tube rotation time of 0.5 s, detector collimation of 80 mm, and matrix size of 512×512. Contrast-enhanced imaging was acquired during the delayed phase (approximately 120–150s after contrast injection) following intravenous administration of 90–100 mL of non-ionic iodinated contrast agent (iohexol, 350 mgI/mL) at a flow rate of 3.0 mL/s using a power injector, slice thickness of 0.625–5 mm, and a standard soft-tissue reconstruction kernel (GE Standard) using filtered back projection. All patients were scanned in the supine, head-first position. In accordance with the guidelines of the Image Biomarker Standardization Initiative (IBSI) (24,25), all images were preprocessed using 3D Slicer software. First, all delayed-phase CT images were isotropically resampled to a voxel size of 1×1×1 mm³ to eliminate inter-patient variation in spatial resolution. Then, intensity standardization was performed by clipping all voxel values to a fixed range of −1,000 to 2,000 Hounsfield units (HU) via a built-in Python script to reduce intensity variations. A fixed bin width of 25 was employed, and the “enforce symmetrical gray-level co-occurrence matrix” option was activated to ensure image comparability and improve data reliability. Because the original DICOM slice thickness varied across patients (0.625–5 mm) and tube current was modulated automatically by body habitus (50–413 mAs), this IBSI-compliant image-level preprocessing was applied to reduce feature variability arising from heterogeneous acquisition settings. No additional statistical harmonization (e.g., ComBat) was performed, as all examinations were acquired on a single scanner with a uniform vendor protocol, and acquisition parameters did not differ systematically between the OPM and non-OPM groups.

Tumor segmentation

All tumor segmentation tasks were independently performed by two abdominal imaging residents with extensive clinical experience, who were blinded to patients’ clinical information. Using 3D Slicer (version 5.8.1), the residents manually contoured the tumor layer by layer on each cross-sectional image, ultimately generating a 3D tumor region of interest (ROI) volume (26) (Figure 1B-1G). The tumor boundary was defined as the visible margin of the primary gastric lesion, including all solid tumor components; necrotic or cystic areas within the tumor were included if they were surrounded by viable tumor tissue. Cases in which the tumor boundary could not be clearly distinguished from adjacent structures were flagged for expert review. Adjacent organs, adipose tissue, and intraluminal contents were excluded from the segmentation. Subsequently, the two residents performed cross-reviews to identify disputed segmentation results, which were defined as discrepancies in tumor boundary delineation exceeding 5 mm over at least three consecutive slices, or disagreements regarding the inclusion of necrotic/peritumoral regions. All contentious images were submitted to a senior abdominal radiology expert for final adjudication. To assess segmentation reproducibility, 30 patients (15 OPM, 15 non-PM) were randomly selected for re-segmentation by two independent radiologists, and the intraclass correlation coefficient (ICC) was calculated for the key radiomics features. An ICC >0.75 was considered to indicate good agreement.

Radiomics feature extraction

The PyRadiomics (version 3.0.1) library in Python was used to extract radiomics features from each segmented 3D tumor ROI. A total of 957 radiomics features were extracted per ROI, including 120 original features, 93 Laplace-Gaussian filtered features (σ=3 mm), and 744 wavelet transform features.

Development of clinical and radiomics models

Study size was determined according to the events-per-variable (EPV) principle for predictive model construction, with a minimum requirement of 10 positive events per predictor. For clinical data, univariate associations between OPM status and potential predictors were evaluated using LR analysis. Variables with a statistically significant association (P<0.05) across cohorts were included in multivariate analysis. Independent clinical risk factors for OPM were identified via stepwise backward LR, and a clinical prediction model was constructed. For radiomics feature selection, the following procedure was applied. First, Z-score normalization parameters were fitted exclusively on the training set to prevent data leakage, and features with near-zero variance were removed. Second, least absolute shrinkage and selection operator (LASSO) with 10-fold cross-validation and the 1 − standard error (1-SE) rule, followed by Spearman rank correlation analysis (threshold =0.75), were sequentially applied to retain key features with non-zero coefficients and no collinearity (i.e., pairwise correlation below the threshold). Given 70 positive events in the training set (164 total, 100 positives, 7:3 split), the EPV criterion (≥10) limited the total predictors to ≤7. Considering at least one clinical variable would be included, the final radiomics signature was capped at 6 features. The Rad-score was computed as the linear combination of these six features weighted by their LASSO coefficients plus the intercept. All models were trained with the class_weight=‘balanced’ parameter to handle class imbalance and internally validated using 10-fold cross-validation. In the validation phase, model predicted probabilities were calculated using the same feature weights and algorithms derived from the training set without further retuning.

Model evaluation

The accuracy of the predictive models was comprehensively evaluated by assessing their discrimination and calibration. Internal validation of model performance was carried out using 10-fold cross-validation to determine stability and robustness. Discrimination ability was evaluated by plotting receiver operating characteristic (ROC) curves and calculating the AUC with 95% CIs derived from 1,000 bootstrap resamples. Calibration was assessed via calibration curves, Brier scores, and the Hosmer-Lemeshow goodness-of-fit test. The clinical utility of the models in decision-making was evaluated by plotting decision curve analysis (DCA) curves. Given the imbalanced nature of the dataset, precision-recall (PR) curves were also plotted, and average precision (AP) was calculated to comprehensively assess the model’s performance in identifying positive samples. Finally, SHAP analysis was employed in this study to interpret the predictive behavior of the trained models at both global and local levels. Derived from the Shapley value in cooperative game theory, SHAP analysis attributes the model’s predictive outcomes fairly to each input feature by considering all possible feature combinations. The baseline value is defined as the expected output of the model on the background dataset, representing the reference predictive result in the absence of feature information. The analysis is conducted based on probabilities. In this study, the training set was used as background samples to estimate the expected output, ensuring computational efficiency while maintaining data representativeness. Global feature importance was quantified by the mean absolute SHAP values across all samples; for representative samples, waterfall plots were used to present the local interpretation results.

Statistical analysis

Continuous variables with a normal distribution were reported as mean ± standard deviation, whereas skewed continuous variables were expressed as median [interquartile range (IQR)] and analyzed using the Mann-Whitney U test or Student’s t-test. Categorical variables were presented as proportions and analyzed using the chi-square test or Fisher’s exact test. The statistical significance of differences in model AUC values was evaluated using the DeLong test. Friedman’s H-statistic derived from bivariate partial dependence plots (PDP) was used to quantify the interaction strength and synergistic contributions between radiomics and clinical features in nonlinear models. The H-statistic was computed on the training dataset with a grid resolution of 50, and numerical integration was performed using the trapezoidal rule. All pairwise two-way interactions among features were evaluated, with an H-statistic value of 0 indicating no interaction effect (27). All data analyses were performed using Python (3.9.23) (Python Software Foundation) and RStudio (4.5.1) (R Foundation for Statistical Computing). A P value <0.05 was considered statistically significant.

Results

Clinical and baseline characteristics

After applying the exclusion criteria, a total of 164 gastric cancer patients from The Affiliated Hospital of Qingdao University were enrolled in this study and divided into the OPM group (OPM, n=100) and the non-metastasis group (gastric cancer, n=64) (Figure 1, Table 1). In the OPM group, the median age was 59.0 (IQR, 13.2) years, 68.0% were male, 96.0% had T3/T4 stage, and 87.0% had lymph node metastasis. In the gastric cancer group, the median age was 63.3 (IQR, 9.1) years, 59.4% were male, 73.4% had T3/T4 stage, and 59.4% had lymph node metastasis.

The OPM group was a younger age (P=0.003), higher serum CA19-9 levels [16.4 (IQR, 46.9) vs. 7.6 (IQR, 11.1) U/mL, P<0.001], and more advanced T and N stages (both P<0.001) compared with the gastric cancer group. AFP levels were lower in the OPM group [3.1 (IQR, 2.1) vs. 4.2 (IQR, 2.5) ng/mL, P=0.01], while no significant difference in CEA levels was observed between the two groups (P=0.08). After stratified random allocation into training and validation cohorts at a 7:3 ratio, no significant differences were found between the two cohorts (Table 2). The training cohort included 114 patients with 70 OPM events, and the validation cohort included 50 patients with 30 OPM events. All predictive analyses were performed on these two cohorts.

Identification of independent predictors and development of the clinical model

To construct a clinical predictive model for OPM, stepwise backward LR was performed to identify independent predictors. Age (OR =0.95; 95% CI: 0.92–0.98; P=0.005) and T stage (OR =3.33; 95% CI: 1.92–5.77; P<0.001) were identified as independent clinical predictors. In the training cohort, the AUC was 0.753; in the validation cohort, the AUC was 0.794. The Brier score in the validation cohort was 0.197 (Figure 2).

Figure 2 ROC curves and calibration curves of the clinical prediction model based on age and T stage. AUC, area under the curve; ROC, receiver operating characteristic; T, tumor.

Radiomics feature selection and radiomics model construction

Inter-observer agreement for all candidate radiomics features was assessed using thirty randomly selected cases independently segmented by two physicians. Features with an ICC >0.75 were retained for further analysis. For radiomics feature selection, after Z-score normalization, LASSO with 10-fold cross-validation and the 1-SE rule was applied to the retained features. The top 15 non-zero coefficients were retained, followed by Spearman correlation analysis (threshold =0.75) to remove redundant features, and the top six features were selected as the final radiomics signature (Figure S1A,S1B). The median ICC of these six key features was 0.857 (range, 0.844–0.883) (Figure S1C). The calibration curve and Hosmer-Lemeshow test (P>0.05) indicated good agreement between predicted and observed probabilities. Based on 10-fold cross-validation, the model demonstrated excellent performance, with ROC-AUC values of 0.919 and 0.813 in the training and validation sets, respectively. The PR curve analysis yielded AP values of 0.929 and 0.869 for the training and validation sets, respectively (Figure 3).

Figure 3 Performance evaluation and feature analysis of the final radiomics prediction model. (A) ROC curves of the model in the training and validation sets, with the AUC values labeled. (B) Calibration curves of the model in the training and validation sets, demonstrating the consistency between predicted probabilities and actual observed outcomes. (C) PR curves of the model in the training and validation sets, with the AP values labeled, evaluating performance in imbalanced datasets. (D) Feature importance plot showing the coefficients of the six radiomics features included in the final model, with positive values indicating a positive association with the outcome and negative values indicating a negative association. AP, average precision; AUC, area under the curve; PR, precision-recall; ROC, receiver operating characteristic.

Development and evaluation of a combined clinical-radiomics model

To balance model interpretability with the ability to detect nonlinear interactions, both LR and RF algorithms were selected: the LR model was used for nomogram construction and direct interpretation of feature contributions, whereas the RF model was used to capture nonlinear relationships among features for subsequent SHAP-based interaction analysis. Age, T stage, and the six selected radiomics features were used as inputs to five machine learning algorithms to construct integrated predictive models (Table 3). After 10-fold cross-validation, the LR algorithm achieved an AUC of 0.907 (95% CI: 0.844–0.960) in the training cohort and 0.868 (95% CI: 0.766–0.957) in the validation cohort. The calibration curves of all models were close to the 45° diagonal line. The LR model achieved the highest accuracy in the validation cohort and showed higher net benefit than the “treat all” and “treat none” strategies across a threshold probability range of 0.15–1.0 (Figure 4). Comparative performance metrics for the integrated, clinical, and radiomics models are summarized in Table 4. DeLong’s test showed an AUC difference of 0.074 between the integrated model and the clinical model (P=0.06). The AUC difference between the integrated model and the radiomics model was positive but not statistically significant (P=0.14). The integrated model achieved an accuracy of 0.800, recall of 0.833, and F1 score of 0.833, compared with 0.760, 0.767, and 0.793, respectively, for the radiomics model. In addition, the RF model achieved an AUC of 0.839 (95% CI: 0.755–0.905) in the training cohort and 0.857 (95% CI: 0.750–0.949) in the validation cohort, and was used for subsequent SHAP analysis and Friedman’s H-statistic to explore nonlinear feature interactions. Further details on the machine learning algorithms are provided in Tables S1,S2.

Figure 4 Performance evaluation of five machine learning models for predicting clinical outcomes. (A,B) ROC curves and AUC values in the training and validation sets, respectively. (C,D) Calibration curves to assess the consistency between predicted probabilities and actual observed frequencies in the training and validation sets. (E,F) PR curves for evaluating model performance in imbalanced datasets in the training and validation sets. (G,H) DCA curves to quantify the net clinical benefit of each model across different threshold probabilities in the training and validation sets. AP, average precision; AUC, area under the curve; DCA, decision curve analysis; LightGBM, light gradient boosting machine; PR, precision-recall; ROC, receiver operating characteristic; XGBoost, extreme gradient boosting.

To decipher the biological patterns captured by the models, SHAP analysis was performed on the LR (Figure 5A-5F) and RF (Figure 6A-6F) models. The feature importance plot showed that original_shape_Maximum2DDiameterRow and wavelet-LLL_glcm_InverseVariance had high mean absolute SHAP values (Figures 5A,6A). In the RF model, the SHAP value distributions of these two features exhibited greater dispersion (Figures 5B,6B). The importance and SHAP dispersion of log-sigma-3-0-mm-3D_glszm_GrayLevelNonUniformity were higher in the RF model than in the LR model (Figures 5B,6B). The decision plot showed crossing of decision paths in the LR model, particularly at the variable wavelet-LLL_glcm_InverseVariance and T stage (Figure 5C). The RF model displayed less crossing of decision paths (Figure 6C). In the LR model, patients with high wavelet-LLL_glcm_InverseVariance values and high T stage were more prone to misclassification (Figure 5D-5F). The PDP of the RF model showed that both original_shape_Maximum2DDiameterRow and wavelet-LLL_glcm_InverseVariance exhibited nonlinear marginal effects, with thresholds near X ≈−1 and X ≈−1.5, respectively; beyond these thresholds, the contribution of the features to the prediction increased (Figure 6D,6E). Age showed a nonlinear negative correlation with the model’s predicted probability (Figure 6F). Friedman’s H-statistic indicated the following pairwise interactions in the RF model (Figure 7): original_shape_Maximum2DDiameterRow and log-sigma-3-0-mm-3D_glszm_SmallAreaEmphasis (H=0.136); original_shape_Maximum2DDiameterRow and T stage (H=0.109); original_shape_Maximum2DDiameterRow and Age (H=0.101); and Age and T stage (H=0.100).

Figure 5 SHAP interpretability analysis of the LR model. (A) Feature importance plot: The mean absolute SHAP value was applied to quantify the contribution of each radiomics and clinical feature to model prediction, with Orig_Max2DRow and WLLL_InverseVariance identified as the two core features with the highest predictive contribution. (B) SHAP summary (bee swarm) plot: each dot represents an individual patient sample. The dot color encodes the feature value (red for high, blue for low), and the X-axis denotes the SHAP value (positive values indicate that higher feature values increase the risk of positive prediction, while negative values indicate the opposite), intuitively illustrating the association between feature values and model prediction contribution, as well as inter-sample heterogeneity. (C) SHAP global decision plot: each line represents the decision path of one sample, starting from the baseline (average predicted value of all samples), and the final predicted probability (X-axis) is obtained by accumulating the SHAP contributions of each feature. Blue lines correspond to samples with true negative outcomes, and red lines correspond to samples with true positive outcomes. (D-F) Representative individual decision plots of the LR model, demonstrating the feature contributions of three samples with distinct prediction performances: (D) excellent prediction sample [Prob =0.990, true positive outcome, f(x)=4.956], where red blocks represent positive contributions to positive prediction and blue blocks represent negative contributions; (E) uncertain prediction sample [Prob =0.503, true negative outcome, f(x)= −0.135]; (F) poor prediction/misclassified sample [Prob =0.945, true negative outcome, f(x)=2.698], revealing that high WLLL_InverseVariance and high T stage are the core driving factors for model misclassification. Log_GrayLevelNonUniformity, log-sigma-3-0-mm-3D_glszm_GrayLevelNonUniformity; Log_IQR, log-sigma-3-0-mm-3D_firstorder_InterquartileRange; Log_SmallAreaEmphasis, log-sigma-3-0-mm-3D_glszm_SmallAreaEmphasis; LR, logistic regression; Orig_Max2DRow, original_shape_Maximum2DDiameterRow; Orig_Mean, original_firstorder_Mean; Prob, probability; SHAP, SHapley Additive exPlanations; T, tumor; WLLL_InverseVariance, wavelet-LLL_glcm_InverseVariance.

Figure 6 SHAP interpretability analysis of the RF model. (A) Feature importance plot: The mean absolute SHAP value was used to quantify the contribution of each radiomics and clinical feature to model prediction, showing the ranking of feature contributions. (B) SHAP summary plot: each dot represents one sample in the training set (n=114). The dot color corresponds to the feature value (red for high; blue for low), and the X-axis indicates the SHAP value, illustrating the association between feature values and model prediction contribution, as well as inter-sample heterogeneity. (C) SHAP global decision plot: each line represents the decision path of one sample, starting from the baseline (average predicted value of all samples), and the final predicted probability is obtained after accumulating the SHAP contributions of each feature. Blue lines correspond to samples with true negative outcomes, and red lines correspond to samples with true positive outcomes. (D-F) SHAP dependence plots (training set, n=114) demonstrating the marginal effects of core features: gray dots represent individual samples, the red line is the LOWESS fitting curve, the pink area is the 95% CI, the histogram at the bottom shows the distribution of feature values, and the color bar on the right indicates the predicted probability of each sample. (D) Dependence plot of Orig_Max2DRow; (E) dependence plot of WLLL_InverseVariance; (F) dependence plot of age. CI, confidence interval; Log_GrayLevelNonUniformity, log-sigma-3-0-mm-3D_glszm_GrayLevelNonUniformity; Log_IQR, log-sigma-3-0-mm-3D_firstorder_InterquartileRange; Log_SmallAreaEmphasis, log-sigma-3-0-mm-3D_glszm_SmallAreaEmphasis; LOWESS, locally weighted scatterplot smoothing; Orig_Max2DRow, original_shape_Maximum2DDiameterRow; Orig_Mean, original_firstorder_Mean; RF, random forest; SHAP, SHapley Additive exPlanations; T, tumor; WLLL_InverseVariance, wavelet-LLL_glcm_InverseVariance.

Figure 7 Heatmap of feature interaction strength (Friedman H-statistic) for the RF model. This heatmap quantifies the interaction strength between radiomics and clinical features using the Friedman H-statistic. Each cell in the heatmap presents the H-statistic value for the corresponding pair of features, where darker color indicates a larger H value and stronger feature interaction. The diagonal entries represent the interaction of a feature with itself (H=0.0000). Classification criteria for H-statistic interaction strength: According to commonly accepted criteria: H<0.1 indicates a weak interaction, 0.1≤ H <0.2 indicates a moderate interaction, and H ≥0.2 indicates a strong interaction. Log_GrayLevelNonUniformity, log-sigma-3-0-mm-3D_glszm_GrayLevelNonUniformity; Log_IQR, log-sigma-3-0-mm-3D_firstorder_InterquartileRange; Log_SmallAreaEmphasis, log-sigma-3-0-mm-3D_glszm_SmallAreaEmphasis; Orig_Max2DRow, original_shape_Maximum2DDiameterRow; Orig_Mean, original_firstorder_Mean; RF, random forest; T, tumor; WLLL_InverseVariance, wavelet-LLL_glcm_InverseVariance.

Construction of the clinical nomogram

Using the six features selected via LASSO regression, the Rad-score was calculated as follows: Rad-score = 0.6140 + 0.0718 × log-sigma-3-0-mm-3D_glszm_SmallAreaEmphasis − 0.0475 × log-sigma-3-0-mm-3D_glszm_GrayLevelNonUniformity + 0.1986 × original_shape_Maximum2DDiameterRow + 0.1639 × log-sigma-3-0-mm-3D_firstorder_InterquartileRange + 0.1440 × diagnostics_Image-original_Mean + 0.1995 × wavelet-LLL_glcm_InverseVariance.

Pearson correlation analysis showed no significant correlations among Rad-score, T stage, and age (Figure S2). To enhance clinical applicability and interpretability, a simplified LR model was constructed based on the core variables of the optimal machine learning LR model, and a clinical nomogram was developed (Figure 8). The regression coefficients in this simplified model were −0.04 for age, 1.29 for T stage, and 7.45 for Rad-score. In the validation cohort, the simplified model achieved an AUC of 0.846 (95% CI: 0.820–0.861), an accuracy of 0.759 (95% CI: 0.660–0.820), a precision of 0.885 (95% CI: 0.842–0.923), and a Brier score of 0.170.

Figure 8 Clinical nomogram based on Rad-score, age, and T stage. GCPM, gastric cancer peritoneal metastasis; Prob, probability; T, tumor.

Discussion

Peritoneal metastasis is a frequent mode of progression in gastric cancer, often occurring even after curative resection. However, when conventional CT shows no definite signs of peritoneal spread—i.e., in patients with OPM—the diagnosis is frequently missed or delayed, leading to understaging in approximately 30–40% of cases and necessitating invasive laparoscopic exploration. In this study, we developed a radiomics model integrating CT features from the primary tumor with clinical data and performed internal validation, aiming to explore the potential of a non-invasive approach for preoperative prediction of OPM in gastric cancer patients with negative conventional CT findings. The model showed consistent performance across training and validation cohorts, suggesting successful integration of radiomics and clinical features. If confirmed in future external validation, this approach may ultimately help avoid unnecessary laparoscopy in low-risk patients and guide individualized treatment in high-risk patients.

Numerous studies have investigated the association between radiomics features and metastasis in solid tumors (28). Chen developed a multimodal model using CT and clinical factors to predict OPM in locally advanced gastric cancer, demonstrating robustness across multiple independent cohorts (AUC: 0.834–0.857) and revealing a potential association between local immune infiltration and radiomics features related to GCPM (15). Sun et al. constructed a model using non-invasive radiomics features of peritoneal recurrence to predict chemotherapy benefit after gastric surgery, achieving effective patient stratification and demonstrating good accuracy in training, validation, and test cohorts with AUC values of 0.732, 0.721, and 0.728, respectively (29). Ding et al. integrated radiological and clinical data to predict peritoneal cytology positivity in gastric cancer patients, achieving AUC values of 0.823–0.883 across training, validation, and prospective cohorts (30). These studies highlight the potential of radiomics in building predictive models. In our study, the machine learning-based LR model achieved an AUC of 0.907 in the training cohort and 0.868 in the validation cohort; the RF model yielded an AUC of 0.839 in the training cohort and 0.857 in the validation cohort. Additionally, the simplified nomogram achieved an AUC of 0.846 on the validation set. Compared with these studies, our work not only achieved comparable or higher AUC values but also provided model interpretability via SHAP analysis and quantified feature interactions using Friedman’s H-statistic, offering insights into the underlying biology of peritoneal metastasis.

OPM is a major determinant of poor prognosis in gastric cancer patients, especially because it is undetectable on routine imaging. Previous studies have identified age, T/N staging, and tumor markers (CEA, CA19-9, and AFP) as clinical risk factors for gastric cancer metastasis (31). Research indicates that serum CEA is significantly associated with poor prognosis in gastric cancer patients, while elevated serum CA19-9 and CEA levels serve as important predictors of peritoneal cancer development (32-34). The “seed and soil” theory posits that peritoneal metastasis relies on interactions between cancer cells (seed) and the peritoneal microenvironment (soil), including exosome-mediated remodeling and cellular interaction networks (35-37). However, OPM is not visible on conventional imaging. Therefore, incorporating established clinical risk factors into radiomics models may help capture the subtle relationship between tumor biological behavior and the likelihood of occult peritoneal dissemination. The integration of clinical and radiomics features enhances understanding of gastric cancer tumor heterogeneity and its surrounding microenvironment in the context of OPM.

Using LASSO analysis, we selected six radiomics features from an initial set of 957, including two original image features, one wavelet-transformed feature, and three log-sigma-3-0-mm-3D filtered features. At the morphological level, original_shape_Maximum2DDiameterRow reflects the maximal two-dimensional growth extent of the tumor. Larger values of this feature suggest a broader infiltration range of the tumor lesion and deeper invasion into the gastric wall, which may increase the likelihood of penetrating the serosal layer and seeding peritoneal metastasis (38,39). At the macroscopic imaging level, diagnostics_Image-original_Mean represents the overall mean CT value within the tumor region, potentially correlating with tumor cell proliferative activity and stromal component distribution. Meanwhile, wavelet-LLL_glcm_InverseVariance primarily measures the global gray-level homogeneity and macro-structural regularity of the tumor (40). This study found that a high value of this feature was associated with an increased risk of peritoneal metastasis. This seemingly counterintuitive result may be explained as follows: macroscopic gray-level homogeneity and structural regularity are often observed in diffusetype gastric cancer. Although such cancers lack a distinct mass contour and appear “homogeneous” macroscopically, they are highly aggressive with diffuse infiltrative growth, thereby potentially predisposing to occult peritoneal dissemination. Therefore, this feature may be regarded as an imaging phenotype marker of highly invasive gastric cancer (41-43). Notably, diffuse-type gastric cancer is often composed of numerous signet-ring cells at the microscopic level, with low differentiation and disorganized arrangement. At the microscopic heterogeneity level, three features derived from log-sigma-3-0-mm-3D filtering—glszm_SmallAreaEmphasis, glszm_GrayLevelNonUniformity, and firstorder_InterquartileRange—capture subtle structural disorder within the tumor. Elevated values of these three features collectively suggest the presence of numerous small cellular foci, highly uneven gray-level distribution, and marked local density differences within the tumor, reflecting fragmented local architecture, heterogeneous cell proliferation, and extensive micro-necrosis or micro-infiltration. These microscopic alterations may further enhance tumor invasiveness and thereby promote peritoneal metastasis. Of note, Pearson correlation analysis showed no significant correlations between Rad-score and age or T stage (Figure S2), indicating that the radiomics features provided information independent of traditional clinical factors, further supporting their incremental value in the predictive model.

Regarding the RF model, Friedman’s H-statistic indicated four moderate-strength interactions between feature pairs. The interaction between original_shape_Maximum2DDiameterRow and log-sigma-3-0-mm-3D_glszm_SmallAreaEmphasis (H=0.136) suggests that larger tumors not only have a broader extent of gastric wall invasion but are also more likely to develop small cellular foci internally or at the margins. The interaction between original_shape_Maximum2DDiameterRow and T stage (H=0.109) implies that, for patients with the same T stage, a larger maximum tumor diameter indicates wider horizontal extension within the gastric wall, increasing the area of serosal involvement and the chance of cancer cell shedding. Conversely, for tumors of the same maximum diameter, a deeper T stage indicates a higher likelihood of serosal breakthrough. The interaction between original_shape_Maximum2DDiameterRow and age (H=0.101) may reflect two potential mechanisms: on one hand, older patients may experience diagnostic delay, leading to larger tumor volumes; on the other hand, age-related host factors, such as declined immune function and reduced peritoneal clearance capacity, may amplify the impact of tumor burden on metastasis. The interaction between age and T stage (H=0.100) may arise from confounding factors in clinical practice: older patients often receive more conservative preoperative evaluation or treatment, which may result in diagnosis at a more advanced T stage. Additionally, while the biological behavior of tumors in elderly patients may exhibit certain indolent features, there may also be a stronger propensity for local invasion. Although the interaction strengths were moderate (H=0.100–0.136), they suggest non-additive synergistic relationships among these variables, indicating that tumor size, age, and T stage should not be treated as independent factors when assessing OPM risk in CT-negative patients.

This study has several strengths. First, the complementary use of LR and RF allowed both interpretable linear relationships (for nomogram construction) and nonlinear feature interactions (relevant to OPM) to be captured. Second, the integrated LR and RF models achieved validation AUCs of 0.868 and 0.857, respectively, significantly outperforming the clinical model (AUC =0.797), with good calibration and net benefit, confirming that primary-tumor CT radiomics features provide incremental value over clinical baselines. Third, whole-tumor 3D segmentation combined with machine learning-based feature extraction fully leveraged latent image information, and the six selected radiomics features showed clear biological interpretability in the OPM context. Fourth, SHAP analysis revealed nonlinear effects, individual decision paths, and moderate feature interactions (H=0.100–0.136), offering transparent and verifiable explanations of model predictions. Fifth, the simplified nomogram achieved a test AUC of 0.846 in internal validation, suggesting potential utility for rapid outpatient risk assessment, although this requires prospective evaluation. The nomogram and the LR/RF models represent complementary approaches that could be considered for future clinical integration following external validation.

To guide clinical practice, we predefined acceptable performance thresholds based on the intended use scenario: a sensitivity of at least 80% to avoid missing OPM cases that would otherwise be understaged, and a specificity of at least 70% to meaningfully reduce unnecessary staging laparoscopies (15,44,45). Both the LR and RF models exceeded these benchmarks in the test set (LR: sensitivity =0.833, specificity =0.750; RF: sensitivity =0.833, specificity =0.800), with negative predictive values of 0.750 and 0.762, respectively. DCA further confirmed positive net benefit across clinically relevant threshold probabilities, supporting the models’ potential utility in preoperative risk stratification. These performance targets, however, require prospective validation in real-world multicenter settings before definitive clinical adoption.

Several limitations should be acknowledged. First, potential verification bias and selection bias may coexist. The reference standard was applied only to CT-negative patients, not to CT-positive individuals; combined with the single-center retrospective design, this may introduce selection bias and limit the generalizability of our findings. Second, the limited total sample size (n=164) may affect model stability and the reliability of interaction detection, especially for the OPM subgroup. Although regularization and cross-validation were applied to reduce overfitting, the small event count raises the risk of over-optimistic internal performance, which necessitates cautious interpretation and future external validation. Third, heterogeneity in CT acquisition parameters—including scanner manufacturers, imaging protocols, and reconstruction settings—may introduce technical variability across different institutions, despite standardized preprocessing. Fourth, the clinical model included only age and T stage; other potential predictors such as serum biomarkers or inflammatory indices were not incorporated, which might further improve OPM risk stratification. Fifth, SHAP analysis explains model behavior rather than causal mechanisms, so the inferred associations should be interpreted with caution. Sixth, no universally accepted threshold exists for interpreting Friedman’s H-statistic; therefore, biological conclusions regarding interactions, particularly those with H values around 0.1, should be drawn cautiously. Taken together, further multi-center, large-scale cohort studies are needed to validate the above findings specifically for OPM.

Conclusions

This study developed and internally validated a machine learning model integrating CT radiomics and clinical features for preoperative prediction of OPM in CT-negative gastric cancer patients, with SHAP analysis revealing biological insights and nonlinear feature interactions. The model demonstrated promising internal performance as a potential non-invasive risk stratification tool, although prospective multicenter external validation is required before clinical implementation.

Acknowledgments

We express our appreciation to Qingdao University Affiliated Hospital for supplying clinical patient data. This research was independently conducted and written by our team. We hereby state this explicitly.

Footnote

Reporting Checklist: The authors have completed the TRIPOD reporting checklist. Available at https://jgo.amegroups.com/article/view/10.21037/jgo-2026-0509/rc

Data Sharing Statement: Available at https://jgo.amegroups.com/article/view/10.21037/jgo-2026-0509/dss

Peer Review File: Available at https://jgo.amegroups.com/article/view/10.21037/jgo-2026-0509/prf

Funding: The study was supported by the National Natural Science Foundation of China (No. 81802888), the Key Technology Research and Development Program of Shandong (No. 2018GSF118088), the General Financial Grant from the China Postdoctoral Science Foundation (No. 2016M592143), and the Weifang Municipal Health Commission (No. WFWSJK-2023-218).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://jgo.amegroups.com/article/view/10.21037/jgo-2026-0509/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. This clinical study was approved by the Ethics Committee of The Affiliated Hospital of Qingdao University (approval No. QYFYWZLL30180), which waived the requirement for informed consent owing to its retrospective design.

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

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