CN117558456A - Construction and application of multi-factor esophageal cancer survival prediction model based on biological probability membrane system - Google Patents
Construction and application of multi-factor esophageal cancer survival prediction model based on biological probability membrane system Download PDFInfo
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- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
- G16H50/00—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics
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- G16H50/00—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics
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Abstract
The application discloses construction and application of a multi-factor esophageal cancer survival prediction model based on a biological probability membrane system. According to the method, firstly, ROC and KM survival analysis are utilized to screen out influence factors influencing the survival state of a sample, secondly, a conceptual model for predicting the prognosis of the esophageal cancer is constructed by utilizing a probability membrane system, a corresponding membrane structure and an object set are set according to the conceptual model, a corresponding evolution rule is designed by combining the characteristics of the disease evolution of the esophageal cancer, and finally, the MeCoSim software is utilized to simulate a multi-factor esophageal cancer survival prediction model based on the biological probability membrane system. And then comparing the model with a traditional machine learning method, and comparing the result with the traditional machine learning method, a back propagation neural network (BP) model and an XGBoost model, the multi-factor esophageal cancer survival prediction model based on the biological probability membrane system has certain advantages in the aspects of accuracy, area under a subject working characteristic curve (AUC), massa coefficient and the like.
Description
Technical Field
The application relates to the technical field of cancer survival prediction models, in particular to construction and application of a multi-factor esophageal cancer survival prediction model based on a biological probability membrane system.
Background
Esophageal squamous cell carcinoma (esophageal squamous cell carcinoma, ESCC) is a clinically common heterogeneous digestive tract malignant tumor disease, and is also a disease with higher incidence in china; patient survival rates after treatment are generally low, particularly in rural areas. Clinical data indicate that patient selection of different treatment regimens can have a significant impact on survival, and therefore selection of appropriate treatment regimens is important. However, because of the complex pathology of ESCC, there is an error in risk assessment, and there is a need to develop a system to predict the survival risk level of a patient in order to provide a more accurate treatment regimen for the patient. While the survival of ESCC patients has increased with the continued introduction of new drugs and new technologies, current risk assessment methods have some limitations and require more accurate predictive systems to guide therapeutic decisions.
Traditional cancer treatment methods are selected based on the "gold standard" method, which includes three tests, clinical examination, radiological imaging, and pathological examination. The doctor depends on own clinical experience and expertise and decides which treatment mode to take in combination with the test result. However, the conventional method is invasive and can cause physical discomfort and pain to the examined population. In addition, the cost is high, and the method is not suitable for large-scale popularization and use. At the same time, the examination results can only be used to prove the existence of cancer, and the risk level of the cancer cannot be determined.
To address the above, machine learning methods are used to predict cancer patient risk levels. Because machine learning offers advantages in terms of complexity in processing large-scale data and finding prognostic factors. Its learning process can be generally divided into: data acquisition, data preprocessing, model training and prediction, model evaluation and the like. Although the machine learning method can utilize clinical data which is easily available to patients and analyze and process relationships among the data more quickly, the machine learning model has the defects of low accuracy, unstable performance and the like when solving the problem of large-scale complexity.
Compared with a single machine learning model, the advantages of membrane calculation have the characteristics of distribution and parallelism in calculation, and the method can effectively conduct biological system evolution analysis, and further can model according to interaction among different components in a biological system. Thereby obtaining more accurate, stable and robust results.
The information disclosed in this background section is only for enhancement of understanding of the background of the disclosure and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art that is well known to a person skilled in the art.
Disclosure of Invention
For esophageal squamous cell carcinoma, the selection of a proper treatment mode is very critical to improving the survival rate and the quality of life of patients, and the accurate prognosis evaluation of esophageal cancer patients is very important. In this regard, the inventor of the application firstly utilizes ROC and KM survival analysis to screen out influencing factors influencing the survival state of a sample, secondly utilizes a probability membrane system to construct a conceptual model for prognosis prediction of esophageal cancer, sets corresponding membrane structures and object sets according to the conceptual model, designs corresponding evolution rules in combination with characteristics of disease evolution of esophageal cancer, and finally utilizes software to verify the prediction model. Compared with the traditional machine learning method (support vector machine (SVM), back propagation neural network (BP) and XGBoost model), the multi-factor esophageal cancer survival prediction model based on the biological probability membrane system has certain advantages in the aspects of accuracy, area under a subject working characteristic curve (AUC), massa coefficient and the like.
According to one aspect of the present disclosure, a method for constructing a multi-factor esophageal cancer survival prediction model based on a biological probability membrane system is provided, comprising the steps of:
(1) Dividing the patients into four stages of esophagus cancer stage I, esophagus cancer stage II, esophagus cancer stage III and esophagus cancer stage IV according to TNM stage conditions of the patients, and screening out influencing factors of survival time of the esophagus cancer patients by ROC analysis and KM survival analysis;
(2) Constructing a module related to the development of esophagus cancer, and giving parameters required by the model;
(3) Based on the corresponding modules divided in the step (2), a specific membrane calculation model system is set, the related structure and object are defined, and calculation rules of each module on disease development are set by combining the characteristics of esophageal cancer disease evolution.
In some embodiments of the present disclosure, in said step (1), based on ROC curve analysis, the age of the continuous variable is determined as one influencing factor for prognosis of esophageal cancer patients.
In some embodiments of the present disclosure, in the step (1), the influence factors of survival of the esophageal cancer patient are selected based on KM survival analysis, including a final differentiation degree, a final infiltration degree, a final tumor site, a final general type, and sex.
In some embodiments of the present disclosure, in the step (2), the following modules related to the progression of the esophageal cancer disease are respectively constructed:
(1) esophageal cancer stage i module: in determining the rule execution probability, considering the influence of age, final differentiation degree and final infiltration degree;
(2) esophageal cancer stage ii module: in determining the rule execution probability, consider the influence of age, final general type, and final infiltration degree;
(3) Esophageal cancer stage iii module: in determining the rule execution probability, consider the influence of age, final gross type, and final tumor site;
(4) esophageal cancer stage iv module: the influence of age, final general type, gender is considered when determining the rule execution probability.
In some embodiments of the present disclosure, in the step (3), the following film calculation model system is set, defined:
Π＝(Γ,μ,{M 1 ,M 2 ,M 3 ,M 4 },R,{p r } r∈R )
wherein Γ= { X i,jk ,Y i,k,l ,Z i,l,g ,W i,l,h ,1<＝i<＝37,1<＝j<＝3,1<＝k<＝4,1<＝l<＝3,1<＝g<＝3,1<＝h<=2 }, in the formula, X i , jk Patients with age i, final differentiation degree j, final infiltration degree k, in stage I esophageal cancer module, subject Y i,k,l Patient, subject Z, defined as stage II esophageal cancer of age i, final degree of infiltration k, final general type l i,l,g Patient defined as stage III esophageal cancer module with age i final gross type i and final tumor site g, subject W i,l,h Patients with age i, final general type l, sex h in stage iv esophageal cancer module; i represents the age of the patient with esophageal cancer; j represents the final degree of differentiation of the patient, where j=1 represents high differentiation, j=2 represents medium differentiation, and j=3 represents low differentiation; k represents the final degree of infiltration of the patient, k=1 represents infiltration to the myometrial portion, k=2 represents infiltration to the carcinoma in situ, k=3 represents infiltration to the submucosa, and k=4 represents infiltration to the submucosa; letter l indicates the final gross type of the patient, l=1 indicates the final gross type is plaque type, l=2 indicates the final gross type is ulcer type, l=3 indicates the final gross type is erosion type, and l=4 indicates the final gross type is medullary type; g represents the final tumor site of the patient, g=1 represents the upper chest segment, g=2 represents the middle chest segment, and g=3 represents the lower chest segment; h represents the sex of the patient, h=1 represents male, h=2 represents female;
u= [ [ [ ]2]101[ [ ]2]102[ [ ]2]103[ [ ]2]104], representing a nested four two-layer film structure in one environment;
initializing object set M 1 ,M 2 ,M 3 ,M 4 Areas of the film structure corresponding to four two layers respectively, whereinWherein q is ijk Represents the total number of patients of all ages i final differentiation degree l final infiltration degree k.
Wherein e ikl Represents the total number of patients of all ages i final gross type i final infiltration degree k.
Wherein t is igl Represents the total number of patients of all ages i final gross type i and final tumor site g.
Wherein t is ihl Representing the total number of patients of all ages i, ultimately of general type i, sex h;
r is the definition of the calculation rule:
r mainly comprises the calculation rules of four modules, corresponding to four parts of the membrane structure. In all subjects, probability selection among three options (a) remains in the same stage (but older) (b) disease progresses to the next stage, or (c) dies. Only in the case of membrane 104, only two options are available, as it corresponds to the last stage of the module. The specific definition is as follows:
the membrane 101 module corresponds to the esophageal cancer stage i module, which mainly includes three disease type rules, disease stabilization rules, disease progression rules, and disease worsening (death) rules.
Disease stabilization rules:
age at minimum 1 and critical threshold k 1 Patients with intermediate stage I esophageal carcinoma with pr 1 Is stable at the current stage but increases in age by one year.
Age at minimum k 1 And a critical threshold k 2 Patients with intermediate stage I esophageal carcinoma with pr 2 Is stable at the current stage but increases in age by one year.
Rules of disease progression:
age at minimum 1 and critical threshold k 1 Patients with intermediate stage I esophageal carcinoma with pr 11 To enter the next stage.
Age at minimum k 1 And a critical threshold k 2 Patients with intermediate stage I esophageal carcinoma with pr 21 To enter the next stage.
Disease exacerbation (death) rule:
age at minimum 1 and critical threshold k 1 Patients with intermediate stage I esophageal cancer with 1-pr 1 -pr 11 Is a probability of death.
Age at minimum k 1 And a critical threshold k 2 Patients with intermediate stage I esophageal cancer with 1-pr 2 -pr 21 Is a probability of death.
The membranes 102 and 103 correspond to esophageal cancer stage ii and stage iii models, respectively, and their evolutionary rules are the same as those of the membrane 101, with only differences in age and probability. And thus are not separately described.
The membrane 104 corresponds to the esophageal cancer stage iv module, and is the last module, so it has only disease stabilization rules and disease exacerbation (death) rules, as follows:
Disease stabilization rules:
age at minimum 1 and critical threshold k 7 Patients with stage IV esophageal cancer in between with pr 7 Is stable at the current stage but increases in age by one year.
Age at minimum k 7 And a critical threshold k 8 Patients with stage IV esophageal cancer in between with pr 8 Is stable at the current stage but increases in age by one year.
Disease exacerbation (death) rule:
age at minimum 1 and critical threshold k 7 Patients with stage IV esophageal cancer in between with 1-pr 7 Is a probability of death.
Age at minimum k 7 And a critical threshold k 8 Patients with stage IV esophageal cancer in between with 1-pr 7 Is a probability of death.
Wherein k is 1 And k 2 A critical threshold and a maximum value respectively representing the ages of patients with first-stage esophagus cancer; k (k) 3 And k 4 A critical threshold and a maximum value respectively representing the ages of patients with second-stage esophageal cancer; k (k) 5 And k 6 A critical threshold and maximum value representing the age of a patient with esophageal cancer stage three; k (k) 7 And k 8 A critical threshold and maximum value representing the age of a patient with esophageal cancer stage three; pr (pr) 1 To pr (pr) 8 Respectively representing the probability of the patient's illness state in the four modules; pr (pr) 11 To pr (pr) 61 The probability of the patient's condition entering the next stage is indicated; yn, zn, wn represent the patient at the time the condition enters the next stage, respectively.
One or more technical solutions provided in the embodiments of the present application at least have the following technical effects or advantages:
compared with a machine learning model, the advantage of the calculation of the biological probability film has the characteristics of distribution and parallelism in the calculation, and the biological probability film can effectively carry out the evolution analysis of a biological system, so that modeling can be carried out according to interaction among different components in the biological system, and more accurate, stable and strong results are obtained. Aiming at the problem of low survival rate of prognosis prediction of esophageal cancer, the invention adopts ROC and KM survival analysis to screen out influencing factors influencing the survival state of a sample, and takes the influencing factors as main factors in the development of simulated illness; simulating the esophageal cancer disease evolution process by using a probability film P system, and completing the risk level prediction of an esophageal cancer patient by designing a conceptual model and a calculation model; the established model is simulated and verified, and compared with the traditional machine learning method, and the results show that the membrane calculation model has higher accuracy in the aspect of disease prediction.
Drawings
FIG. 1 shows the result of a stage I KM analysis of food esophageal cancer according to an embodiment of the present application.
FIG. 2 shows the results of a stage II KM analysis of tube cancer in an embodiment of the present application.
FIG. 3 shows the result of stage III KM analysis of esophageal cancer in one embodiment of the present application.
FIG. 4 shows the result of KM analysis of stage IV esophageal cancer according to an embodiment of the invention.
FIG. 5 is a flow chart of the construction of a probabilistic membrane system-based multi-factor esophageal cancer prognosis prediction model in an embodiment of the application.
FIG. 6 is a diagram of a membrane structure of a membrane system according to an embodiment of the present application.
FIG. 7 is a rule diagram of various modules of a probabilistic membrane system-based multi-factor esophageal cancer prognosis prediction model in an embodiment of the application.
FIG. 8 is a simulation result of MeCoSim of a probabilistic membrane system-based multi-factor esophageal cancer prognosis model in an embodiment of the application.
FIG. 9 is a comparison of confusion matrix with machine learning model in one embodiment of the present application.
FIG. 10 is a graph showing the comparison of the evaluation index of each model in an embodiment of the present application.
Detailed Description
For better understanding of the technical solutions of the present application, the following detailed description will refer to the accompanying drawings and specific embodiments.
Embodiment one: analysis of influence of various classified variables in different phases of esophageal cancer on survival state of patient
The sample data of the patients are derived from 534 cases of esophageal squamous carcinoma patients co-admitted to the first affiliated hospital of Zhengzhou university from 1 month in 2007 to 12 months in 2018. According to TNM stage conditions of patients, the data mainly comprises an esophagus cancer stage I (115 cases), an esophagus cancer stage II (189 cases), an esophagus cancer stage III (179 cases) and an esophagus cancer stage IV (51 cases), and detailed information of each stage is shown in table 1.
Table 1 patient sample data
1. Influence factor analysis
Prognosis of patients with esophageal cancer is affected by many factors, mainly including age, sex, type and degree of differentiation of cancer, physical health status, stage of cancer, and the like of the patient. Stage of esophageal cancer is the most important factor affecting prognosis of patients, and is an important index describing pathological characteristics, spread range, prognosis of patients and the like of tumors. Determining the severity and spread of cancer according to three factors of T (Tumor) of Tumor, N (Node) of lymph Node and M (metatasis) of Metastasis, wherein T stage describes the spread degree and invasion depth of Tumor in esophagus; n-staging describes whether cancer has invaded nearby lymph nodes; m stage describes whether cancer has metastasized to distant organs. In the case, according to TNM stage conditions of patients, influence factors such as age, sex, cancer type differentiation degree and the like of the patients are combined, and prognosis influence factors of the patients in each stage are respectively analyzed.
The influence of each index on survival conditions in each period is discussed respectively aiming at the characteristic that in the TNM stage of esophageal cancer, each period is different. For the index of the classification, whether the index is obviously related to the survival condition or not is analyzed by using Kaplan-Meier survival, and the variables of the classification mainly comprise the sex of a patient, the differentiation degree of a tumor, the final position of the tumor, the final general type and the final infiltration degree. For continuous variables, calculating continuous thresholds of indexes by using an ROC curve method, classifying the indexes into two types, and analyzing whether a significant difference exists in survival states between the two types of indexes according to the size of a P value.
(1) ROC Curve analysis
In the existing data, continuous variables exist in each period, and mainly comprise the age of a patient and the length, width and thickness of tumors; for continuous variables, whether indexes have significant differences on survival or not is analyzed by adopting an ROC analysis method, the critical threshold value of each index is obtained, and the continuous indexes are divided into discrete indexes. The results of the continuity analysis variables are shown in table 2, and as can be seen from the results of the ROC analysis, the P values for the ages in the four periods were all less than 0.05, and the AUC values were all greater than 0.5. Indicating that there is a significant difference between the age and survival of the patient, the age of the continuous variable can be a factor in prognosis of an esophageal cancer patient.
TABLE 2 ROC analysis results for patients
(2) KM survival analysis
In this example, classified variants in different phases of esophageal cancer were analyzed by Kaplan-Meier survival analysis. Survival analysis can estimate the probability of a patient experiencing an event at a certain point in time and is therefore of great advantage in predicting disease progression, etc. First, survival analysis was performed on stage I esophageal cancer, and from fig. 2, it was found that P values of the final differentiation degree and the final infiltration degree were less than 0.05, indicating that these two factors were significantly different for the survival state of the patient. Further analysis showed that both factors had a greater effect on patient prognosis during stage I esophageal cancer (see figure 1). Next, survival analysis was performed on stage II esophageal cancer, and the KM survival analysis results of stage II esophageal cancer influencing factors are shown in fig. 2, wherein the P value of the final general type and the final degree of infiltration is less than 0.05, suggesting that the influence of these two factors on the survival state of the patient needs to be considered in stage II esophageal cancer. Similarly, in stage III and stage IV esophageal cancer, as can be seen in FIGS. 3 and 4, the P-values for both the final gross type and final tumor location, and the final gross type and sex are less than 0.05, indicating that these factors have a greater impact on the patient in the progression of the condition at each stage. By carrying out survival analysis on all the classification variables in each period, corresponding influencing factors in the disease development in each period are obtained, and advice is provided for later modeling.
In summary, the present case systematically analyzes the influence of each classification variable on the survival state of the patient in different phases of esophageal cancer by using the Kaplan-Meier survival analysis method. These results may provide important references and suggestions for subsequent studies and treatments.
Embodiment two: multi-factor esophageal cancer prognosis prediction model based on probability membrane system
In the method, 534 cases of esophageal squamous carcinoma patients co-treated in a first affiliated hospital of Zhengzhou university are taken as study objects, main influencing factors of esophageal cancer prognosis in each period are analyzed, and then prediction analysis is carried out on the prognosis of the esophageal cancer patients by establishing a multi-factor probability membrane system. An esophageal cancer prognosis prediction model based on a probability membrane system is provided. The modeling of the model is mainly divided into two stages, namely the design of a conceptual model and the design of a calculation model; the conceptual model is mainly used for constructing a module related to the development of esophageal cancer disease and giving parameters required by the model. The calculation model is mainly responsible for designing a specific membrane system according to the corresponding module designed in the previous stage, describing the related structure and object in detail, and setting the calculation rule of each module about the disease development. The specific steps are as follows (see fig. 5):
Step1: a data set is acquired and processed. The method comprises the steps of preprocessing esophageal cancer patient data collected from a first affiliated hospital of Zhengzhou university, deleting missing values, dividing the patient into four periods according to TNM staging conditions of the patient, and analyzing influence factors of prognosis of the patient in each period by ROC analysis and KM survival analysis.
Step2: initializing. Some parameters in the membrane system are initialized, and a better parameter setting is provided for the model.
Step3: and (3) designing a basic conceptual model. Corresponding modules are arranged according to the evolution process of the esophagus cancer condition, and rules including the rules of disease development, stable disease condition and the like are arranged in each module; an existing base probability model is determined.
Step4: and (5) designing a calculation model. The corresponding mathematical model application framework is formulated based on the previously determined conceptual model and can be used for calculation rather than approximate calculation.
Step5: and outputting. And obtaining the predicted data of the esophageal cancer patient through MeCoSim simulation calculation.
1. Concept model design
The model mainly simulates the evolution of each stage of disease to death of each patient, and the development of esophageal cancer disease is a progressive process, and is generally divided into four stages, namely stage I: esophageal cancer is limited to the mucosal lining in the esophagus and does not invade deep tissues of the esophageal wall. Stage II: esophageal cancer invades deep tissues of the esophageal wall, but does not spread to adjacent lymph nodes. Stage III: esophageal cancer has spread to adjacent lymph nodes. Stage IV: esophageal cancer has spread to other parts of the body, distant metastasis. Based on this design, the corresponding four modules, in any case, all the individuals are evolving at the same time, although each individual in the module has undergone its own evolution. And a description is given of four modules: a stage I esophageal cancer module, a stage II esophageal cancer module, a stage IV esophageal cancer module, and a stage IV esophageal cancer module.
(1) Esophageal cancer stage i module: the module designs rules for simulating the possibility of the disease development of the stage I esophageal cancer. These possibilities include stable disease, progression and death. Based on earlier analysis, the progression of the disease is mainly affected by the age, final degree of differentiation and final degree of infiltration of the patient. The influence of these three factors should be fully considered in determining the rule execution probability. According to the data analysis results, patients with older ages, high differentiation degree and invasive degree invading in situ cancer have shorter survival time. Therefore, the probability should be set in consideration with specific information of the patient. The rules can help better simulate the disease development process of patients with esophageal cancer stage I, and further improve the accuracy of a prediction model.
(2) Esophageal cancer stage ii module: in simulating the progression of stage II esophageal cancer, it should be noted that the severity of the condition is already more severe than stage I, and therefore the probability of exacerbation is higher. Based on previous analysis results, the progression of stage ii esophageal cancer is mainly affected by age, final general type, and final degree of infiltration. Therefore, the probability of occurrence of a stable condition, an aggravated condition and death of a patient should be set according to these three factors. In particular, for older patients, who are ultimately of the general type invasive and who are ultimately severely infiltrated, there is a higher probability of exacerbation and more immediate attention is required. For other patients, the corresponding probability value needs to be set according to the specific situation.
(3) Esophageal cancer stage iii module: in this module, the patient's condition is more severe, and thus the probability of exacerbation and death is higher. Age, final general type and final tumor location are important factors affecting the progression of the esophageal cancer stage iii condition, and their effects on stable condition, exacerbation and probability of mortality need to be fully considered. Different probabilities are set according to different combinations of these factors to simulate patient condition changes and predict patient survival. Meanwhile, the data show that the mortality rate of the patient in the module is high, so that the situation needs to be fully considered in the rule making process to accurately simulate the disease development condition of the patient.
(4) Esophageal cancer stage iv module: in stage IV of esophageal cancer, the disease condition of the patient is extremely worsened, so that the development of the disease condition has higher uncertainty and complexity, and even rapid worsening, slow worsening and the like can occur. As can be seen from the earlier analysis, the development of the disease is mainly affected by age, final general type, sex and other factors, wherein the survival states of men and women in the stage IV of esophageal cancer are obviously different. Therefore, in designing the simulation rules, the influence of these factors needs to be fully considered to set different probability rules, simulate the patient's condition change and predict the patient's survival condition. In addition, different influencing factors can lead to stable disease conditions of patients, aggravated disease conditions and different probability of death occurrence, so that different rules and probability distribution are designed according to specific conditions and disease characteristics of the patients, so that the disease development of the patients is more accurately simulated and the survival condition is predicted.
2. Computing model design
This example is directed to the use of a model based on a membrane system to evaluate and predict esophageal cancer patients to understand the evolution of their survival state over time under certain specific conditions. The model will involve a number of processes and parameters for population biology and disease progression. In order to translate these processes and parameters into formal model concepts, it is necessary to design the corresponding elements of the membrane system, including the environment, membrane structure, objects, and evolutionary rules, etc. Appropriate semantic constraints and details inherent to the membrane system need to be considered to ensure accuracy of the model. For example, in modeling the evolution of the condition involved, certain probabilities associated with rules need to be applied to account for uncertainty factors. In designing a membrane system, a major concern is designing rules to simulate the progression of esophageal cancer conditions. This will include rules regarding changes in patient survival status, cancer cell growth and metastasis under specific conditions. By modeling these rules, the patient's condition can be simulated and the time-dependent progression of the esophageal cancer patient's condition can be assessed.
First, a membrane structure of a membrane system needs to be defined, and according to a module designed in a probability model, only one environment e and four two-layer nested membrane structures need to be designed, wherein the two-layer nested membrane structures consist of an inner membrane marked with 2 and an outer membrane marked with 1, and particularly shown in fig. 6.
Based on the defined membrane structure, the definition of the constructed membrane calculation model system is as follows:
Π＝(Γ,μ,{M 1 ,M 2 ,M 3 ,M 4 },R,{p r } r∈R )
1) Wherein Γ= { X i,jk ,Y i,k,l ,Z i,l,g ,W i,l,h ,1<＝i<＝37,1<＝j<＝3,1<＝k<＝4,1<＝l<＝3,1<＝g<＝3,1<＝h<＝2}
In all esophageal cancer patients, the letter i indicates the age of the patient, the letter j indicates the final degree of differentiation of the patient, where j=1 indicates high differentiation, j=2 indicates medium differentiation, j=3 indicates low differentiation, the letter k indicates the final degree of infiltration of the patient, k=1 indicates infiltration into the muscular layer portion, k=2 indicates infiltration into carcinoma in situ, k=3 indicates infiltration into the mucosal layer, and k=4 indicates infiltration into the submucosa; letter l indicates the final gross type of the patient, l=1 indicates the final gross type is plaque type, l=2 indicates the final gross type is ulcer type, l=3 indicates the final gross type is erosion type, and l=4 indicates the final gross type is medullary type; the letter g represents the final tumor site of the patient, g=1 represents the upper chest segment, g=2 represents the middle chest segment, and g=3 represents the lower chest segment; the letter h denotes the sex of the patient, h=1 denotes male, h=2 denotes female;
2) Abstracting all patients into four objects X according to TNM staging of patients i,jk ,Y i,k,l ,Z i,l,g ,W i,l,h Which is defined in terms of the progression of the esophageal cancer condition, the transition between states is as follows: x is X i,jk →Y ik,l, →Z il,,g →W i,l Wherein object X i,jk Patients with age i, final differentiation degree j, final infiltration degree k in esophageal cancer stage one module, subject Y i,k,l Patient, subject Z, defined as esophageal cancer stage two age i, final degree of infiltration k, final general type l i,l,g Patient defined as patient with age i final general type i and final tumor site g in esophageal cancer stage three module, subject W i,l,h Patients with age i, ultimately of general type l, sex h in the esophageal cancer four-stage module are defined.
3) u= [ [ [ ]2]101[ [ ]2]102[ [ [ ]2]103[ [ ]2]104] represents a structure of nesting four two-layer films in one environment.
4) The rules in R are shown in fig. 7.
The corresponding rules for each module are given in fig. 7, which divide the case of regular esophageal cancer progression into three parts, stable disease, progression and worsening (death). The rule is set by combining expert experience according to the prognosis factor of each module and the factor with the biggest influence on survival among three factors obtained by using random forests. Four modules of prognosis factors are analyzed by using a random forest method, and the result shows that the influence of the age on the prognosis of the patient is maximum, so that the age threshold value obtained according to roc is segmented and combined with expert experience And patient survival rates of three years and five years set some parameters required in the rules. Next, some parameters of the rule are described, where k 1 And k 2 The critical threshold and maximum values of the age of the patient with stage one esophageal cancer are indicated, respectively. k (k) 3 And k 4 The critical threshold and maximum values of the age of patients with second stage esophageal cancer are indicated, respectively. k (k) 5 And k 6 A critical threshold and a maximum value representing the age of patients with esophageal cancer in the third stage. k (k) 7 And k 8 A critical threshold and a maximum value representing the age of patients with esophageal cancer in the third stage. pr (pr) 1 To pr (pr) 8 The probabilities of the patient's condition being in steady state in the four modules are represented, respectively. pr (pr) 11 To pr (pr) 61 The probability of the patient's condition going to the next stage (i.e., the progression of the condition) is indicated. yn, zn, wn represent the patient at the time the condition goes to the next stage (the present model does not consider the condition of such patients).
5) With respect to initializing object set M 1 ,M 2 ,M 3 ,M 4 Areas of the film structure corresponding to four two layers respectively, whereinWherein q is ijk Represents the total number of patients of all ages i final differentiation degree l final infiltration degree k.
Wherein e ikl Represents the total number of patients of all ages i final gross type i final infiltration degree k.
Wherein t is igl Represents the total number of patients of all ages i final gross type i and final tumor site g.
Wherein t is ihl Represents the total number of patients of all ages i, ultimately of general type i, sex h.
Embodiment III: esophageal cancer survival prediction model based experimental simulation and result analysis
In order to verify the validity and correctness of the model, data from 534 cases of esophageal cancer patients provided by the first affiliated hospital of Zhengzhou university are used as a basis, and experiments are performed by using simulation software MeCoSim as a simulation platform. In the simulation experiment, the simulation period was set to 11. One simulation cycle represents a natural year, in which the patient experiences a random course of disease transformation during a natural year. Thus, simulation experiments can be performed by adjusting parameters in the model. In the simulation process, rule execution in the PMS system is performed in a probabilistic manner, so that data containing randomness and uncertainty can be effectively processed. In order to ensure the reliability of the experimental result, 1000 times of simulation operation are performed.
1. Prediction result of multi-factor esophageal cancer lifetime prediction model based on biological probability membrane system
By processing the follow-up information of 534 patients, the information and survival condition of the patients in each year after the follow-up are counted respectively. The first year follow-up information of the patient is entered as initial parameters of the model, and the data of follow-up for 2-6 years is compared as output of the results. The simulation result is shown in fig. 8 by using MeCoSim software, and the result in the graph shows that the simulation result of the multi-factor esophageal cancer survival prediction model based on the biological probability membrane system designed in the embodiment is compared with real data, the relative error of each year in each period is controlled within +10%, and the designed model can well simulate the disease evolution process.
2. Comparison with predicted Performance of other methods
To further evaluate the effectiveness of the proposed model, the probabilistic membrane model presented herein was compared to other four predictive models, including Support Vector Machines (SVMs), back propagation neural networks (BP) and XGBoost based on Boosting framework, in esophageal cancer patient datasets. And comprehensively judging the performance of the model by comparing indexes such as classification accuracy, precision, recall rate, F1 score, false positive, false negative, ma Erxiu-second correlation coefficient (MCC), AUC and the like of the seed model.
(1) Evaluation index
Accuracy (ACC): probability that all samples are correctly predicted.
TP is the number of positive examples of correct classification; TN is correctly divided into negative cases; FP is misclassified as the number of positive samples; FN is correctly divided into negative cases.
Precision, also known as Precision, is an evaluation index for the predicted outcome. The number of positive samples which are correctly classified is the proportion of the number of samples which are judged to be positive by the classifier. The accuracy is the statistic on the partial samples, focusing on the statistics of the data that the classifier determines as positive class. It is defined as:
Precision＝TP/(TP+FP)
recall (Recall) the ratio of the number of correctly classified positive samples to the number of true positive samples. Recall is also a statistic on some samples, focusing on statistics on true positive class samples. It is defined as:
Recall＝TP/(TP+FN)
f1 Score is the harmonic mean of precision and recall, an index in statistics that is used to measure the accuracy of a two-class (or multi-task two-class) model:
FPR:False positive rate；
FPR＝FP/(FP+TN)
FNR:False-negative rate；
FNR＝FN/(FN+TP)
the Ma Xiusi correlation coefficient (Matthews correlation coefficient) MCC is mainly used for measuring the classification problem, and TP, TN, FP, FN is comprehensively considered and is an index of comparative equalization. Ma Xiusi correlation coefficient formula is:
AUC (area under the curve): AUC is the area under ROC curve, which is an index of a comprehensive evaluation model, and chinese name is "subject work characteristic curve". ROC curves originate from the military field and are then widely used in the medical field, the name "subject work characteristics" also coming from the medical field. The abscissa of the ROC curve is the false positive rate (False Positive Rate; FPR), namely the probability of misclassification of negative cases into positive cases, and is medically called misdiagnosis rate; the ordinate is true positive rate (True Positive Rate; TPR), probability of pairing positive cases.
(2) Comparative analysis
False positives and false negatives of the four models are shown in fig. 9, false positives can reflect the misdiagnosis rate of the model, the lower the false positive is, the better the false positive is, the numerical value of the SVM model is highest, and the numerical value reaches 45%, which indicates that the misdiagnosis rate of the SVM model is highest, the PMS misdiagnosis rate is lowest, the value is only 11%, and BP and XGBoost are 18% and 29% respectively. False negatives can reflect the missed diagnosis rate of the model, the lower the value is, the better the value is, in the aspect of false negatives, the membrane calculation model can be within 10%, the missed diagnosis rate is the lowest and is only 7%, the XGBoost is 18%, the SVM model missed diagnosis rate is the highest, the missed diagnosis rate is 24%, and the BP is 20%.
Performance of accuracy, recall, precision, F1 score, and MCC figure 10 shows: in terms of accuracy, the accuracy can intuitively judge the performance of the model, and the average accuracy of the four models is 76%, 81%, 87% and 92% respectively. The accuracy of the SVM model is only 76%, the BP neural network model reaches 81%, XGBoost is 6% higher than the BP neural network model, 87% is reached, and PMS is 92%. In terms of recall, the higher the recall, the more discriminative the model is to the positive sample. PMS reached 88%, four models maximum, XGBoost 4% less than PMS, 84% and SVM and BP 64% and 81%, respectively. In terms of accuracy, the higher the accuracy, the more the model is able to distinguish negative samples. PMS is the maximum value of four models and reaches 89%, which shows that the model has the strongest distinguishing capability for negative samples, SVM is 13% lower than PMS and 63%, BP and XGBoost are relatively similar and reach 81% and 80% respectively. The comparison of the accuracy and the recall shows that the PMS has stronger positive and negative sample distinguishing capability.
In terms of F1 score, F1 score gives attention to the accuracy and recall of the classification model, the maximum value of the classification model is 1, the minimum value of the classification model is 0, and the larger the value is, the better the classification model is. PMS is the highest value of five models, reaches 0.83, BP is the smallest value of four models, and is only 0.71, and XGBoost and SVM are respectively 0.82 and 0.75. In the MCC aspect, the MCC has a value range of [ -1,1], wherein a value of 1 indicates that the prediction is completely consistent with the actual result, a value of 0 indicates that the predicted result is not as much as the random predicted result, and a value of-1 indicates that the predicted result is completely inconsistent with the actual result, and the MCC essentially describes the correlation coefficient between the predicted result and the actual result. The MCC of the four models is above 0.5, which shows that the four models can reflect the actual results to a certain extent, the four models have the best PMS performance, the MCC reaches 0.82, XGBoost is inferior to PMS, 0.72 is achieved, and SVM and BP are respectively 0.59 and 0.52.
In terms of AUC, AUC is the area under the ROC curve, the numerical value of the area is between 0 and 1, the quality of the classifier can be intuitively evaluated, and the larger the AUC value is, the better the classifier effect is. Of the four models, PMS can reach up to 0.91, xgboost is next to PMS, 0.86, bp and SVM are 0.78 and 0.77, respectively. See fig. 10.
By comparing 6 indexes, the PMS provided by the study can be verified to have excellent prediction performance, and BP and SVM are single machine learning, so that the PMS is weak in four models. And XGBoost adopts the idea of integrated processing, so that the prediction performance is better than that of a single machine learning model. Aiming at the characteristics of patient data, the multi-factor esophageal cancer survival time prediction model based on the biological probability membrane system simulates the development of illness state by designing corresponding rules, and is more in line with the biological evolution process, so that the multi-factor esophageal cancer survival time prediction model shows more excellent performance in the research, can accurately predict the survival risk level of ESCC patients, and provides support for the selection of treatment modes of ESCC patients.
3. Conclusion(s)
Because different treatment modes have significant influence on the survival time of ESCC patients, in order to help medical staff to more accurately select the treatment modes of ESCC patients, a multi-factor esophageal cancer prognosis Prediction Model (PMS) based on a probability membrane system is provided and applied to ESCC survival risk level prediction, so that support is provided for the medical staff to select the treatment modes. Firstly, analyzing esophageal cancer patient data by ROC curve analysis and KM survival analysis, respectively obtaining influencing factors influencing the survival state of the patient, performing conceptual modeling by using a probability film P system disease evolution process, dividing the patient disease development process into four stages according to TNM stage conditions of the patient, designing a corresponding rule model disease development process, performing modeling by using a model provided by designing a corresponding calculation model, performing simulation verification on the calculation model by using MeCoSim software according to the probability of facility rule operation by methods such as random forests, expert experience and the like, and analyzing the output result. The result shows that the method has excellent performance on 6 performance indexes, can accurately judge the survival risk level of ESCC patients, and customizes personalized treatment scheme for the patients.
While certain preferred embodiments of the present application have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the application.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (6)
1. The method for constructing the multi-factor esophageal cancer survival prediction model based on the biological probability membrane system is characterized by comprising the following steps of:
(1) Dividing the patients into four stages of esophagus cancer stage I, esophagus cancer stage II, esophagus cancer stage III and esophagus cancer stage IV according to TNM stage conditions of the patients, and screening out influencing factors of survival time of the esophagus cancer patients by ROC analysis and KM survival analysis;
(2) Constructing a module related to the development of esophagus cancer, and giving parameters required by the model;
(3) Based on the corresponding modules divided in the step (2), a specific membrane calculation model system is set, the related structure and object are defined, and calculation rules of each module on disease development are set by combining the characteristics of esophageal cancer disease evolution.
2. The method for constructing a multi-factor esophageal cancer survival prediction model based on a biological probability membrane system according to claim 1, wherein in said step (1), based on ROC curve analysis, continuous variable age is determined as an influencing factor of prognosis of esophageal cancer patients.
3. The method for constructing a multi-factor esophageal cancer survival prediction model based on a biological probability membrane system according to claim 2, wherein in the step (1), the influence factors of survival of esophageal cancer patients, including the final differentiation degree, the final infiltration degree, the final tumor site, the final general type and the sex, are screened based on KM survival analysis.
4. The method for constructing a multi-factor esophageal cancer survival prediction model based on a biological probability membrane system according to claim 3, wherein in the step (2), the following modules related to esophageal cancer disease development are respectively constructed:
(1) esophageal cancer stage i module: in determining the rule execution probability, considering the influence of age, final differentiation degree and final infiltration degree;
(2) Esophageal cancer stage ii module: in determining the rule execution probability, consider the influence of age, final general type, and final infiltration degree;
(3) esophageal cancer stage iii module: in determining the rule execution probability, consider the influence of age, final gross type, and final tumor site;
(4) esophageal cancer stage iv module: the influence of age, final general type, gender is considered when determining the rule execution probability.
5. The method for constructing a multi-factor esophageal cancer survival prediction model based on a biological probability membrane system according to claim 4, wherein in the step (3), the following membrane calculation model system is set and defined:
∏＝(Γ,μ,{M 1 ,M 2 ,M 3 ,M 4 },R,{p r } r∈R )
wherein Γ= { X i,jk ,Y i,k,l ,Z i,l,g ,W i,l,h ,1<＝i<＝37,1<＝j<＝3,1<＝k<＝4,1<＝l<＝3,1<＝g<＝3,1<＝h<=2 }, in the formula, X i,jk Patients with age i, final differentiation degree j, final infiltration degree k, in stage I esophageal cancer module, subject Y i,k,l Patient, subject Z, defined as stage II esophageal cancer of age i, final degree of infiltration k, final general type l i,l,g Patient defined as stage III esophageal cancer module with age i final gross type i and final tumor site g, subject W i,l,h Patients with age i, final general type l, sex h in stage iv esophageal cancer module; i represents the age of the patient with esophageal cancer; j represents the final degree of differentiation of the patient, where j=1 represents high differentiation, j=2 represents medium differentiation, and j=3 represents low differentiation; k represents the final degree of infiltration of the patient, k=1 represents infiltration to the myometrial portion, k=2 represents infiltration to the carcinoma in situ, k=3 represents infiltration to the submucosa, and k=4 represents infiltration to the submucosa; letter l indicates the final general type of patient, l=1 indicates that the final general type is plaque-like L=2 indicates that the final general type is an ulcer type, l=3 indicates that the final general type is an erosion type, and l=4 indicates that the final general type is a medullary type; g represents the final tumor site of the patient, g=1 represents the upper chest segment, g=2 represents the middle chest segment, and g=3 represents the lower chest segment; h represents the sex of the patient, h=1 represents male, h=2 represents female;
u= [ [ [ ]2]101[ [ ]2]102[ [ ]2]103[ [ ]2]104], representing a nested four two-layer film structure in one environment;
initializing object set M 1 ,M 2 ,M 3 ,M 4 Areas of the film structure corresponding to four two layers respectively, whereinWherein q is ijk Represents the total number of patients of all ages i final differentiation degree l final infiltration degree k.
Wherein e ikl Represents the total number of patients of all ages i final gross type i final infiltration degree k.
Wherein t is igl Represents the total number of patients of all ages i final gross type i and final tumor site g.
Wherein t is ihl Representing the total number of patients of all ages i, ultimately of general type i, sex h;
r is the calculation rule of four modules, and corresponds to four parts of the membrane structure, and is specifically defined as follows:
the membrane 101 module corresponds to the esophageal cancer stage i module and includes three disease types of rules, disease stabilization rules, disease progression rules and disease exacerbation rules:
Disease stabilization rules:
age at minimum 1 and critical threshold k 1 Patients with intermediate stage I esophageal carcinoma with pr 1 Is stable in the current stage, but the age increases by one year;
age at minimum k 1 And a critical threshold k 2 Patients with intermediate stage I esophageal carcinoma with pr 2 Is stable in the current stage, but the age increases by one year;
rules of disease progression:
age at minimum 1 and critical threshold k 1 Patients with intermediate stage I esophageal carcinoma with pr 11 The probability of entering the next stage;
age at minimum k 1 And a critical threshold k 2 Patients with intermediate stage I esophageal carcinoma with pr 21 The probability of entering the next stage;
disease exacerbation rules:
age at minimum 1 and critical threshold k 1 Patients with intermediate stage I esophageal cancer with 1-pr 1 -pr 11 Is dead;
age at minimum k 1 And a critical threshold k 2 Patients with intermediate stage I esophageal cancer with 1-pr 2 -pr 21 Is dead;
the film 102 and the film 103 respectively correspond to an esophageal cancer stage II module and an esophageal cancer stage III model, and the evolution rules of the film 102 and the film 103 are the same as those of the film 101, and only have differences in age and probability;
the membrane 104 corresponds to the esophageal cancer stage iv module, with only the rules of disease stabilization and disease progression:
disease stabilization rules:
age at minimum 1 and critical threshold k 7 Patients with stage IV esophageal cancer in between with pr 7 Is stable in the current stage, but the age increases by one year;
age at minimum k 7 And a critical threshold k 8 Patients with stage IV esophageal cancer in between with pr 8 Is stable in the current stage but increases in age by one year;
disease exacerbation (death) rule:
age at minimum 1 and critical threshold k 7 Patients with stage IV esophageal cancer in between with 1-pr 7 Is dead;
age at minimum k 7 And a critical threshold k 8 Patients with stage IV esophageal cancer in between with 1-pr 7 Is dead;
wherein k is 1 And k 2 A critical threshold and a maximum value respectively representing the ages of patients with first-stage esophagus cancer; k (k) 3 And k 4 A critical threshold and a maximum value respectively representing the ages of patients with second-stage esophageal cancer; k (k) 5 And k 6 A critical threshold and maximum value representing the age of a patient with esophageal cancer stage three; k (k) 7 And k 8 A critical threshold and maximum value representing the age of a patient with esophageal cancer stage three; pr (pr) 1 To pr (pr) 8 Respectively representing the probability of the patient's illness state in the four modules; pr (pr) 11 To pr (pr) 61 The probability of the patient's condition entering the next stage is indicated; yn, zn, wn represent the patient at the time the condition enters the next stage, respectively.
6. A method for predicting survival of an esophageal cancer patient is characterized in that age, sex, final differentiation degree, final infiltration degree, final tumor position and final general type related to the survival of the esophageal cancer patient to be predicted are obtained, an esophageal cancer survival prediction model constructed by the method in claim 1 is input, and the survival prediction of the esophageal cancer patient is obtained.
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