Serological marker-based breast cancer postoperative recurrence risk prediction modeling algorithm

Abstract

The invention discloses a breast cancer postoperative recurrence risk prediction modeling algorithm based on serological markers, aims to realize non-invasive evaluation of breast cancer postoperative recurrence risk by analyzing serological markers detected in different postoperative periods of a patient to construct a prediction model, and relates to the technical field of breast cancer prediction. The method comprises the following steps of data acquisition and preprocessing, data quality control and arrangement, multi-cycle time sequence alignment and feature extraction, dynamic causal convolutional network modeling, and risk prediction and verification. According to the method, serological marker data detected in different postoperative periods of a patient is collected and finely preprocessed, an improved algorithm is utilized to align a time sequence and extract features, a specific convolutional network and a proportional risk model are constructed, and the relationship between serological marker features in different periods and postoperative recurrence of breast cancer is accurately mined; the breast cancer recurrence risk can be predicted more accurately, the clinical verification module visually presents the risk, and the scientificity and practicability of breast cancer recurrence prediction are greatly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of breast cancer prediction, and in particular to a modeling algorithm for predicting the risk of breast cancer recurrence after surgery based on serological markers. Background Art

[0002] Breast cancer is the most common malignant tumor in women worldwide, and postoperative recurrence is the main threat to patients' long-term survival. According to statistics, even after standardized treatment, 30%-40% of patients will experience recurrence and metastasis within 5 years after surgery, and the 5-year survival rate of recurrent patients is significantly reduced. Currently, commonly used postoperative monitoring methods in clinical practice, such as the tumor marker CA15-3 and imaging examinations, are not sensitive enough to detect early micrometastases and have a significant detection lag. Recent studies have found that breast cancer recurrence is closely related to changes in characteristic serum markers and protein markers. Therefore, the choice of dynamically monitoring the temporal changes in serological markers of postoperative patients is expected to establish a more accurate recurrence prediction model to provide a critical time window for clinical intervention, thereby improving patient prognosis.

[0003] The current mainstream methods mainly adopt two types of technical solutions:

[0004] Statistical machine learning model: The random forest algorithm is used to construct a classifier by screening differential markers (usually 20-30 types), but only uses single sampling data and ignores the temporal characteristics of marker fluctuations;

[0005] A deep learning time series model uses an LSTM network to analyze marker concentration curves for six consecutive months. However, its time alignment module relies on a fixed sampling interval (once every 21 days) and cannot adapt to the non-uniform sampling scenario that is more suitable for patient sampling.

[0006] Traditional methods only perform simple normalization on the first collected serum marker data, without distinguishing the differences in serum marker patterns at different periods, resulting in loss of cycle phase information. Existing algorithms generally have the following limitations:

[0007] Lack of causal relationship: Only the risk probability is output, and the dynamic causal regulatory relationship between key markers (such as the inhibitory mechanism of CEA and CA153) is not revealed, resulting in insufficient confidence among clinicians in the prediction results.

[0008] Poor data robustness: When faced with first-time sampling data (interference factors such as equipment errors, operation differences, and patient differences), the integrity and consistency of the obtained data are difficult to guarantee, resulting in large fluctuations in model analysis results.

[0009] Single feature capture: Traditional time series modeling methods do not consider the multi-scale characteristics of marker fluctuations (such as dynamic changes at the minute and hour levels), and lack refined processing of periodic phase correction and time series alignment, resulting in incomplete feature extraction.

[0010] To this end, we provide a breast cancer recurrence risk prediction modeling algorithm based on serological markers to solve the above problems. Summary of the Invention

[0011] The purpose of the present invention is to provide a modeling algorithm for predicting the risk of postoperative recurrence of breast cancer based on serological markers. By combining the collection and analysis of serum marker time series data with dynamic causal convolutional network modeling, the present invention solves the problems of low accuracy in diagnosing early recurrence of breast cancer and lack of dynamic monitoring of disease progression in the existing technology.

[0012] To solve the above technical problems, the present invention is achieved through the following technical solutions:

[0013] The present invention is a modeling algorithm for predicting the risk of breast cancer recurrence after surgery based on serological markers, and the method comprises the following steps:

[0014] Step A: Collection and preprocessing of serum marker time series data: Through the collection and preprocessing of clinical data, the serum marker data of breast cancer patients tested at different periods after surgery are retrospectively collected to form the original time series data set. Where N is the number of markers and T is the total number of time points;

[0015] Step B: Data collation and quality control: Missing values ​​in the original time series data set are filled using professional methods, outliers are removed, and the markers are periodically corrected and standardized to ensure the quality of subsequent modeling data. Specifically, for missing values, reasonable filling is performed based on the characteristics of the markers and related mechanisms; for outliers, thresholds are set based on the data distribution of the non-recurrence group for screening and elimination; the amplitude A of each marker is estimated using the Lomb-Scargle periodogram. i and phase By formula:

[0016]

[0017] Perform periodic phase correction on the data to eliminate the interference caused by periodic fluctuations;

[0018] Step C: Multi-cycle timing alignment and feature extraction: The improved dynamic time warping (DTW) algorithm is used to align the marker fluctuation curves of different chemotherapy cycles. The alignment error function is defined as:

[0019]

[0020] in:

[0021] σ k : population standard deviation of marker k;

[0022] λ: time decay factor;

[0023] D: marker dimension;

[0024] Step D: Dynamic Causal Convolutional Network Modeling: Construct a causal temporal convolutional network (Causal-TCN) with an expansion factor in the Fibonacci sequence (1, 2, 3, 5, 8). The hidden layer is calculated as:

[0025]

[0026] in:

[0027] *: Causal convolution operation (only depends on data before time td);

[0028] d: dilation factor of layer l;

[0029] Step E: Risk prediction and verification: The output layer calculates the probability of breast cancer recurrence through the Sigmoid function:

[0030]

[0031] Where: w i is the weight parameter, which is optimized by the cross entropy loss function.

[0032] The present invention is further configured such that, in step B, the Z-score normalization method is finally used to adjust the corrected data to a standard distribution with a mean of 0 and a standard deviation of 1, thereby improving the consistency and reliability of the data and laying the foundation for subsequent modeling and analysis.

[0033] The present invention is further configured such that the time decay factor λ of the improved DTW algorithm in step C is adaptively adjusted in the following manner:

[0034]

[0035] When the marker fluctuation rate is above the median, the local sensitivity of the time alignment is increased.

[0036] The present invention is further configured such that the gating mechanism of the causal convolutional network in step D is designed as follows:

[0037]

[0038] Where: ⊙ represents the Hadamard product, σ is the Sigmoid function.

[0039] The present invention is further configured to further include a dynamic causal discovery module after step D:

[0040] (1) Calculate the time-varying transfer entropy matrix:

[0041]

[0042] (2) Screening significant causal edges:

[0043] For each TE k→m A permutation test (1000 resamplings) was performed, and edges with p < 0.01 and TE > 0.05 were retained to construct the causal network.

[0044] The present invention is further configured such that the specific steps of the permutation test are:

[0045] (1) Randomly shuffle the time series data of marker k to generate k′;

[0046] (2) Calculate the pseudo transfer entropy TE after scrambling k′→m

[0047] (3) Repeat 1000 times and calculate the significance level:

[0048]

[0049] The present invention is further configured such that the weight in step E is determined by:

[0050] (1) Constructing the Cox proportional hazards model:

[0051]

[0052] (2) Use the gradient descent method to solve the maximum likelihood estimate:

[0053]

[0054] Where: R j At time t j A collection of samples at risk.

[0055] The present invention is further configured such that the data preprocessing in step A further comprises:

[0056] (1) Perform periodic phase correction on each marker:

[0057]

[0058] Among them: A i 、φ i Estimation through Lomb-Scargle periodogram;

[0059] (2) Z-score standardization of the corrected data:

[0060]

[0061] The present invention is further configured such that the expansion factor configuration rule of the causal convolutional network is as follows: layer 1: d = 1 (sampling interval = 21 days);

[0062] Stratum 2: d = 2 (sampling interval = 42 days);

[0063] Stratum 3: d = 3 (sampling interval = 63 days);

[0064] Stratum 4: d = 4 (sampling interval = 84 days);

[0065] Stratum 5: d = 5 (sampling interval = 105 days);

[0066] Form multi-scale temporal feature fusion.

[0067] The present invention is further configured to include a clinical verification module:

[0068] (1) Define high-risk threshold: φ = μ 未复发组 +2.5σ 复发组 ;

[0069] (2) Generate risk heat map:

[0070] The time-varying trajectories of key serological markers in the causal network were plotted, and the periods exceeding the threshold were marked.

[0071] The present invention has the following beneficial effects:

[0072] 1. This invention estimates the periodic characteristics of markers based on professional algorithms, eliminates the interference caused by periodic rhythm fluctuations, retains the true signal characteristics, improves the dynamic time warping (DTW) algorithm to introduce population data distribution characteristics and time decay mechanism, can dynamically adjust the alignment sensitivity according to the marker fluctuation rate, effectively solves the problem of sampling time drift, uses the Z-score normalization method to unify the data scale, and improves the consistency and reliability of the modeling data.

[0073] 2. The expansion factor of the present invention adopts the Fibonacci sequence (1, 2, 3, 4, 5), corresponding to different sampling intervals, to achieve multi-scale feature fusion, capture the dynamic changes of markers in different time dimensions, introduce a gating mechanism, and enhance the model's selective extraction ability of key features through activation functions and feature weighting operations. By calculating the time-varying transfer entropy matrix and permutation test, the associated edges of markers with significant causal relationships are screened out, a causal network is constructed, and the dynamic regulatory relationship between markers is clearly displayed, providing an intuitive basis for mechanism research.

[0074] 3. This invention combines survival analysis theory with a gradient descent optimization algorithm to improve the accuracy of breast cancer recurrence risk probability prediction. It defines a high-risk threshold based on data from a non-recurrence group, quantifies individual risk levels, generates a time-varying trajectory heat map of key markers, and intuitively marks periods of abnormal risk, assisting clinicians in quickly locating high-risk states.

[0075] 4. In view of the characteristics of single postoperative review data (poor stability and large time drift), the present invention significantly enhances the robustness of the model to low-quality data through dynamic time series alignment technology and multi-scale feature modeling, making it not only suitable for single review scenarios, but also able to meet the clinical needs of long-term and multiple follow-up after surgery. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments.

[0077] Figure 1 This is the main flow chart of the modeling algorithm for predicting the risk of breast cancer recurrence after surgery based on serological markers;

[0078] Figure 2 This is a flowchart for the collection and preprocessing of clinical data in the modeling algorithm for predicting the risk of postoperative recurrence of breast cancer based on serological markers;

[0079] Figure 3 This is a flowchart for data collation and quality control in the modeling algorithm for predicting the risk of postoperative recurrence of breast cancer based on serological markers.

[0080] Figure 4 This is a flowchart of multi-cycle time series alignment and feature extraction in the modeling algorithm for predicting the risk of postoperative recurrence of breast cancer based on serological markers.

[0081] Figure 5 Flowchart for modeling a dynamic causal convolutional network in a serological marker-based modeling algorithm for predicting the risk of postoperative recurrence of breast cancer.

[0082] Figure 6 Flowchart for risk prediction and validation of the modeling algorithm for predicting the risk of breast cancer recurrence after surgery based on serological markers. DETAILED DESCRIPTION

[0083] The technical solutions in the embodiments of the present invention will be described below in conjunction with the drawings in the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0084] Example 1

[0085] See also Figure 1A modeling algorithm for predicting the risk of breast cancer recurrence after surgery based on serological markers, the method comprises the following steps:

[0086] Step A: Serum marker time series data collection and preprocessing: Retrospectively collect serum marker data from breast cancer patients at different postoperative periods to form the original time series data set Where N is the number of markers and T is the total number of time points;

[0087] Step B: Data collation and quality control: Missing values ​​in the original time series data set are filled using professional methods, outliers are removed, and the markers are periodically corrected and standardized to ensure the quality of subsequent modeling data. Specifically, for missing values, reasonable filling is performed based on the characteristics of the markers and related mechanisms; for outliers, thresholds are set based on the data distribution of the non-recurrence group for screening and elimination; the amplitude A of each marker is estimated using the Lomb-Scargle periodogram. i and phase By formula:

[0088]

[0089] Perform periodic phase correction on the data to eliminate the interference caused by periodic fluctuations;

[0090] Step C: Multi-cycle timing alignment and feature extraction: The improved dynamic time warping (DTW) algorithm is used to align the marker fluctuation curves of different chemotherapy cycles. The alignment error function is defined as:

[0091]

[0092] in:

[0093] σ k : population standard deviation of marker k;

[0094] λ: time decay factor;

[0095] D: marker dimension;

[0096] Step D: Dynamic Causal Convolutional Network Modeling: Construct a causal temporal convolutional network (Causal-TCN) with an expansion factor in the Fibonacci sequence (1, 2, 3, 4, 5). The hidden layer is calculated as:

[0097]

[0098] in:

[0099] *: Causal convolution operation (only depends on data before time td);

[0100] d: dilation factor of layer l;

[0101] Step E: Risk prediction and verification: The output layer calculates the breast cancer risk probability through the Sigmoid function:

[0102]

[0103] Where: w i is the weight parameter, which is optimized by the cross entropy loss function.

[0104] Example 2

[0105] See also Figure 1-5 A modeling algorithm for predicting the risk of breast cancer recurrence after surgery based on serological markers, the method comprises the following steps:

[0106] Serum marker time series data collection and preprocessing: The original time series data set is formed by retrospectively collecting the serum marker data detected at different periods after breast cancer surgery Where N is the number of markers and T is the total number of time points;

[0107] Data collation and quality control: Missing values ​​in the original time series data set are filled using professional methods, outliers are removed, and the markers are periodically corrected and standardized to ensure the quality of subsequent modeling data. Specifically, for missing values, reasonable filling is performed based on the characteristics of the markers and related mechanisms; for outliers, thresholds are set based on the data distribution of the non-recurrence group for screening and elimination; the amplitude A of each marker is estimated using the Lomb-Scargle periodogram. i and phase By formula:

[0108]

[0109] Perform periodic phase correction on the data to eliminate the interference caused by periodic fluctuations;

[0110] Finally, the Z-score standardization method was used to adjust the corrected data to a standard distribution with a mean of 0 and a standard deviation of 1, improving the consistency and reliability of the data and laying the foundation for subsequent modeling and analysis.

[0111] Multi-cycle timing alignment and feature extraction: An improved dynamic time warping (DTW) algorithm is used to align the marker fluctuation curves of different detection cycles. The alignment error function is defined as:

[0112]

[0113] in:

[0114] σ k : population standard deviation of marker k;

[0115] λ: time decay factor;

[0116] D: marker dimension;

[0117] The time decay factor λ of the improved DTW algorithm is adaptively adjusted in the following way:

[0118]

[0119] When the marker fluctuation rate is above the median, the local sensitivity of the time alignment is increased.

[0120] Dynamic Causal Convolutional Network Modeling: Construct a Causal Temporal Convolutional Network (Causal-TCN) with an expansion factor in the Fibonacci sequence (1, 2, 3, 4, 5). The hidden layer is calculated as:

[0121]

[0122] in:

[0123] *: Causal convolution operation (only depends on data before time td);

[0124] d: dilation factor of layer l;

[0125] The gating mechanism of the causal convolutional network is designed as follows:

[0126]

[0127] Where: ⊙ represents the Hadamard product, σ is the Sigmoid function.

[0128] Also includes a dynamic causal discovery module:

[0129] (1) Calculate the time-varying transfer entropy matrix:

[0130]

[0131] (2) Screening significant causal edges:

[0132] For each TE k→m A permutation test (1000 resamplings) was performed, and edges with p < 0.01 and TE > 0.05 were retained to construct the causal network;

[0133] The specific steps of the permutation test are:

[0134] (1) Randomly shuffle the time series data of marker k to generate k′;

[0135] (2) Calculate the pseudo transfer entropy TE after scrambling k′→m

[0136] (3) Repeat 1000 times and calculate the significance level:

[0137]

[0138] Risk prediction and verification: The output layer calculates the risk of breast cancer recurrence using the Sigmoid function:

[0139]

[0140] Where: w i is the weight parameter, which is optimized by the cross entropy loss function.

[0141] Example 3

[0142] See also Figure 1-6 A modeling algorithm for predicting the risk of breast cancer recurrence after surgery based on serological markers, the method comprises the following steps:

[0143] Serum marker time series data collection and preprocessing: The original time series data set is formed by retrospectively collecting the serum marker data detected at different periods after breast cancer surgery Where N is the number of markers and T is the total number of time points;

[0144] Data collation and quality control: Missing values ​​in the original time series data set are filled using professional methods, outliers are removed, and the markers are periodically corrected and standardized to ensure the quality of subsequent modeling data. Specifically, for missing values, reasonable filling is performed based on the characteristics of the markers and related mechanisms; for outliers, thresholds are set based on the data distribution of the non-recurrence group for screening and elimination; the amplitude A of each marker is estimated using the Lomb-Scargle periodogram. i and phase By formula:

[0145]

[0146] Perform periodic phase correction on the data to eliminate the interference caused by periodic fluctuations;

[0147] Finally, the Z-score standardization method was used to adjust the corrected data to a standard distribution with a mean of 0 and a standard deviation of 1, improving the consistency and reliability of the data and laying the foundation for subsequent modeling and analysis.

[0148] Multi-cycle time series alignment and feature extraction: An improved dynamic time warping (DTW) algorithm is used to align the marker fluctuation curves of different detection cycles. The alignment error function is defined as:

[0149]

[0150] in:

[0151] σ k: population standard deviation of marker k;

[0152] λ: time decay factor;

[0153] D: marker dimension;

[0154] The time decay factor λ of the improved DTW algorithm is adaptively adjusted in the following way:

[0155]

[0156] When the marker fluctuation rate is above the median, the local sensitivity of the time alignment is increased.

[0157] Dynamic Causal Convolutional Network Modeling: Construct a Causal Temporal Convolutional Network (Causal-TCN) with an expansion factor in the Fibonacci sequence (1, 2, 3, 4, 5). The hidden layer is calculated as:

[0158]

[0159] in:

[0160] *: Causal convolution operation (only depends on data before time td);

[0161] d: dilation factor of layer l;

[0162] The gating mechanism of the causal convolutional network is designed as follows:

[0163]

[0164] Where: ⊙ represents the Hadamard product, σ is the Sigmoid function.

[0165] Also includes a dynamic causal discovery module:

[0166] (1) Calculate the time-varying transfer entropy matrix:

[0167]

[0168] (2) Screening significant causal edges:

[0169] For each TE k→m A permutation test (1000 resamplings) was performed, and edges with p < 0.01 and TE > 0.05 were retained to construct the causal network;

[0170] The expansion factor configuration rule of the causal convolutional network is:

[0171] Stratum 1: d = 1 (sampling interval = 21 days);

[0172] Stratum 2: d = 2 (sampling interval = 42 days);

[0173] Stratum 3: d = 3 (sampling interval = 63 days);

[0174] Stratum 4: d = 4 (sampling interval = 84 days);

[0175] Stratum 5: d = 5 (sampling interval = 105 days);

[0176] Form multi-scale temporal feature fusion;

[0177] The specific steps of the permutation test are:

[0178] (1) Randomly shuffle the time series data of marker k to generate k′;

[0179] (2) Calculate the pseudo transfer entropy TE after scrambling k′→m

[0180] (3) Repeat 1000 times and calculate the significance level:

[0181]

[0182] Risk prediction and verification: The output layer calculates the risk of breast cancer recurrence using the Sigmoid function:

[0183]

[0184] Where: w i is the weight parameter, which is optimized by the cross entropy loss function.

[0185] The weights are determined as follows:

[0186] (1) Constructing the Cox proportional hazards model:

[0187]

[0188] (2) Use the gradient descent method to solve the maximum likelihood estimate:

[0189]

[0190] Where: R j At time t j A collection of samples at risk.

[0191] Also includes clinically validated modules:

[0192] (1) Define high-risk threshold: φ = μ 未复发组 +2.5σ 复发组 ;

[0193] (2) Generate risk heat map:

[0194] The time-varying trajectories of key serological markers in the causal network were plotted, and the periods exceeding the threshold were marked.

[0195] Example 4

[0196] Postoperative recurrence risk prediction process based on serological markers

[0197] Data collection and preprocessing

[0198] Data source: Serological marker data of 150 patients after breast cancer surgery were retrospectively collected, including 10 markers such as CEA, CA153, and CRP. Six cycles of data were collected for each patient to form the original time series dataset (N=10, T=6).

[0199] Preprocessing steps:

[0200] Missing value filling: For missing serum markers (such as CA153), linear interpolation is used to fill missing values ​​based on the distribution patterns of patients in each cycle;

[0201] Outlier elimination: refer to the data distribution of the non-recurrence group, set a threshold of ±3 times the standard deviation, and eliminate outliers;

[0202] Periodic phase correction: The amplitude and phase of each marker are estimated through the Lomb-Scargle periodogram to eliminate the interference of detection period fluctuations;

[0203] Z-score standardization: adjust the corrected data to a standard distribution with a mean of 0 and a standard deviation of 1.

[0204] Multi-cycle timing alignment and feature extraction

[0205] Improved DTW algorithm application:

[0206] The alignment error function introduces the group standard deviation (σ k ) and a time decay factor (λ), where λ is adaptively adjusted according to the marker fluctuation rate (when the fluctuation rate is higher than the median, the local alignment sensitivity is enhanced);

[0207] Achieve precise alignment of marker fluctuation curves in different periods and maintain the consistency of timing characteristics.

[0208] Dynamic Causal Convolutional Network Modeling

[0209] Network structure:

[0210] The hidden layer expansion factor is set according to the Fibonacci sequence (1, 2, 3, 4, 5), and the corresponding sampling intervals are 21 days, 42 days, 63 days, 84 days, and 105 days, respectively, to achieve multi-scale feature fusion;

[0211] The gating mechanism enhances feature selectivity through the Sigmoid function and the Hadamard product.

[0212] Risk prediction: The output layer calculates the recurrence risk probability using the Sigmoid function, and the weight parameters are optimized using the Cox proportional hazards model and gradient descent method.

[0213] Clinical validation

[0214] High-risk threshold: set as the mean of the non-recurrence group + 2.5 times the standard deviation of the recurrence group;

[0215] Risk heat map: Plot the time-varying trajectory of key serological markers, mark periods exceeding thresholds, and assist doctors in developing personalized follow-up plans

[0216] Example 5

[0217] Dynamic causal network construction and verification

[0218] Time-varying transfer entropy calculation

[0219] Research subjects: The serum marker time series data of 50 patients with postoperative recurrence and 50 patients without recurrence in Example 1 were selected.

[0220] Causal analysis:

[0221] Calculate the time-varying transfer entropy matrix (TE k → m (t)), which measures the predictive ability of marker k for m;

[0222] The focus was on analyzing the differences in the causal relationships of serological markers in different periods.

[0223] Significant causal edge screening

[0224] Permutation test steps:

[0225] Randomly shuffle the time series data of marker k to generate 1000 pseudo samples;

[0226] Calculate the pseudo transfer entropy (TE k ′→ m );

[0227] The causal edges with p < 0.01 and TE > 0.05 were retained to construct a dynamic causal network.

[0228] Results and Verification

[0229] Key causal edges:

[0230] Early stage (1-3 months after surgery): Inflammatory markers CRP and neutrophil / lymphocyte ratio (NLR) → recurrence risk (TE=0.12, p=0.003) (TE=0.10, p=0.005), suggesting that systemic inflammation is associated with recurrence risk;

[0231] Late period (4-6 months after surgery): Inflammatory marker IL-6, tumor marker CEA → recurrence risk (TE=0.08, p=0.007) (TE=0.15, p=0.002), revealing that chronic inflammation and tumor markers are associated with recurrence risk.

[0232] Clinical value: The causal network identifies key pathways and marker combinations related to recurrence, providing direction for biomarker screening and mechanism research.

[0233] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all details in detail, nor do they limit the invention to only the specific implementation methods described. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can better understand and utilize the present invention.

Claims

1. A modeling algorithm for predicting the risk of postoperative recurrence of breast cancer based on serological markers, characterized in that: The method comprises the following steps: Step A: Collection and preprocessing of clinical data: Retrospectively collect serum marker data of breast cancer patients at different postoperative periods to form the original time series data set Where N is the number of markers and T is the total number of time points; Step B: Data collation and quality control: Missing values ​​in the original time series data set are filled using professional methods, outliers are removed, and the markers are periodically corrected and standardized to ensure the quality of subsequent modeling data. Specifically, for missing values, reasonable filling is performed based on the characteristics of the markers and related mechanisms; for outliers, thresholds are set based on the data distribution of the non-recurrence group for screening and elimination; the amplitude A of each marker is estimated using the Lomb-Scargle periodogram. i and phase By formula: Perform periodic phase correction on the data to eliminate the interference caused by periodic fluctuations; Step C: Multi-cycle time series alignment and feature extraction: The improved dynamic time warping (DTW) algorithm is used to align the serum marker fluctuation curves of different detection cycles. The alignment error function is defined as: in: σ k : population standard deviation of marker k; λ: time decay factor; D: marker dimension; Step D: Dynamic Causal Convolutional Network Modeling: Construct a causal temporal convolutional network (Causal-TCN) with an expansion factor in the Fibonacci sequence (1, 2, 3, 4, 5). The hidden layer is calculated as: in: *: Causal convolution operation (only depends on data before time td); d: dilation factor of layer l; Step E: Risk prediction and verification: The output layer calculates the breast cancer risk probability through the Sigmoid function: Where: w i is the weight parameter, which is optimized by the cross entropy loss function.

2. The breast cancer postoperative recurrence risk prediction modeling algorithm based on serological markers according to claim 1, characterized in that: Finally, the Z-score normalization method is used in step B to adjust the corrected data to a standard distribution with a mean of 0 and a standard deviation of 1, thereby improving the consistency and reliability of the data and laying the foundation for subsequent modeling and analysis.

3. The breast cancer postoperative recurrence risk prediction modeling algorithm based on serological markers according to claim 1, characterized in that: The time decay factor λ of the improved DTW algorithm in step C is adaptively adjusted in the following manner: When the marker fluctuation rate is above the median, the local sensitivity of the time alignment is increased.

4. The breast cancer postoperative recurrence risk prediction modeling algorithm based on serological markers according to claim 1, characterized in that: The gating mechanism of the causal convolutional network in step D is designed as follows: Where: ⊙ represents the Hadamard product, σ is the Sigmoid function.

5. The breast cancer postoperative recurrence risk prediction modeling algorithm based on serological markers according to claim 1, characterized in that: The step D further includes a dynamic causal discovery module: (1) Calculate the time-varying transfer entropy matrix: (2) Screening significant causal edges: For each TE k→m A permutation test (1000 resamplings) was performed, and edges with p < 0.01 and TE > 0.05 were retained to construct the causal network.

6. The breast cancer postoperative recurrence risk prediction modeling algorithm based on serological markers according to claim 5, characterized in that: The specific steps of the permutation test are: (1) Randomly shuffle the time series data of marker k to generate k′; (2) Calculate the pseudo transfer entropy TE after scrambling k′→m (3) Repeat 1000 times and calculate the significance level:

7. The breast cancer postoperative recurrence risk prediction modeling algorithm based on serological markers according to claim 1, characterized in that: The weight in step E is determined by: (1) Constructing the Cox proportional hazards model: (2) Use the gradient descent method to solve the maximum likelihood estimate: Where: R j At time t j A collection of samples at risk.

8. The breast cancer postoperative recurrence risk prediction modeling algorithm based on serological markers according to claim 1, characterized in that: The data preprocessing in step A further includes: (1) Perform periodic phase correction on each marker: Among them: A i 、φ i Estimation through Lomb-Scargle periodogram; (2) Z-score standardization of the corrected data:

9. The breast cancer postoperative recurrence risk prediction modeling algorithm based on serological markers according to claim 1, characterized in that: The expansion factor configuration rule of the causal convolutional network is: Stratum 1: d = 1 (sampling interval = 21 days); Stratum 2: d = 2 (sampling interval = 42 days); Stratum 3: d = 3 (sampling interval = 63 days); Stratum 4: d = 4 (sampling interval = 84 days); Stratum 5: d = 5 (sampling interval = 105 days); Form multi-scale temporal feature fusion.

10. The breast cancer postoperative recurrence risk prediction modeling algorithm based on serological markers according to claim 1, characterized in that: Also includes clinically validated modules: (1) Define high-risk threshold: φ = μ 未复发组 +2.5σ 复发组 ; (2) Generate risk heat map: The time-varying trajectories of key serological markers in the causal network were plotted, and the periods exceeding the threshold were marked.

Images