Evaluating the prognostic value of tumor deposits in non-metastatic lymph node-positive colon adenocarcinoma using Cox regression and machine learning

Background The 8th AJCC TNM staging for non-metastatic lymph node-positive colon adenocarcinoma patients(NMLP-CA) stages solely by lymph node status, irrespective of the positivity of tumor deposits (TD). This study uses machine learning and Cox regression to predict the prognostic value of tumor deposits in NMLP-CA. Methods Patient data from the SEER registry (2010–2019) was used to develop CSS nomograms based on prognostic factors identified via multivariate Cox regression. Model performance was evaluated by c-index, dynamic calibration, and Schmid score. Shapley additive explanations (SHAP) were used to explain the selected models. Results The study included 16,548 NMLP-CA patients, randomized 7:3 into training (n = 11,584) and test (n = 4964) sets. Multivariate Cox analysis identified TD, age, marital status, primary site, grade, pT stage, and pN stage as prognostic for cancer-specific survival (CSS). In the test set, the gradient boosting machine (GBM) model achieved the best C-index (0.733) for CSS prediction, while the Cox model and GAMBoost model optimized dynamic calibration(6.473) and Schmid score (0.285), respectively. TD ranked among the top 3 most important features in the models, with increasing predictive significance over time. Conclusions Positive tumor deposit status confers worse prognosis in NMLP-CA patients. Tumor deposits may confer higher TNM staging. Furthermore, TD could play a more significant role in the staging system.

decision-making.The American Joint Committee on Cancer (AJCC) TNM staging system is the standard for guiding CRC treatment and prognosis [3].However, for non-metastatic lymph node-positive colon adenocarcinoma (NMLP-CA), the current AJCC guidelines do not fully capture the prognostic impact of tumor deposits (TD) [4].Emerging evidence indicates patients with both TD and lymph node metastases (LNM) have poorer outcomes compared to either condition alone [5,6].While some studies explore TD prognostic value in stage III colon cancer [7,8], this population includes N1c patients, potentially introducing bias.The prognostic role of TD specifically in NMLP-CA remains unclear.
Moreover, current research on the prognosis assessment of TD primarily relies on classical statistical models, such as Cox regression.Cox models require adherence to the proportional hazards assumption, which means that the overall quality of these models may not have reached the optimal state in some cases.Machine learning is a novel form of artificial intelligence that has found extensive application in medical data analysis, making it a potent tool for enhancing clinical strategies [9][10][11].In numerous studies where the dependent variable was categorical, machine learning has demonstrated superior prediction performance compared to traditional models [10,[12][13][14].However, few studies compare survival prediction models to assess TD in NMLP-CA, where outputs include survival status and time.It remains unclear if new machine learning models outperform Cox regression for this purpose [6,[15][16][17].Our aim is to assess the impact of TD on the prognosis of NMLP-CA and to compare traditional prognostic models with machine learning models to identify an optimal prognostic model for NMLP-CA.

Patients and data sources
This study analyzed non-metastatic lymph node-positive colon cancer patients using data from the Surveillance, Epidemiology, and End Results (SEER) registry from 2010-2019.According to the AJCC/UICC TNM7 and TNM8 staging systems, TDs are defined as cancerous nodules located in the lymph drainage area of the peritumoral fatty tissue, characterized by the histologically proven absence of residual lymphatic tissue and regional lymph node metastasis [18][19][20].The defining features of TDs include their proximity to the main tumoral front, size, and the absence of a lymphoid rim and fibrous capsule, rather than the presence of lymphoid structures or lymph nodes within the surrounding adipose tissue [21].Inclusion criteria were as follows: (1) colon cancer as the sole primary tumor with pathologically confirmed adenocarcinoma; (2) availability of demographic variables, including age, sex, marital status, and race; (3) access to clinical pathological information, encompassing tumor site, TNM staging, histological grade, TD, and specific treatment details; (4) acquisition of survival time and survival status.The exclusion criteria included the following: (1) patients with other primary malignant tumors; (2) patients who did not undergo surgery and chemotherapy; (3) patients with distant metastasis or regional lymph node negativity; (4) individuals with incomplete follow-up information; (5) patients with less than 1-month postoperative survival, in order to minimize confounding from surgical mortality.In this study, The primary outcome was cancer-specific survival (CSS), measured from diagnosis to cancer-related death.Figure 1 illustrates the data selection process.In accordance with the Equator Network guidelines, we followed the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) guidelines for this study.

Establishment of predictive model
This study performed a comparative analysis of clinicopathologic characteristics from the SEER database and assessed prognostic factors via univariate and multivariate logistic regression.Six machine learning models were developed, including Cforest, gradient boosting machine (GBM), generalized linear model boosting (GLMboost), random forestSRC (Rfsrc), generalized additive model boosting (GAMboost), and deep learning survival analysis (DeepSurv).The data was split 70:30 into training and test sets.Ten-fold cross-validation tuned hyperparameters during training to ensure model stability.The best parameters for each model in the training cohort were determined by the grid search method.Model evaluation on the test set employed C-index, dynamic calibration, and Schmid score.Comparative assessment identified optimal techniques for predicting prognosis in this cohort.

Statistical analysis
Data extraction from SEER utilized the SEER*Stat software (version 8.4.2).Analysis was performed in R (version 4.3.1).Continuous variables were analyzed by Wilcoxon rank-sum test, while categorical variables used chi-squared or Fisher's exact test.Univariate and multivariate logistic regression assessed the prognostic value of TDs at a significance level of p < 0.05.Adjusted odds ratios (OR) and 95% confidence intervals (CI) were computed.
The modeling process was implemented using the mlr3 package (version 0.16.1) in R. We tested the training set with Cox, Cforest, GBM, GLMboost, Rfsrc, GAMboost, and Deepsurv to establish prediction models.Additionally, Shapley additive explanations (SHAP) were utilized to interpret these models [22,23].SHAP is a model interpretation package developed in R that can explain the output of any machine-learning model.Permutation importance was calculated using the survex package (version 1.1.3)in R.

Baseline characteristics
This study analyzed 572,367 colon cancer patients from the SEER database between 2010 and 2019.After applying exclusion criteria, 16,548 patients remained.Figure 1 displays the data screening flowchart.The baseline characteristics of the patients are summarized in Table 1.After screening, the median follow-up time for patients was 51 months (range 1-119).The data was randomized 7:3 into training (n = 11,584) and testing (n = 4964) sets.No significant differences or survival discrepancies (p = 0.96) existed between the sets.

Univariable and multivariable Cox regression analysis
Univariate analysis identified age, race, marital status, primary site, TD, AJCC pT/N stage, grade, and sex as variables significantly influencing CSS (Table 2).Kaplan-Meier analysis demonstrated worse survival for patients with positive versus negative tumor deposits (p < 0.001) (Fig. 2a).Subgroup analyses revealed TD may respectively impact survival across T and N stages.Survival for T1 + 2 TD positive patients resembled T3 + 4 TD negative patients, while N1 TD + patients resembled N2 TD patients (Fig. 2b and c).These findings suggest TD may confer higher TNM staging and portend worse prognosis, despite not being incorporated in the current 8th edition AJCC guidelines.Multivariable Cox regression confirmed positive TD as an independent predictor of worse CSS, alongside age > 60 years, unmarried status, right-sided tumors, advanced T/N stage, and poor Grade (Fig. 3).A prognostic nomogram for 6-, 12-, and 24-month CSS was constructed using the Cox model (Fig. 4).Model discrimination assessed by the C-index was 0.717.3).GBM achieved the best cindex (0.733), Cox had optimal dynamic calibration (6.473), and GAMBoost maximized the overall performance of the Schmid score (0.285).Thus, GBM, Cox, and GAMBoost were chosen for further analysis.

Establishing and evaluating predictive models for estimating the prognosis
SHAP values demonstrated time-varying feature importance (Fig. 5).For GBM, T and N stage importance increased then decreased over time, while TD importance steadily rose.Grade and age remained relatively stable (Fig. 5a).Similar patterns were observed in the Cox and GAMBoost models (Fig. 5c and e), with TD significance progressively increasing.Overall, even though TD's importance is not as significant as T or N in the early stages of survival, its importance gradually increases over time and may even surpass the N stage in some models.
In the feature ranking plot (Fig. 5), within the GBM model, the T stage, N stage, and TD are the top three most important features.Age, grade, and primary site are moderately important, while marital status, race, and sex appear to be less important for the model (Fig. 5b).Similar results can be observed in the Cox model (Fig. 5d).In the GAMboost model, T stage, N stage, and TD are the three most important features, followed by grade and age.Primary site, marital status, and other features have lower importance (Fig. 5f).This analysis demonstrates that, overall, TD is the third most important factor for the survival prediction of colon patients in all three models.
As shown in the partial dependence plots (Figs. 6, 7, and 8), all models show minimal survival impact of age, race, sex, and primary site.And higher histological grade emerges as a key differentiator of diminished prognosis.AJCC pT and pN stage stratification were also proved influential, alongside positive TD status being associated with poorer outcomes.However, distinctions arise in time-varying prognostic effects.The GBM model reveals dynamic relationships, with fluctuating TD significance and greater discrimination by AJCC pT and pN stage over time (Fig. 6).In contrast, the Cox and GAMBoost models demonstrate more static prognostic patterns for tumor factors (Figs. 7 and  8).In summary, while variable selection is aligned, GBM uniquely captures temporal shifts in the prognostic utility of pathological markers, specifically TD and histological grade.

Disscusion
Our study demonstrates TD as a highly significant prognostic indicator in NMLP-CA patients, evidenced by machine learning and Cox regression analysis.Among evaluated models, GBM, Cox regression, and GAMBoost achieved optimal predictive performance based on metrics like c-index and calibration.The prognostic value of TD indicates potential limitations in the current AJCC TNM staging system for lymph node-positive patients.By integrating TD status alongside other key predictors, our machine learning models exhibit robust generalization ability for clinical application.They provide actionable insights on survival prediction to inform prognostic awareness and treatment decision-making.
In recent years, an increasing number of articles have indicated the association between cancer deposits and the prognosis of colorectal cancer [5,6,24,25].However, most current research primarily focuses on stage III colorectal cancer, with limited studies specifically investigating the role of TD in patients with NMLP-CA.Presently, scholars tend to consider TD merely as a substage component within the TNM staging system.The 7th edition of AJCC stipulates that "regardless of the number, size, or morphology of tumor deposits when they are present without accompanying regional lymph node metastasis, patients are classified as N1c stage [4].However, when positive lymph nodes are present, only the count of positive lymph nodes is used for N staging."The 8th edition extends the definition of N1c from the 7th edition [26].The specific classification of tumor deposits in the TNM staging system remains a subject of debate.Lord et al. argue that the criteria for classifying TD under the N1c substage need adjustment, and they do not agree with the viewpoint that the presence of tumor deposits should be disregarded when positive lymph nodes are present [27].Currently, some research suggests that combining the number of tumor deposits with the number of positive lymph nodes for N staging can enhance the accuracy of colon cancer staging [28].Uneo et al. while comparing the impact of tumor deposits (TD) on T-stage categories and N-stage categories, found that the C-index confidence interval for T-staging was smaller than that for N-staging (0.6731-0.6760 vs. 0.6909-0.7167).Consequently, they proposed the inclusion of TD in N-staging [29].Mirkin et al. conducted a retrospective analysis of stage III resectable colorectal cancer using the US National Cancer Database (2010-2012).They found that there was no significant difference in survival rates between patients in the T1-4 stage with TD ( +) and LN ( −) and those with LN ( +) and TD ( −).They suggested that tumor deposits should be considered lymph nodes and included in the N-staging [6].Studies by Cohen et al. and Delattre et al. incorporated the number of TD into the lymph node count to create a new N-staging system.When comparing the prognosis of the newly restaged N2 with those initially classified as N2, both studies found similar outcomes [30,31], and our study yielded similar results: we observed that the survival curves for patients with T1/2 and positive tumor deposits were similar to those of T3/4 and negative tumor deposits.Similarly, the curves for patients with N1  stage [32].Some scholars believe that considering TD ( +) as "N3" stage may better reflect its prognostic value in colorectal cancer [27].Additionally, several studies have reported a high percentage of positive tumor deposits in node-negative (N0) cases [6,33,34].This observation is of paramount importance and warrants further investigation.Several factors may contribute to this phenomenon, including the evolving definitions and diagnostic criteria of TDs, the inherent heterogeneity of colorectal cancer, the distinct biological characteristics of TDs compared to lymph node metastases, and advancements in pathological examination techniques [35][36][37][38][39][40][41].
Machine learning can enhance survival prediction efficiency, aiding disease prognosis and clinical decision-making [42,43].Compared to traditional analysis, machine learning better handles complex multidimensional data [44].This study pioneered machine learning models using diverse prognostic features to predict the prognostic value of TD in NMLP-CA, demonstrating stable performance on test data and clinical utility.Additionally, we uniquely modeled time-varying feature importance with high accuracy, providing unprecedented insights into evolving predictor roles.Overall, this work highlights machine learning's potential for advancing colon cancer outcomes via data-driven prognostic models.
This study has some limitations.The retrospective design may introduce biases, necessitating large-scale prospective validation of our models.We did not assess modern immunotherapies and targeted therapies, which represent prominent advances in colorectal cancer treatment [45][46][47][48].Additionally, while race lacked prognostic significance in some models, our predominantly white cohort restricts generalizability across ethnicities.Moving forward, we aim to develop deep learning prognostic models by analyzing expanded, more diverse data.This could enhance risk stratification and personalized treatment for colon cancer patients.
In summary, there is currently a degree of controversy surrounding TD, from their definition to their clinical value, making it a hot topic in clinical research.Concerning clinical staging, the criteria for categorizing TD into the N1c substage may need adjustment, but there is no unified standard for including them in the T, N, or M substage.Most research results suggest that considering the combined count of tumor deposits and positive lymph nodes for N staging can improve the accuracy of colorectal cancer staging.While TD is associated with colorectal cancer prognosis, there is still no consensus on the cutoff values that define the number of tumor deposits affecting prognosis.

Conclusion
In conclusion, this study identified tumor deposits (TD) as an independent prognostic factor for non-metastatic lymph node-positive colon adenocarcinoma (NMLP-CA), evidenced by Cox regression analysis.Machine learning models GBM and GAMBoost further demonstrated the significant prognostic value of TD for NMLP-CA patient survival.Given the potential influence of TD status on TNM staging, incorporation of TD as a parameter in future AJCC guidelines could improve prognostic performance.Overall, these findings underline the   adverse impact of TD in NMLP-CA and support the expanded emphasis of TD in risk stratification for precision oncology.
Six machine learning models (cforest, GBN, GLMboost, rfsrc, GAMboost, Deepsurv) were developed to predict CSS.The data was split 7:3 into training and testing sets.Ten-fold cross-validation tuned hyperparameters and evaluated model performance on the training data.C-index (cindex), dynamic calibration (dcalib), and Schmid score (Schmid) comparisons on the test set informed the final model selection (Table

Fig. 1
Fig. 1 The inclusion criteria flowchart of recruited patients in SEER database and positive tumor deposits resembled those of N2 and negative tumor deposits, suggesting that positive tumor deposits may elevate the T/N staging of patients.In addition to the existing N substage, Pricolo et al. proposed the staging of the "N2c" substage.They recommend categorizing patients with LN ( +) TD ( +) or LN ( −) TD ( +) with three or more tumor deposits as N2c stage, and those with LN ( −) TD ( +) and two or fewer tumor deposits as N1c

Fig. 2 Fig. 3
Fig. 2 Kaplan-Meier cancer-specific survival (CSS) estimates and 95% confidence intervals for patients in groups combined with or without tumor deposit (TD) (a), groups with different T stages com-

Table 2
Univariate and multivariate analysis of overall survival in the training cohort

Table 3
Model evaluation indexs in the training and test cohort for the Cox, Cforest, GBM, GLMboost, Rfsrc, GAMboost, and Deepsurv models