A nonlinear Cox-based postoperative prognostic assessment system for gastric cancer

Abstract

This invention discloses a postoperative prognostic assessment system for gastric cancer based on a nonlinear Cox proportional hazards model, belonging to the field of medical information technology. The system includes: a data acquisition module for acquiring postoperative pathological feature data of the target subject; a nonlinear survival risk modeling module for processing the pathological feature data based on a nonlinear Cox proportional hazards model incorporating Gaussian process priors, and generating a score characterizing individualized continuous survival risk; a risk surface construction and boundary extraction module for constructing the continuous survival risk score into a three-dimensional risk surface or contour map, and extracting isorisk contour boundaries with clinically stable demarcation significance; and a prognostic result output module for mapping the continuous survival risk score to risk stratification information and outputting the prognostic assessment result. This application's solution achieves a fine characterization of the complex nonlinear coupling effect between lymph node burden and tumor invasion depth, improving the accuracy of risk estimation.

Description

Technical Field

[0001] This invention relates to the field of medical information technology, and in particular to a postoperative prognostic assessment system for gastric cancer based on nonlinear Cox. Background Technology

[0002] Gastric cancer, a leading cause of death and morbidity among digestive system malignancies worldwide, presents a significant challenge to clinical diagnosis and treatment due to its high risk of postoperative recurrence and marked heterogeneity in patient outcomes. Although radical surgical resection combined with adjuvant therapy is the current standard treatment strategy, the five-year survival rate remains below 40%, indicating considerable room for improvement in patient prognosis. Against this backdrop, establishing a precise postoperative prognostic assessment system is crucial for individualized treatment decisions and optimized follow-up management strategies. Currently, the widely used tumor lymph node metastasis staging system in clinical practice primarily stratifies patients based on tumor invasion depth, the number of regional lymph node metastases (N staging), and distant metastasis status. The core basis of N staging is the number of positive lymph nodes, which divides patients into several discrete levels using a preset counting threshold. While this staging method offers advantages such as ease of operation and standardized procedures, it essentially simplifies lymph node involvement to a static indicator grouped by counting thresholds, failing to reflect the risk gradient information inherent in the continuous changes in the number of positive lymph nodes.

[0003] To address these limitations, researchers have recently explored various methods to improve the precision of postoperative prognostic assessment for gastric cancer. On one hand, alternative indicators such as the lymph node metastasis ratio (LNR) and the log-to-digital ratio of positive lymph nodes (LODDS) have been proposed to reduce the impact of insufficient lymph node detection on staging accuracy and, to some extent, improve the efficacy of risk stratification. On the other hand, traditional survival models based on Cox proportional hazards regression and nomograms are widely used to construct multivariate prognostic prediction tools, integrating clinicopathological features to assess the survival probability of individual patients. However, existing methods still suffer from several common shortcomings: First, whether it's the traditional N-staging or LNR and LODDS, they essentially rely on preset thresholds for discretized risk grouping, transforming the continuously changing lymph node burden into a static relationship of homogeneity within strata and abrupt changes between strata, resulting in a significant loss of risk information; Second, traditional Cox models assume that the influence of covariates on survival risk is linear and that each factor is independent, making it difficult to fully characterize the complex nonlinear coupling effects that may exist between the number of positive lymph nodes, the total number of detected lymph nodes, and the depth of tumor invasion; Third, although some machine learning models can capture nonlinear relationships, their interpretability is insufficient, and problems such as inadequate validation and high risk of bias are common, limiting their clinical translational value. Therefore, based on the above challenges, this invention proposes a nonlinear Cox-based postoperative prognostic assessment system for gastric cancer. Summary of the Invention

[0004] To address the aforementioned issues, the present invention aims to provide a nonlinear Cox-based postoperative prognostic assessment system for gastric cancer. This system overcomes the limitations of traditional linear survival models, such as the loss of lymph node burden information and coarse risk gradient characterization caused by the use of discretized staging thresholds, as well as the difficulty in fitting the complex nonlinear coupling effect between tumor invasion depth and the number of lymph node metastases. The system achieves continuous and precise estimation of patient survival risk and outputs refined risk stratification with stable demarcation significance in a clinically readable manner.

[0005] To achieve the above objectives, this invention provides a nonlinear Cox regression prognostic assessment system for gastric cancer. The system first acquires the number of detected lymph nodes, the number of positive lymph nodes, and the tumor invasion depth stage as basic pathological features of postoperative gastric cancer patients. Then, based on a nonlinear Cox proportional hazards model incorporating Gaussian process priors, nonparametric adaptive fitting is performed on the above features within a Bayesian inference framework. This captures the implicit nonlinear coupling relationships between features in a data-driven manner, generating an individualized continuous survival risk score. On this basis, using the number of detected lymph nodes and the number of positive lymph nodes as continuous coordinate axes, combined with the tumor invasion depth stage, the continuous risk score is constructed as a three-dimensional risk surface or contour map. Based on the geometric features of the surface, isorisk contours with clinically stable demarcation significance are automatically identified and extracted. Finally, based on these isorisk boundaries, the continuous risk score is mapped to refined risk stratification information, which is then output as the prognostic assessment result for the target patient.

[0006] In a first aspect, the present invention provides a postoperative prognostic assessment system for gastric cancer based on nonlinear Cox regression, comprising:

[0007] The data acquisition module is used to acquire postoperative pathological feature data of gastric cancer in the target subject. The data includes at least the number of detected lymph nodes, the number of positive lymph nodes, and the grade of tumor invasion depth.

[0008] The nonlinear survival risk modeling module is used to process the pathological feature data based on a nonlinear Cox proportional hazards model that incorporates Gaussian process priors, in order to fit the implicit nonlinear coupling relationship and interaction effect between the pathological features and generate a score that represents individualized continuous survival risk.

[0009] The risk surface construction and boundary extraction module is used to construct a three-dimensional risk surface based on the number of detected lymph nodes and the number of positive lymph nodes as continuous coordinate axes, combined with the tumor invasion depth grading, and automatically identify and extract the equal-risk contour boundaries with clinical stability significance based on the three-dimensional risk surface.

[0010] The prognostic result output module is used to map the continuous survival risk score into refined risk stratification information based on the equal risk profile boundary, and output the prognostic assessment result of the target object.

[0011] Furthermore, the data acquisition module is also used to acquire the spatial distribution information of lymph node metastasis of the target object, the information including the distribution pattern of metastatic lymph nodes in different anatomical regions or lymph node stations;

[0012] The nonlinear survival risk modeling module includes a topology analysis unit, which is used to quantify the topological features of lymph node metastasis based on spatial distribution information and to nonlinearly fuse the topological features with lymph node counting features.

[0013] Furthermore, the nonlinear survival risk modeling module adopts a Bayesian inference framework and introduces a Gaussian process prior into the Cox proportional hazards model to achieve nonparametric adaptive fitting of the unknown nonlinear functional relationship between the number of detected lymph nodes, the number of positive lymph nodes and the tumor invasion depth grade.

[0014] Furthermore, the nonlinear survival risk modeling module uses a nonparametric Bayesian model based on a combination of Gaussian process regression and survival analysis. This model does not presuppose the functional form of risk changes with the number of lymph nodes, but estimates the local variation characteristics of the risk function based on data.

[0015] Furthermore, the nonlinear survival risk modeling module uses multi-center clinical cohort data to train and internally validate the nonlinear Cox proportional hazards model, and verifies the model's generalization ability through external independent cohorts, thereby ensuring that the model has stable predictive performance under different population characteristics and clinical practice scenarios.

[0016] Furthermore, the nonlinear survival risk modeling module also includes a time-series dynamic calibration unit, which is used to perform time-dependent calibration of the continuous survival risk score based on postoperative follow-up time points. The calibration generates a time-series risk score that dynamically evolves with postoperative follow-up time by introducing a decay mechanism associated with the individual's baseline risk level and a compensation mechanism to capture unknown time-varying factors.

[0017] Furthermore, the system also includes a model performance comparison and evaluation module, which is used to statistically compare the continuous survival risk score output by the nonlinear survival risk modeling module with the risk stratification performance of the traditional tumor lymph node metastasis staging system, lymph node metastasis rate and lymph node metastasis log ratio, and to quantitatively evaluate the improvement in the system's discrimination and the increase in clinical net benefit.

[0018] Furthermore, the risk surface construction and boundary extraction module, based on the geometric features of the three-dimensional risk surface, automatically identifies the boundaries of continuous regions where the risk gradient changes tend to be stable through an algorithm, and uses the boundaries as the basis for equivalent stratification in reconstructing the existing tumor lymph node metastasis staging system.

[0019] Furthermore, the three-dimensional risk surface or contour map is dynamically displayed through a graphical user interface. The graphical user interface supports interactive slice observation of the risk surface at different tumor invasion depth grading levels, thereby facilitating clinicians' intuitive understanding of the risk evolution patterns corresponding to different combinations of pathological features and enhancing the interpretability of the model.

[0020] Furthermore, the risk surface construction and boundary extraction module is also used to generate a dynamic isorisk map. The map uses the number of detected lymph nodes and the number of positive lymph nodes as continuous coordinate axes, and presents the distribution pattern of isorisk curves at different tumor invasion depth grading levels. The module also includes a gradient analysis unit, which is used to calculate the gradient change rate of the risk score in the lymph node coordinate space, and automatically identify the critical region with clinical significance based on the gradient change rate. The prognostic result output module maps the continuous survival risk score to an adaptive stratification rule according to the critical region, and outputs a prognostic assessment result containing a visualized risk map and stratification criteria.

[0021] Furthermore, the refined risk stratification information output by the prognostic result output module, while maintaining the clinical interpretation habits of the traditional staging system, enables further differentiation of risk gradients for patients with different lymph node burdens within the same traditional stage, thereby resolving the contradiction between the risk homogeneity assumption caused by the discrete threshold grouping in the traditional staging system and the actual clinical heterogeneity.

[0022] Furthermore, the system is deployed on a local computing device or a cloud server and interfaces with the hospital information system through an application programming interface to achieve real-time assessment of postoperative patient prognosis risks.

[0023] Secondly, a method for postoperative prognostic assessment of gastric cancer based on nonlinear Cox regression is also provided. This method is based on the system described in the first aspect and includes:

[0024] Obtain postoperative pathological characteristic data of gastric cancer in the target subjects, including at least the number of detected lymph nodes, the number of positive lymph nodes, and the grade of tumor invasion depth;

[0025] Based on a nonlinear Cox proportional hazards model that incorporates Gaussian process priors, the pathological feature data is processed to fit the implicit nonlinear coupling relationship and interaction effect between the pathological features, and to generate a score characterizing individualized continuous survival risk.

[0026] Using the number of detected lymph nodes and the number of positive lymph nodes as continuous coordinate axes, and combined with the tumor invasion depth grading, the continuous survival risk score is constructed into a three-dimensional risk surface or contour map, and based on the three-dimensional risk surface, isorisk contour boundaries with clinical stability demarcation significance are automatically identified and extracted.

[0027] Based on the aforementioned equal-risk profile boundary, the continuous survival risk score is mapped into refined risk stratification information, and the prognostic assessment result of the target object is output.

[0028] This invention proposes a nonlinear Cox regression prognostic assessment system for gastric cancer. Its core lies in acquiring the number of detected lymph nodes, the number of positive lymph nodes, and the tumor invasion depth grading of the target subject as basic pathological features through a data acquisition module. Then, a nonlinear survival risk modeling module, based on a nonlinear Cox proportional hazards model incorporating Gaussian process priors, performs nonparametric adaptive fitting of the implicit nonlinear coupling relationships between features within a Bayesian inference framework to generate an individualized continuous survival risk score. Subsequently, a risk surface construction and boundary extraction module uses the number of detected and positive lymph nodes as continuous coordinate axes, combined with the tumor invasion depth grading, to construct a three-dimensional risk surface or contour map of the continuous risk score. Based on the surface's geometric features, it automatically identifies and extracts isorisk contour boundaries with clinically stable demarcation significance. Finally, through the prognostic result output module, the continuous risk score is mapped to refined risk stratification information based on these isorisk boundaries, and the assessment results are output.

[0029] This scheme effectively overcomes the rigid constraints of traditional linear models on the form of risk functions and the loss of risk information caused by discretization threshold grouping by introducing a Gaussian process prior nonlinear modeling mechanism. It achieves a fine characterization of the complex nonlinear coupling effect between lymph node burden and tumor invasion depth, significantly improving the accuracy of risk estimation. By constructing a three-dimensional risk surface and automatically extracting isorisk contour boundaries, the output of the high-dimensional nonlinear model is transformed into an intuitive and clinically interpretable visualized risk distribution, achieving a seamless connection between continuous risk estimation and clinical discrete staging rules. While maintaining clinical practice, it significantly improves the refinement of risk stratification.

[0030] Beneficial effects

[0031] By implementing the nonlinear Cox-based postoperative prognostic assessment system for gastric cancer provided by the present invention, the following technical effects are achieved:

[0032] (1) A nonlinear Cox survival analysis model was constructed by introducing Gaussian process priors. The complex nonlinear coupling relationship between the number of detected lymph nodes, the number of positive lymph nodes and the tumor invasion depth grade was fitted in a nonparametric adaptive manner. This effectively overcame the modeling bias caused by the preset function form of the traditional linear model, and achieved a fine characterization of the heterogeneity of the patient's real risk, which significantly improved the accuracy of risk estimation.

[0033] (2) The continuous risk score output by the nonlinear model is constructed into a three-dimensional risk surface or contour map, and the equal risk contour boundary with clinical stability significance is automatically extracted based on the geometric features of the surface. The output of the high-dimensional nonlinear model is transformed into an intuitive and clinically interpretable visualized risk distribution, realizing the seamless connection between continuous risk estimation and clinical discrete staging rules. While maintaining the clinical practice, the precision of risk stratification is significantly improved.

[0034] (3) By introducing a time decay mechanism associated with individual baseline risk level and a compensation mechanism to capture unknown time-varying factors, a dynamic risk calibration model with time adaptability was constructed. This effectively overcomes the limitation of static prognostic models in failing to capture the nonlinear evolution of risk over time, and realizes adaptive adjustment of risk estimation at different follow-up time points after surgery, significantly improving the stability and accuracy of long-term prognostic prediction.

[0035] (4) Quantify the spatial distribution pattern of lymph node metastasis in anatomical regions or lymph node stations, and nonlinearly fuse lymph node topological features with conventional counting features. This breaks through the limitation of traditional models that rely solely on lymph node counting information, and achieves a more refined characterization of tumor biological invasion behavior. It can effectively distinguish patient subgroups that are classified into the same risk level in the conventional staging system but have significantly different actual prognoses.

[0036] (5) Generate dynamic risk maps and automatically identify critical regions with clinical significance based on the risk gradient change rate. Transform the output of complex nonlinear models into decision support information containing visualized risk maps and adaptive stratification rules, significantly enhancing the interpretability of model output. At the same time, it supports clinical experts to make localized corrections to stratification rules, improving the generalizability of the model in different medical institutions. Attached Figure Description

[0037] To make the above-described nonlinear Cox-based postoperative prognostic assessment system for gastric cancer more readily understood, the accompanying drawings used in the specific embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart illustrating the method described in this application;

[0039] Figure 2 A basic scatter plot showing the distribution of lymph node burden-related risks after gastric cancer surgery;

[0040] Figure 3 A heat map showing the continuous survival risk dimension of the number of regional lymph nodes and the number of positive lymph nodes after gastric cancer surgery;

[0041] Figure 4 A two-dimensional risk gradient contour map showing the pT stage and regional lymph node count after gastric cancer surgery;

[0042] Figure 5 A two-dimensional risk distribution heatmap showing the number of positive lymph nodes after gastric cancer surgery pT staging. Detailed Implementation

[0043] Example 1:

[0044] This embodiment provides a system and method for postoperative prognostic assessment of gastric cancer based on nonlinear Cox regression. The method flow is as follows: Figure 1 As shown, the details are as follows.

[0045] First, a multicenter retrospective study was conducted, collecting data from 2370 gastric cancer patients who underwent radical gastrectomy at three tertiary medical centers over the past decade. These patients were randomly assigned to a training set (1659 cases) and an internal validation set (711 cases) at a 7:3 ratio. To further evaluate the model's generalization ability, an external validation cohort was selected from the SEER database. Inclusion criteria for the external validation cohort included: diagnosis and radical gastrectomy between 2010 and 2015, pathological confirmation of gastric adenocarcinoma, and complete follow-up information and key variable records; patients who received neoadjuvant therapy preoperatively, had other malignancies, or had a follow-up period of less than 60 months were excluded. After screening, the initial SEER gastric cancer cohort identified 12847 potential cases, and 724 eligible patients were ultimately included in the external validation cohort. The external validation cohort was comparable to the training set in key clinical characteristics such as age, sex, pT stage distribution, and median number of positive lymph nodes. The clinicopathological data of all enrolled patients were systematically collected, including at least the following core variables: number of detected lymph nodes (rLNs), number of positive lymph nodes (pLNs), and pathological stage of tumor invasion depth (pT stage). During data preprocessing, uniform quality control was performed on these variables: samples with more than 20% missing key variables were removed, and the remaining missing values ​​were processed using multiple imputation; considering the right-skewed distribution of count variables, appropriate logarithmic or Box-Cox transformations were implemented to improve data normality; finally, all continuous features were Z-score standardized to eliminate the influence of dimensions and provide a standardized input data format for subsequent modeling.

[0046] Based on data preprocessing, a nonlinear Cox survival analysis model enhanced by Gaussian processes was constructed. This model is based on the traditional Cox proportional hazards model, but improves the form of the covariate effect function: instead of assuming a linear relationship between the hazard function and the covariates or pre-setting specific parameter forms, it introduces a Gaussian process prior as a nonparametric representation of the unknown nonlinear function. Specifically, rLNs, pLNs, and pT stage are used as joint inputs. The similarity of different patients in a high-dimensional feature space is measured through a Gaussian process kernel function, and then the posterior hazard function is estimated through Bayesian inference. The modeling process was implemented using the GPstuff toolkit, which provides efficient Bayesian inference algorithms for Gaussian process models, capable of handling large-scale survival data and automatically estimating model hyperparameters. Through this modeling strategy, the model can capture the complex nonlinear coupling effects that may exist between rLNs, pLNs, and pT stage in a data-driven manner. For example, at a specific pT stage, the impact of the number of positive lymph nodes on risk may exhibit a threshold effect that is initially gradual and then steepens; or, in cases with a low number of detected lymph nodes, the risk weight represented by a single positive lymph node is significantly higher than that of similar findings in scenarios with a high number of detected lymph nodes. These potential nonlinear relationships and interaction effects that cannot be characterized by traditional linear models are effectively integrated into the continuous estimation results of individualized survival risk, forming an initial continuous risk score.

[0047] To further enhance the clinical interpretability of the model, a three-dimensional visualization and iso-risk boundary extraction mechanism are introduced based on the continuous risk score. Specifically, using rLNs as the X-axis, pLNs as the Y-axis, and pT stage as the stratification plane (the Z-axis direction is presented as a discrete plane), each individual patient is mapped to a corresponding point in the three-dimensional coordinate system. Their risk score is represented by color intensity or surface height, thereby generating a continuous three-dimensional risk surface, such as... Figure 2 As shown. Based on this, the contour tracking algorithm is used to extract the isorisk curves corresponding to specific risk thresholds on each pT stage plane, forming a dynamic isorisk map, such as... Figure 3As shown. Further calculation of the gradient rate of change of the risk score in the lymph node coordinate space, i.e., the partial derivative vector of risk with respect to rLNs and pLNs, is performed. Critical points with clinical significance are automatically located by identifying regions with significantly increased gradient norms. The isorisk curves are overlaid with the critical point distribution for analysis, ultimately generating a set of contour-like continuous stratification rules, namely the Con-pTN stratification system. In this system's name, "Con" represents continuity, emphasizing its core feature of abandoning traditional discrete thresholds and adopting continuous risk scores; "pT" represents the pathological tumor invasion depth; and "N" represents the lymph node metastasis status, indicating its inheritance relationship with the existing pTNM staging system. The Con-pTN stratification system aims to reconstruct the traditional discrete pTNM staging into a continuous risk surface through nonlinear modeling with Gaussian process priors. While retaining clinical conventions, it achieves further risk gradient differentiation for patients with different lymph node burdens within the same traditional stage. This stratification system retains the detailed information of the original continuous risk score while presenting it in a clinically familiar discrete stratification form, achieving seamless integration from model output to clinical decision-making.

[0048] Simultaneously, two-dimensional risk visualization charts were constructed, one for pT stage and the other for pT stage and the other for positive lymph nodes, to visually demonstrate the correlation between lymph node number and survival risk at different tumor invasion depths. Figure 4 , Figure 5 As shown. Among them, Figure 4 The risk gradient shown is defined as the local rate of change of continuous survival risk score in the dimension of regional lymph node number. It is derived from the fitted nonlinear risk function using numerical differentiation based on the posterior predicted distribution of a Gaussian process model. This gradient value quantifies the magnitude of risk fluctuation caused by small changes in the number of regional lymph nodes. Regions with larger gradients correspond to sensitive intervals with steep slopes in the risk surface, indicating that even subtle differences in lymph node burden in that region can lead to significant differentiation in patient prognosis; regions with gradients approaching zero indicate that risk changes tend to be stable. By overlaying the gradient information onto a two-dimensional contour map, the risk threshold regions for lymph node number at different pT stages can be visually identified, providing a visual basis for developing individualized intervention strategies in clinical practice.

[0049] During the model validation phase, a multi-cohort external validation strategy was employed to comprehensively evaluate the performance of the Con-pTN model. In the training cohort, the area under the curve (AUC) reached 0.797 (95% CI: 0.773–0.820); the AUC in the internal validation cohort was 0.804 (95% CI: 0.768–0.840); the AUC in external validation cohort 1 was 0.748 (95% CI: 0.705–0.790); and the AUC in external validation cohort 2 was 0.813 (95% CI: 0.601–1.000). While cohort 2 had a wider confidence interval due to its relatively small sample size and limited number of events, its point estimates, consistent with the other cohorts, pointed to the good discriminative power of the Con-pTN model. The combined validation results of the four cohorts (AUC range 0.748–0.813) indicate that the model possesses stable generalization ability. Calibration curve analysis showed good consistency between the predicted survival probabilities and the actual Kaplan-Meier estimates in each cohort. Decision curve analysis showed that within the clinically relevant risk threshold range (0.2-0.6), the net benefit of the Con-pTN model was consistently higher than that of traditional pTNM staging (postoperative pathological tumor lymph node metastasis staging system for gastric cancer), simple rN staging (lymph node staging based on the number of detected lymph nodes), and the LODDS index (log ratio of lymph node metastasis). Comparison with existing staging systems showed that the Con-pTN model exhibited statistically significant discriminative advantage in multiple cohorts. Survival curve analysis further confirmed that within patient subgroups with the same traditional pTNM stage, the risk subgroups reclassified according to the Con-pTN stratification rules exhibited significantly separated survival curves, validating the method's ability to achieve more refined risk differentiation within the same traditional stage.

[0050] Example 2:

[0051] The core of this embodiment lies in introducing a temporal bias compensation mechanism to address the technical challenge that traditional static prognostic models cannot capture the dynamic changes in postoperative survival risk over time, such as its decay or enhancement. The survival risk of patients after gastric cancer surgery is not constant; as time progresses, the influence of initial pathological features on survival outcomes exhibits a non-linear decay trend, and the boundaries between different risk intervals may also drift. This mechanism constructs a dynamic risk calibration layer with time-adaptive capabilities by embedding a temporal decay kernel function into a non-linear Cox model. This allows the model to automatically adjust the contribution weight of each pathological feature to the current risk score based on different postoperative follow-up time points.

[0052] First, based on the Gaussian process-enhanced Cox proportional hazards model, a baseline risk scoring function was obtained by training the number of detected lymph nodes, the number of positive lymph nodes, and the tumor invasion depth grade of patients after gastric cancer surgery in the training cohort. This function is used to characterize the individualized continuous survival risk at the postoperative baseline time.

[0053] To capture the dynamic characteristics of risk evolution over time, a time-decay kernel function is constructed. This function takes the postoperative follow-up time as input and outputs the risk contribution decay coefficient of each pathological feature at the current time. The function is defined as follows:

[0054]

[0055] In the formula, Here is the time-decaying kernel function, representing the time at which the virus is followed up post-surgery. At that time, the baseline risk needs to be multiplied by a decay factor; This is a global decay rate control parameter, a positive real number, obtained through training queue optimization. It controls the overall speed at which the risk decays over time; the larger the value, the faster the decay. This is the time scale scaling factor, in months, and a positive value is used to ensure... For any The constant condition is used to adjust the shape of the decay curve. The risk-dependent adjustment factor is a non-negative real number, expressed through the denominator. To achieve dynamic adjustment where higher risk results in slower decay, enabling the model to have individualized time-series calibration capabilities; Postoperative follow-up time, expressed in months, represents the time interval from the surgery date to the current assessment date; The baseline risk score is an individualized continuous survival risk value output by the basic nonlinear Cox model, reflecting the risk level at the postoperative baseline.

[0056] The baseline risk score is coupled with the time-series decay kernel function to form a time-series dynamic risk calibration model:

[0057]

[0058] In the formula, This is a time-series dynamic risk score, representing the risk level at postoperative follow-up time. At that time, the patient's overall survival risk value; For individual baseline feature vectors; The number of lymph nodes detected refers to the total number of lymph nodes actually detected in the postoperative pathological examination; The number of positive lymph nodes refers to the number of lymph nodes found to have metastatic cancer cells that have been pathologically confirmed. The grading of tumor invasion depth reflects the depth of invasion of the primary tumor into the gastric wall; It is a nonparametric risk compensation function, with postoperative time as the criterion. and individual baseline feature vectors As input, it is learned from the data through Gaussian process regression to capture individualized risk variability introduced by unknown time-varying factors; Let be the integral variable, representing any moment within the postoperative time interval.

[0059] Using multi-center follow-up data, a phased optimization strategy was employed to train the model: the first phase fixed... ,optimization , , Three time-series decay parameters; in the second stage, the time-series decay parameters are fixed, and a nonparametric compensation function is learned through Bayesian inference. The training objective is to maximize the weighted composite index of the consistency index and the time-dependent AUC of the time-series dynamic model.

[0060] For newly enrolled postoperative gastric cancer patients, the system generates a dynamic risk curve that changes over postoperative follow-up time after obtaining their baseline pathological characteristics. This curve is plotted with follow-up time on the horizontal axis and dynamic risk score on the horizontal axis. The vertical axis visually displays the changing trends of patients' survival probability at different postoperative time points. Based on the intersection of the dynamic risk curve and the preset clinical intervention threshold, the system automatically generates personalized follow-up plan recommendations, including the time of the first follow-up examination, the frequency of follow-up examinations, and the timing of intensive interventions.

[0061] This mechanism constructs a time-adaptive dynamic risk calibration model by introducing a time-decaying kernel function and a cumulative risk compensation term, contrasting it with the traditional static Cox proportional hazards model. The comparative trial used a multicenter postoperative follow-up cohort for gastric cancer, with standardized inclusion criteria: radical gastrectomy, pathological confirmation of gastric adenocarcinoma, and a follow-up time ≥60 months. Comparison conditions included: both models used the same baseline pathological features (number of detected lymph nodes, number of positive lymph nodes, T stage) as input; the traditional static Cox model uses the assumption of fixed covariates, while this model embeds a time-decaying kernel function based on the same data. The comparative process used time-dependent receiver operating characteristic (ROC) curves and AUC as evaluation indicators, calculating predictive power at five time points: 12, 24, 36, 48, and 60 months postoperatively. The results showed that the traditional static Cox model had an AUC of 0.783 (95% CI: 0.761-0.805) at 12 months post-surgery, but its predictive power declined continuously with longer follow-up periods, decreasing to 0.712 (95% CI: 0.688-0.736) at 60 months, reflecting the inapplicability of the proportional hazards assumption in actual clinical data. The new model had an AUC of 0.791 (95% CI: 0.769-0.813) at 12 months post-surgery, with no significant difference from the traditional model (P>0.05); however, the AUC increased to 0.802 (95% CI: 0.778-0.826) at 36 months, a 9.7% improvement over the traditional model; and remained at 0.794 (95% CI: 0.770-0.818) at 60 months, an 11.5% improvement over the traditional model.

[0062] Example 3:

[0063] The core of this embodiment lies in overcoming the limitations of traditional prognostic models that rely solely on the "quantity" of positive lymph nodes. It introduces the "topological structure" characteristics of lymph node metastasis to quantify the impact of the spatial distribution patterns of lymph node metastasis on patient prognosis. Existing count-based prognostic indicators treat lymph nodes as independent discrete units, neglecting the structural information inherent in the lymph node chain as a holistic system. For example, whether metastatic lymph nodes are concentrated in the primary drainage area of ​​the tumor or are distributed in a discontinuous manner across distant lymph node chains significantly alters their biological invasiveness. This model constructs a lymph node topological heterogeneity index, transforming the spatial distribution patterns of lymph node metastasis into quantifiable structural risk characteristics. This index is then nonlinearly fused with traditional count characteristics to achieve a more refined characterization of tumor biological behavior.

[0064] We obtained the pathology reports and lymph node dissection atlases from patients after gastric cancer surgery. The detected lymph nodes were divided into several lymph node stations according to their anatomical location, and the total number of lymph nodes detected and the number of positive lymph nodes in each station were recorded. Based on this, a lymph node topology map was constructed. , where the set of nodes Representatives from each lymph node station gathered. It represents the anatomical drainage relationship between lymph node stations, forming a directed graph structure with direction and weight.

[0065] Based on the constructed lymph node topology map, a lymph node topological heterogeneity index is defined to quantify the spatial dispersion of positive lymph nodes throughout the lymph node system:

[0066]

[0067] In the formula, The lymph node topological heterogeneity index is a dimensionless numerical value used to quantify the spatial dispersion of positive lymph nodes in the lymph node system. The total number of lymph node stations, representing the number of lymph node regions divided according to anatomical criteria; Anatomical connection weights represent lymph node stations. and The strength of the lymphatic drainage relationship between them is pre-defined based on anatomical knowledge, with the main drainage path having a higher weight and the collateral path having a lower weight; For the first The number of positive lymph nodes in the station; Anatomical distance, measuring lymph node stations and The anatomical distance between lymph nodes is usually calculated by the absolute difference of the lymph node station number or the difference of the anatomical grade. The difference of the anatomical grade is the preferred method because it truly reflects the biological significance of the lymphatic drainage path. Only when the data lacks detailed anatomical path information, the absolute difference of the lymph node station number is used as an approximate substitute, and its effectiveness needs to be verified through sensitivity analysis. Shannon entropy for the distribution of positive lymph nodes is used to quantify the degree of dispersion of positive lymph nodes among different lymph node stations. The maximum possible entropy value is calculated using the following formula: ,in The total number of lymph node stations is defined based on the maximum value property of discrete uniform distribution entropy in information theory, and is used to normalize the Shannon entropy of the actual positive lymph node distribution.

[0068] The numerator of this index measures the spatial clustering of positive lymph nodes in the topological map. A smaller numerator indicates positive lymph nodes concentrated in adjacent lymph node stations, while a larger numerator indicates positive lymph nodes distributed in a disjointed manner across non-adjacent stations. The denominator is a normalization constant to ensure comparability of the index among patients with different lymph node dissection ranges. The entropy term amplifies the weight of dispersed metastasis; that is, the more lymph node stations positive lymph nodes are scattered across, the higher the heterogeneity index, suggesting a stronger ability for tumor dissemination.

[0069] Simultaneously extract lymph node-related features used in traditional prognostic models, including: total number of positive lymph nodes, total number of detected lymph nodes, lymph node metastasis rate, and lymph node metastasis log ratio.

[0070] A multimodal feature fusion nonlinear survival model is constructed using LNTHI, traditional lymph node features, and tumor invasion depth grading as inputs. The model architecture employs a multi-kernel Gaussian process fusion strategy: independent kernel functions are constructed for different feature categories, and then weighted fusion of these kernel functions achieves nonlinear interaction in the feature space. Specifically, the fusion covariance function is defined as:

[0071]

[0072] In the formula, To fuse the covariance function, we represent the covariance between two samples in the multimodal feature space. and A similarity metric between them, used for Gaussian process modeling; , , , The fusion weight parameters are non-negative real numbers and satisfy the following conditions: The model is optimized by averaging Bayesian models to reflect the relative importance of various features to the model's predictions. This is a topological feature kernel function used to measure the similarity between two samples in the topological feature space; This is the counting feature kernel function, used to measure the similarity between two samples in the counting feature space; This is a hierarchical feature kernel function used to measure the similarity between two samples in a hierarchical feature space; This is a cross kernel function used to capture the interaction effects between different types of features; For the first The and the first The feature vector of each sample includes topological features, count features, and hierarchical features; It is a subset of the topological features of the sample, mainly including LNTHI and other possible spatial distribution features; This is a subset of the counting features of the sample, including the total number of positive lymph nodes, the total number of detected lymph nodes, the lymph node metastasis rate, and the log ratio of lymph node metastasis. This is a subset of the graded features of the samples, mainly including the grade of tumor invasion depth.

[0073] Model training was performed using multicenter cohort data containing detailed lymph node station distribution information. After training, leave-one-out cross-validation was used to evaluate the incremental predictive value of LNTHI, comparing the performance of models including LNTHI with those without, to verify the independent contribution of topological heterogeneity features to prognostic prediction. For routine clinical data lacking detailed lymph node station distribution information, the system provides a simplified mode: estimating approximate LNTHI based on limited lymph node grouping information, or using multiple imputation methods to handle missing values.

[0074] Using LNTHI as the third continuous coordinate axis, together with the number of detected lymph nodes and the number of positive lymph nodes, a three-dimensional risk space is constructed. Combined with different tumor invasion depth grading levels, a four-dimensional dynamic risk visualization system is built. Clinicians can rotate and observe the changing trends of the risk surface under different levels of topological heterogeneity through an interactive interface, intuitively understanding the independent impact of the spatial distribution pattern of lymph node metastasis on patient prognosis.

[0075] This model quantifies the spatial distribution pattern of lymph node metastasis into a calculable structural risk characteristic by constructing a lymph node topological heterogeneity index, contrasting it with conventional methods that rely solely on the count of positive lymph nodes. The comparative trial employed a multicenter cohort containing detailed information on lymph node station distribution. All patients underwent D2 radical lymph node dissection, and pathology reports fully documented the detection and metastasis status of each lymph node station. Comparative conditions included: the conventional method group used only the total number of positive lymph nodes as the N-staging criterion; this model group, based on the same total number of positive lymph nodes, added LNTHI as a second dimension feature and employed a multi-kernel Gaussian process fusion strategy for joint modeling. The comparison process used the consistency index, the Akaike Information Criterion, and the net weight classification improvement index as evaluation indicators, while also referencing evaluation paradigms from previous lymph node topology studies. The results showed that the consistency index of the conventional pN staging model was 0.748 (95% CI: 0.724-0.772), and the Akaike Information Criterion was 5842.7. The consistency index of this new model on the same data improved to 0.793 (95% CI: 0.769-0.817), an improvement of 6.0% compared to the conventional method, while the Akaike Information Criterion decreased to 5671.3, a reduction of 171.4, indicating a significant improvement in model fit. Further analysis showed that in the subgroup of patients with the same total number of positive lymph nodes, the 5-year survival rate was 31.2% (95% CI: 26.8-35.6%) for patients with LNTHI in the high quartile, while the 5-year survival rate was 48.7% (95% CI: 43.9-53.5%) for patients with LNTHI in the low quartile, and the survival difference between the two groups was statistically significant.

[0076] Example 4:

[0077] The core of this embodiment lies in addressing the clinical trust crisis caused by the black box nature of complex nonlinear models. By constructing a dynamic isorisk map and an adaptive hierarchical system, it achieves seamless integration between model output and clinical decision-making logic. While existing machine learning prognostic models boast high predictive accuracy, their internal decision-making mechanisms are difficult for clinicians to understand, resulting in low adoption rates in real-world clinical scenarios. This system introduces a clinical interpretability enhancement mechanism, transforming the output of high-dimensional nonlinear models into a dynamic isorisk map highly aligned with clinical cognitive habits. Based on map features, it automatically generates clinically operable adaptive hierarchical rules. This mechanism uses a two-dimensional coordinate system familiar to clinicians as a foundation, overlaying different tumor invasion depth grading levels to generate a series of isorisk curves. Furthermore, it introduces a risk gradient change rate index to automatically identify critical points where the isorisk curve morphology undergoes significant changes, using these critical points as the basis for reconstructing the staging system. Simultaneously, the system supports clinicians in fine-tuning the isorisk curves based on local data characteristics, achieving localized adaptation of the model.

[0078] A nonlinear Cox model enhanced by Gaussian processes is used to construct a three-dimensional risk surface, with the number of detected lymph nodes and the number of positive lymph nodes as continuous coordinate axes, combined with the tumor invasion depth grade as a stratification plane. Each point on this surface corresponds to a specific risk score, which is jointly determined by three variables: the number of detected lymph nodes, the number of positive lymph nodes, and the tumor invasion depth grade. The surface uses different colors or heights to represent continuous changes in risk levels, allowing clinicians to intuitively observe the impact of changes in lymph node burden on risk, thus transforming the abstract high-dimensional model output into a visualized geometric expression.

[0079] Based on the three-dimensional risk surface, stratified sections are created along the dimension of tumor invasion depth grading to obtain two-dimensional risk contour maps for each T-stage. A contour tracking algorithm is used to automatically extract isorisk curves with clinically stable demarcation significance—that is, curves formed by all points whose risk scores equal a preset threshold. The preset threshold can be flexibly set according to clinical needs, for example, using the ternary or quartile of the overall population risk distribution, or a cutoff value determined based on clinical outcome optimization as the isorisk threshold. Through this process, a series of isorisk curve families are extracted from the continuous risk surface, collectively forming a dynamic isorisk atlas. This atlas is presented in a two-dimensional coordinate system familiar to clinicians, with each curve representing a lymph node combination trajectory with the same risk level.

[0080] Based on the dynamic isorisk map, the risk gradient change rate is further calculated, which is the partial derivative vector of the risk score with respect to the number of detected lymph nodes and the number of positive lymph nodes. The physical meaning of this vector is the magnitude of the change in risk level when moving a unit distance in a certain direction within the lymph node coordinate space. By analyzing the distribution characteristics of the risk gradient change rate throughout the entire lymph node coordinate space, the system automatically identifies steep risk regions—regions where even small changes in lymph node burden can lead to a significant jump in risk level. The boundaries of these regions constitute the set of critical points with clinical significance.

[0081] To achieve automatic identification of critical points, a critical point identification function is constructed. This function first calculates the risk gradient norm at each spatial location, which is a comprehensive strength index of the risk change rate. Then, a gradient threshold parameter is set. This parameter is not a fixed constant but is automatically determined based on the statistical characteristics of the risk gradient distribution of all samples in the training queue, typically using the percentile of the gradient distribution as the threshold benchmark. Spatial locations where the risk gradient norm exceeds this dynamic threshold are marked as candidate critical points. A smoothing mechanism is further introduced to perform local weighted averaging or kernel density estimation on the candidate critical points, eliminating isolated points and false boundaries caused by data sparsity or noise, thereby obtaining continuous, stable, and anatomically significant critical region boundaries.

[0082] By overlaying the critical point with the isorisk curve, the curve that meets both the isorisk threshold requirements and highly coincides with the boundary of the critical region is determined as the final stratification boundary. The system automatically outputs a stratification rule table. For example, for patients with a specific T stage, risk levels such as low-risk, intermediate-risk, and high-risk are determined based on the numerical range of the number of detected and positive lymph nodes. This rule table can be directly embedded into the clinical electronic medical record system to automate the calculation of risk stratification, transforming continuous risk scores into clinically operable discrete decision rules.

[0083] The system provides an interactive graphical user interface, allowing clinical experts to visually review and manually correct automatically generated stratification rules. If a clinical expert at a center believes that an automatically identified stratification boundary is inconsistent with their clinical experience—for example, being too aggressive or too conservative—they can adjust the position of the isohazard curves by dragging and dropping on the interface. The system recalculates the adjusted stratification efficacy in real time, including indicators such as the log-rank test p-value for differences in survival curves between groups and hazard ratios, and provides intuitive feedback on the impact of the adjustment on stratification effectiveness. After manual correction, the system saves the corrected stratification rules as a localized version for that center for subsequent patient prognostic assessments. This mechanism achieves an adaptive optimization closed loop of global model learning and local knowledge injection, significantly improving the model's generalizability across different medical institutions.

[0084] The final prognostic assessment results not only include the patient's risk stratification labels but also come with visual explanations: individual patient characteristic points are marked on a dynamic isorisk map, visually displaying their position relative to various isorisk curves and critical regions; simultaneously, natural language descriptions are generated, such as indicating that the patient is on the edge of a high-risk area, suggesting shorter follow-up intervals, or considering enhanced adjuvant therapy. This dual presentation of visual maps and textual explanations significantly enhances clinicians' trust in and understanding of the model's output, promoting its adoption and application in real-world clinical scenarios, and ultimately achieving effective transformation from technical output to clinical decision-making.

Claims

1. A postoperative prognostic assessment system for gastric cancer based on nonlinear Cox regression, characterized in that, include: The data acquisition module is used to acquire postoperative pathological feature data of gastric cancer in the target subject. The data includes at least the number of detected lymph nodes, the number of positive lymph nodes, and the grade of tumor invasion depth. The nonlinear survival risk modeling module is used to process the pathological feature data based on a nonlinear Cox proportional hazards model that incorporates Gaussian process priors, in order to fit the implicit nonlinear coupling relationship and interaction effect between the pathological features and generate a score representing individualized continuous survival risk. The nonlinear survival risk modeling module includes a topology analysis unit, which is used to quantify the topology features of lymph node metastasis based on spatial distribution information, and to nonlinearly fuse the topology features with lymph node counting features. The risk surface construction and boundary extraction module is used to construct a three-dimensional risk surface based on the number of detected lymph nodes and the number of positive lymph nodes as continuous coordinate axes, combined with the tumor invasion depth grading, and automatically identify and extract isorisk contour boundaries with clinically stable demarcation significance based on the three-dimensional risk surface. The risk surface construction and boundary extraction module, based on the geometric features of the three-dimensional risk surface, automatically identifies the boundaries of continuous regions where the risk gradient changes tend to be stable through algorithms, and uses these boundaries as the basis for reconstructing equivalent stratification in the existing tumor lymph node metastasis staging system. The prognostic result output module is used to map the continuous survival risk score into refined risk stratification information based on the equal risk profile boundary, and output the prognostic assessment result of the target object.

2. The system according to claim 1, characterized in that: The nonlinear survival risk modeling module adopts a Bayesian inference framework and introduces Gaussian process priors into the Cox proportional hazards model.

3. The system according to claim 2, characterized in that: The nonlinear survival risk modeling module uses a nonparametric Bayesian model based on a combination of Gaussian process regression and survival analysis. This model does not presuppose the functional form of risk changes with the number of lymph nodes, but estimates the local variation characteristics of the risk function based on data.

4. The system according to claim 1, characterized in that: The nonlinear survival risk modeling module uses multicenter clinical cohort data to train and internally validate the nonlinear Cox proportional hazards model, and verifies the model's generalization ability through an external independent cohort.

5. The system according to claim 1, characterized in that: The nonlinear survival risk modeling module also includes a time-series dynamic calibration unit, which is used to perform time-dependent calibration of the continuous survival risk score based on postoperative follow-up time points. The calibration generates a time-series risk score that dynamically evolves with postoperative follow-up time by introducing a decay mechanism associated with the individual's baseline risk level and a compensation mechanism to capture unknown time-varying factors.

6. The system according to claim 1, characterized in that: The system also includes a model performance comparison and evaluation module, which is used to statistically compare the continuous survival risk score output by the nonlinear survival risk modeling module with the risk stratification performance of the traditional tumor lymph node metastasis staging system, lymph node metastasis rate and lymph node metastasis log ratio, and to quantitatively evaluate the improvement in the system's discrimination and the increase in clinical net benefit.

7. The system according to claim 1, characterized in that: The refined risk stratification information output by the prognostic result output module, while maintaining the clinical interpretation habits of the traditional staging system, enables further risk gradient differentiation among patients with different lymph node burdens within the same traditional stage.

8. A method for postoperative prognostic assessment of gastric cancer based on nonlinear Cox regression, characterized in that: The method is implemented based on the system described in any one of claims 1-7: The method includes: Obtain postoperative pathological characteristic data of gastric cancer in the target subjects, including at least the number of detected lymph nodes, the number of positive lymph nodes, and the grade of tumor invasion depth; Based on a nonlinear Cox proportional hazards model that incorporates Gaussian process priors, the pathological feature data is processed to fit the implicit nonlinear coupling relationship and interaction effect between the pathological features, and to generate a score characterizing individualized continuous survival risk. Using the number of detected lymph nodes and the number of positive lymph nodes as continuous coordinate axes, and combined with the tumor invasion depth grading, the continuous survival risk score is constructed into a three-dimensional risk surface or contour map, and based on the three-dimensional risk surface, isorisk contour boundaries with clinical stability demarcation significance are automatically identified and extracted. Based on the aforementioned equal-risk profile boundary, the continuous survival risk score is mapped into refined risk stratification information, and the prognostic assessment results of the target object are output.

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