The primary training dataset was obtained by collecting all 2010–2019 gastric cancer patient data from the Surveillance, Epidemiology, and End Results (SEER) database. The SEER database is the most detailed publicly available cancer database. Moreover, we collected the clinical data of MDGA patients treated at the Second Affiliated Hospital of Nanchang University between 2008 and 2010 as an external validation dataset. The inclusion criteria were as follows: 1) had a diagnosis of MDGA, 2) did not receive preoperative radiotherapy or immunotherapy, and 3) had comprehensive and searchable prognostic data. The exclusion criteria were as follows: 1) patients whose primary tumor was not gastric cancer, 2) patients whose tumor and lymph node status were not clear, and 3) patients whose other basic information was incomplete. The specific data selection steps are illustrated below in Figure 1 .

Variables in the present study included age, TNM stage, primary site, tumor size, sex (male or female), and two therapeutic variables (chemotherapy and radiation) obtained from the diagnostic information, as well as several lymph node indicators. Multiple lymph node indicators included the number of Reg LNs, number of all LNs, number of Reg LNs, number of Neg LNs, gross LN metastasis, LN positivity rate, log odds of metastatic LNs, and lymph node ratio (number of metastatic LNs to total number of LNs examined).

OS and CSS are the main outcomes for predicting the prognosis of patients with DM. In OS, deaths due to any cause will be counted, while in CSS analysis, only deaths due to MDGA will be considered events, and deaths due to other factors as well as survival will be excluded.

The research procedure is illustrated in Figure 2 . Heatmapping was first developed to correlate the proposed study variables. We use regression analysis and machine learning for dual validation of risk factors; regression analysis is performed using the full SEER data, and machine learning uses the training set, the test set, and the external validation set to construct predictive models. Independent risk factors influencing DM in moderately differentiated gastric adenocarcinoma patients were screened by logistic regression analysis. The outcomes are expressed as hazard ratios (HRs) and 95% confidence intervals (CIs). The patient data screened from the SEER dataset were randomized 7:3 into a training set and a test set. Then, the training set will be utilized to build the predictive model. The constructed predictive models are then tested and evaluated using the test set data. We constructed nine ML algorithms in the training set, including RF (random forest), LR (logistic regression), LASSO (least absolute shrinkage and selection operator), SVM (support vector machine), KNN (K-nearest neighbor), NBC (naive Bayes classifier), and ANN (artificial neural network). The receiver operating characteristic (ROC) curve, the area under the ROC curve (AUC), sensitivity, specificity, F1 score, and accuracy were used to compare the performance of the models. Additionally, the predictive models were evaluated and validated using test set data. Self-collected hospital patient data were used as an external validation set to validate the best predictive model that assessed the generalization ability of the model.

We used several R packages in R for data analysis and visualization. The createDataPartition function of the caret package was used for grouping the training and validation sets. The imp function of randomForest package was used to construct the importance scores of RF. The coords function of the pROC package was used to construct the confusion matrix. The randomForest package, the MASS package, the rms package, the glmnet package, the e1071 package, the xgboost package, the adabag package, and the neuralnet package were all used for machine learning model construction. The MASS package, rms package, glmnet package, e1071 package, xgboost package, adabag package, and neuralnet package were used for the construction of machine learning models. The ggplot package and pROC package were used for the visualization of ROC curves and importance scores.

For survival prognostic analyses, single-variable Cox regression analysis was first adopted to screen the relevant variables that could influence the prognosis (P < 0.05), and then multifactorial analyses were carried out on the screened variables. Moreover, we used the Kaplan−Meier curves to assess the differences in survival prognosis among patients stratified by different variables and compared the results by means of the log-rank test. The independent risk factors identified through Cox regression analysis were used to construct the nomogram. Moreover, using multifactor Cox regression analysis, the regression coefficients β (coe β) for each variable were normalized and are displayed as risk scores on the nomograms. The accuracy and discriminatory power of the generated nomograms were assessed with the AUC, calibration curves, and consistency index (C-index). In addition, we evaluated the clinical value of the nomograms by using decision curve analysis (DCA). This is a commonly used measure to assess model validity by quantitatively estimating the net effectiveness under the exposure threshold.

Finally, the impact of multiple nuanced tumor-associated LN indicators on the development of DM in MDGA patients was investigated by logistic regression analysis of patient data collected at our institution, as well as factors affecting patient prognosis. For descriptive statistics, categorical variables were compared using the chi-square test or Fisher’s exact probability method. P <0.05 indicated statistical significance.

The use of patient data in this research has been authorized. The approval document from the Ethics Committee is shown in the attachment. Patients from the SEER database provided consent for open research in any scientific study worldwide.

Altogether, 5,377 patients from the database were included in this study; 749 (13.93%) had DM, and 4,628 (86.07%) had no DM. The local patient dataset, which served as an external validation set, included a total of 109 patients, of whom 15 (13.76%) had DM and 94 (86.24%) had no DM. The patient data screened from the SEER dataset were randomized 7:3 into training and testing sets. The results of the analyses, as shown in Table 1 , show the comprehensive demographic and clinical characteristics of the three groups of MDGA patients. Additionally, there were no statistically significant differences (P > 0.05) in any of the clinical characteristics analyzed, such as tumor size, primary site, TNM stage, or number of Reg LNs, between the patients in the training and testing sets.

Pearson correlation analysis was used to examine the relationship between each variable ( Figure 3A ). Moreover, with the comprehensive consideration of the type of data, distribution characteristics, and other factors, all the variables are independent and well-distributed and can be included in the following statistical analysis. By multifactorial logistic regression analysis, this study revealed that six variables were statistically significant in predicting the occurrence of DM in patients with MDGA ( Table 2 ). These included the T and N stages, but the M stage seemed to be not significantly different. Other variables included primary site, tumor size, number of Reg LNs, and chemotherapy. In addition, the importance scores from the random forest model indicated variable significance (as displayed in Figure 3B ). The number of Reg LNs, N stage, T stage, chemotherapy, age, tumor size, and primary site were positively related to the occurrence of DM in MDGA patients. Specifically, the outcome was the same as the findings of the former correlation analyses, except for age. With distant metastasis as the outcome variable, we conducted single- and multiple-factor logistic regression analyses on eight factors: primary site, tumor size, age, sex, T stage, N stage, number of positive LNs, and chemotherapy. Multiple factor regression was performed, and step-forward analysis revealed that the P-values for T stage, N stage, primary site, number of positive LNs, tumor size, and chemotherapy were less than 0.05 and were considered statistically significant independent risk factors. The results of forward regression analysis indicated the meaningful impact of six variables on distant metastasis: sex, T stage, N stage, primary site, tumor size, and number of positive LNs (the detailed results are presented in the Supplementary Material ).

This research used nine distinct machine learning models individually to construct a distant metastasis prediction model for MDGA patients. The built models were trained with data from the training set. The symptoms were finely tuned to stabilize the models and prevent them from overfitting.

Table 3 and Figure 4A present the evaluation standards for each model comparison, including ROC curves, specificity, sensitivity, accuracy, recall, and F1 score. Based on the comparison results, it is concluded that the random forest model has the highest predictive value. Its AUC (0.913), specificity (0.891), and accuracy (0.880) were the best among the nine models. The results in the testing set verified this point again. The AUC of the ROC curve for the RF model was 0.848 ( Figure 4B ), which was noticeably superior to those of the other eight models. Finally, the RF models were externally validated using our 109 hospital patients (AUC = 0.728) ( Figure 4C ). We also made an aggregation of the previous ROC curves ( Figure 4D ). In summary, we trained eight machine learning prediction models with data from the training set. Through the experimental results of the test set and validation set, it was determined that the RF model has a relatively accurate ability to predict the risk of DM in MDGA patients and has high clinical value.

The 749 eligible MDGA patients with DM were randomized into two groups in the same 7:3 split. The training set included 524 patients, while the testing set included 225 patients. In terms of clinical characteristics, 40–60 years of age was the most common age for distant metastasis according to the MDGA (55.41% according to the SEER data), and the highest proportion of distant metastases according to the MDGA originated in cardia (42.86% according to the SEER data). Descriptions of other clinical characteristics are summarized in the accompanying table ( Table 4 ). The results suggested that no statistically significant differences were found between the basic information of the two datasets.

Using OS and CSS as prognostic endpoints, we performed univariate and multivariate Cox regression analyses on data from eligible patients screened from the SEER database. Nine variables were included in the univariate analysis, and the detailed results are shown in the left half of Tables 5 and 6 . Afterward, according to the outcome, statistically significant variables were included in the multivariate analyses.

The Cox regression results for OS are shown in Table 5 . The detailed outcomes suggested that age, T stage, primary site, chemotherapy, radiation, and the number of Reg LNs were correlated with OS in MDGA patients. Multifactorial analysis for OS revealed that only T stage (2 and 3), primary site, chemotherapy, and number of Reg LNs were statistically significant independent risk factors for MDGA patients with established DM. Moreover, patients with higher T stages (T3 and 4) and without chemotherapy had significantly shorter survival and worse outcomes. Patients with superficial primary sites (gastric antrum and greater curvature) and a greater number of Reg LNs could have improved outcomes. More comprehensive OS analysis information, such as the analytical CIs and P-values for each variable, is collated and displayed in Table 5 .

The outcome of the Cox regression analysis using CSS as the endpoint is presented in Table 6 . The primary site, number of Reg LNs, age, T stage, chemotherapy, and radiotherapy variables were integrated into the multifactorial analysis. The analysis indicated that the number of Reg LNs, T stage, primary site, and chemotherapy were considered statistically significant independent risk factors for CSS. The CIs and the corresponding P-values are summarized in Table 6 .

According to the outcomes obtained in the previous steps, this study developed a visual nomogram to predict the survival time of MDGA patients with established DM. The nomogram, derived from the prognostically relevant risk factors that have been identified, provides a score based on the patient’s current condition. Physicians can assess a patient’s probability of 1-, 3-, and 5-year OS/CSS based on this nomogram ( Figure 5 ). According to the OS nomogram ( Figure 5A ), of the five independent risk factors, chemotherapy had the greatest impact on survival, followed by the primary tumor site, while T stage had the least impact. According to the CSS nomogram ( Figure 5B ), the presence or absence of chemotherapy was considered to be the most influential factor for survival, followed by the lymph node positivity rate.

A simple example of how to use a nomogram is given below. Suppose a 60-year-old patient with distant metastases from MDGA has received conventional chemotherapy but no radiotherapy. At the same time, the pathological findings suggest that the tumor originated in the greater curvature, the current T stage is 3, and the number of regional LNs reaches more than four. At this point, an approximate score can be calculated based on the nomogram (age, 17.5 points; T stage 3, 2 points; primary site, 17 points; number of regional LNs, 11 points; received chemotherapy, 0; not received radiotherapy, 18 points). This hypothetical patient would therefore have a total score of 65.5, and this score was plotted against a scale of total scores. By plotting vertically on a straight line of survival probability, one can derive the probability that the overall survival available for reference is approximately 0.78, 0.55, and 0.45 for 1, 3, and 5 years, respectively. Similarly, the corresponding CSS for this patient can be calculated using the same steps as above.

The predictive results and clinical value of the nomograms were assessed and verified by the C-index, AUC, calibration curve, and DCA. In the training set, the AUC values for predicting 1-, 3-, and 5-year OS were 0.797, 0.807, and 0.737, respectively ( Figure 6A ), while in the validation set, they were 0.757, 0.737, and 0.718, respectively ( Figure 6B ). The C-index of the nomograms was 0.726 (95% CI, 0.703–0.748) in the training set for OS and 0.703 (95% CI, 0.663–0.744) in the validation set. The fit of the 1-, 3-, and 5-year calibration curves for predicting OS was satisfactory ( Figures 6C–H ). In the calibration curves of the nomograms in the training and validation cohorts, the red curve fit line matches the gray diagonal line (representing the predicted probability of the ideal state) to a high degree, suggesting that the predicted probability of survival via the nomograms remains generally consistent with the observed probability of survival, with no excessive overestimation or underestimation of risk. The DCA curve presented graphically in Figures 6I–N suggests that this nomogram for OS has excellent net clinical efficacy.

Similarly, the results for evaluating the CSS nomograms show a positive applicability. The C-index was 0.727 (95% CI, 0.703–0.751) for the training set and 0.705 (95% CI, 0.663–0.748) for the validation set. In addition, the AUCs of the nomograms were 0.747, 0.737, and 0.699 for 1-, 3-, and 5-year CSS, respectively, in the training cohort ( Figure 7A ), and in the validation cohort, the AUCs were 0.661, 0.713, and 0.892, respectively ( Figure 7B ). Moreover, both the calibration curves and DCA curves used for the 1-, 3-, and 5-year CSS forecasts also exhibited satisfactory fits and net gains ( Figures 7C–N ). In summary, the nomograms produced to predict the prognosis of MDGA patients with DM had considerable discriminatory and calibrating power.