A method for predicting the category structure of elderly people in disease populations based on grey component prediction modeling

Abstract

This invention provides a method for predicting the elderly category structure in disease populations based on grey component prediction modeling. The method includes: collecting multi-component elderly population structure data influenced by specific diseases and analyzing the characteristics of the component data; constructing a modeling framework that integrates a time elasticity mechanism and component structure analysis based on the data characteristics; establishing a novel dynamic nonlinear grey component prediction model based on the framework, which is adapted to irregular time-series component data and optimized with multiple parameters; solving the grey component prediction model parameters and estimating the structural evolution of each component of the elderly disease population, thereby solving the problem of predicting the elderly category structure and managing health in disease populations with small sample sequences. The method proposed in this invention can accurately depict the proportional changes of elderly people in different health states within a disease population, enabling health managers to more accurately grasp the changing trends of the elderly population in the disease burden, and thus formulate more reasonable resource allocation and intervention strategies.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of disease health management system, in particular to a disease population old age category structure prediction method based on grey component prediction modeling. BACKGROUND

[0002] Old-age population disease prediction is an important research direction in the cross field of public health and health management, and the prediction results have important decision value for optimizing medical policy, improving resource allocation efficiency and developing intervention strategies. Old-age population disease prediction research is usually based on historical health data and predicts the prevalence rate of a specific disease in the old age population through various statistical and calculation models, mainly focusing on chronic diseases and acute diseases related to age.

[0003] Various models are used for old-age population disease prediction, mainly including statistical models, machine learning and system modeling, etc. Statistical methods such as exponential smoothing method; Cox regression model; Logistic regression analysis. Machine learning such as using SVM; Random forest prediction. System modeling methods such as using dynamic modeling technology; state transition model; dynamic Markov model. On the one hand, existing old-age disease prediction research mainly focuses on the overall prevalence rate of the old age population, however, with the aggravation of the old age population problem, more refined disease prevention and resource allocation are needed, and it is crucial to focus on the component dynamic analysis of the disease structure within the old age population. On the other hand, most of the existing methods are based on single sequence and other time interval assumptions, which are difficult to adapt to the characteristics of small sample, non-equidistant and component constraints commonly existing in refined survey data, resulting in the limitation of traditional time series model in practical application. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of the prior art, and to provide a disease population old age category structure prediction method based on grey component prediction modeling, which constructs a non-equidistant grey component prediction model to predict the structure of different old age categories in the disease population. On the one hand, the system research of grey component model is an important breakthrough for the expansion of grey system theory to more complex structure data, which not only helps to break the dependence of component data on ideal time interval and enhance the adaptability of the model to non-ideal data environment, but also provides theoretical support for the construction of prediction framework for structural data. On the other hand, this method is used for the evolution prediction of the structure of old age population with a certain disease under the background of population aging, which helps to identify the evolution trend, optimize resource allocation, and shows significant practical significance in health risk warning and precise management.

[0005] To achieve the above purpose, the present application adopts the following technical scheme: a disease population old age category structure prediction method based on grey component prediction modeling, comprising:

[0006] S1, collect multi-component old population structure data affected by a certain type of disease, and analyze the characteristics of the component data;

[0007] S2, according to the data characteristics, build a modeling framework that integrates time elasticity mechanism and component structure analysis;

[0008] S3, based on the modeling framework, establish a non-equidistant gray dynamic component prediction model suitable for irregular time series component data, optimize the parameters and mine the implicit cumulative law, background value coefficient and nonlinear characteristics through parameter combination, and the expression contains the order, index, background value and fixed parameters to be solved and dynamic parameters;

[0009] S4, solve the parameters of the gray component prediction model based on logarithmic transformation, and perform anti-logarithmic transformation to estimate the structure evolution of each component old disease population, including: solving the fixed parameters of the model by least squares method, using particle swarm algorithm to globally optimize the dynamic parameters to minimize the global average relative simulation error, obtaining the cumulative sequence prediction value of each sequence based on the solved parameters and restoring it to the original sequence prediction value through cumulative reduction, and finally obtaining the simulation or prediction results of the original proportion sequence through anti-logarithmic transformation, connecting the prediction values at each discrete time to obtain the component evolution curve of different categories of old people in the disease population.

[0010] Further, in S1, multi-component old population structure data affected by a certain type of disease is collected, the data is derived from a database containing multiple surveys, and the survey time points form a non-equidistant time series; the old people with the disease are divided into four clear component categories according to whether they are disabled and the degree of disability, and after obtaining the original proportion sequence of the four categories, the core features of the sequence are identified and quantified, namely the time non-equidistance and the component structure constraint;

[0011] By calculating the actual interval length between consecutive time points in the sequence and analyzing the coefficient of variation of these interval lengths, the non-uniformity degree of the time series is numerically characterized; at the same time, the addition consistency verification is performed on all category proportion data at each time point; the change pattern of each component sequence with time is analyzed, the absolute change amount and direction of each component proportion between adjacent time points are calculated, and the heterogeneity of the evolution trend of the proportion of different disabled population categories is identified, that is, some categories show monotonic change while other categories show fluctuation or turning point.

[0012] Further, in S2, the original multi-component old population structure data collected is subjected to asymmetric logarithmic ratio transformation to convert the original proportion sequence into a modeling sequence, wherein the transformation process is realized by calculating the natural logarithm of the ratio of each component proportion to the reference component proportion, thereby eliminating the constant and constraint of the component data, and making the transformed sequence suitable for gray modeling;

[0013] The transformed component structure data is taken as a modeling sequence to construct a gray dynamic component prediction model, which can process irregular time intervals and integrate component structure analysis to capture the dynamic evolution characteristics of a multi-component system;

[0014] An asymmetric anti-logarithmic transformation is performed on the output simulation and prediction sequence to restore the sequence to the original proportion sequence, wherein the anti-transformation process is performed through exponential operation and normalization processing to ensure that the restored sequence satisfies the constraint condition that the sum of all component proportions is 1;

[0015] The average relative percentage error, the standard deviation of the relative percentage error, and the average absolute scaled error are taken as evaluation criteria to evaluate the prediction curve of the old age category structure in the disease population obtained by the gray component model, wherein the average relative percentage error is calculated as the average value of the absolute values of the relative errors at each time point, the standard deviation of the relative percentage error is calculated as a dispersion index of the relative errors, and the average absolute scaled error is calculated as the ratio of the prediction error to the average absolute value of the first-order difference of the sequence.

[0016] Further, in the S3, based on the modeling framework, the system structural characteristics reflected by the old age category component data in the disease population, and the characteristics that the data presents different change rules in different periods due to the interference of the system as a whole and each component, a non-equidistant gray dynamic component prediction model is constructed;

[0017] The gray dynamic component prediction model includes the optimized parameters, the index parameters, and the parameters of the background values of the generated sequence in the vicinity, and simultaneously includes the fixed parameters and the dynamic parameters to be solved.

[0018] In the specific model construction process, based on the non-uniformity of the time intervals of the non-equidistant sequence, a new sequence is defined as an accumulated generated sequence of the original sequence, wherein the accumulation order is dynamically determined through an intelligent optimization algorithm to capture the implicit accumulation law of the data; secondly, the coefficient of the background value of the gray dynamic component prediction model is adjusted through the index parameter to reflect the non-linear characteristics of the sequence, and the dynamic parameter is used to represent the uncertainty of the evolution over time;

[0019] The gray dynamic component prediction model integrates the fixed parameters to describe the basic trend of the system, and the dynamic parameters to adapt to the variability of the component structure, and through parameter combination optimization, the model mines the accumulation law size, the background value coefficient size, and the non-linear characteristics hidden in the non-equidistant component data, thereby forming a gray prediction model structure that adapts to irregular time series component data.

[0020] Further, the intelligent optimization algorithm mines the accumulation law size, the background value coefficient size, and the non-linear characteristics to construct a non-equidistant gray component prediction model, and the formula expression is:

[0021] ;

[0022] wherein, , is the number of components, is the number of points contained in each sequence, represents a certain time point corresponding to the sequence; is the order of the operator applied to the original sequence, used to characterize the strength of the grey operator in generating time, which is defined as a real number, i.e. , is the index, is the background value of the sequence generated immediately before, which is a dynamic parameter to be solved; is a fixed parameter to be solved, wherein is called the development coefficient, whose size and sign reflect the development trend of the original sequence, represents the grey action amount, whose size is related to the time point ; the parameter is a random disturbance term, used to represent information with accidental or weak factors; and is a new sequence, satisfies the formula:

[0023] ;

[0024] represents the interval between the time point and the time point , , and have the same meaning, wherein is the summation index, used to represent each historical data point from time 1 to time .

[0025] Further, in the S4, based on the non-equidistant grey dynamic component prediction model, the fixed parameter estimation matrix in the model is solved by using the least square method, and the solving process is realized by constructing a matrix operation containing non-equidistant time intervals;

[0026] Then, the particle swarm algorithm is used to globally combine and optimize the dynamic parameters in the grey dynamic component prediction model, and the optimization process takes the minimization of the global average relative simulation error as the objective function, and determines the optimal parameter combination through iterative optimization;

[0027] After obtaining the fixed parameters and the dynamic parameters, they are substituted into the grey dynamic component prediction model, and the accumulated sequence prediction values of each sequence at the prediction time are calculated;

[0028] Next, the cumulative subtraction operator is used as the recursive formula to restore the cumulative sequence prediction value to the original sequence prediction value. This restoration process is achieved through successive difference operations.

[0029] Furthermore, an asymmetric anti-logarithmic transformation is performed on the original sequence prediction values ​​obtained by cumulative subtraction to convert the modeled sequence back to the original proportion sequence. This transformation process ensures that the sum of the proportions of each component meets the unit constraint through exponential operation and normalization.

[0030] By connecting the predicted values ​​at discrete time points, component evolution curves of different elderly categories in the disease population are formed. The accuracy of the prediction results is quantitatively evaluated using mean relative percentage error, standard deviation of relative percentage error, and mean absolute scaling error as evaluation indicators. The mean relative percentage error reflects the average accuracy of the prediction, the standard deviation of relative percentage error characterizes the stability of the prediction, and the mean absolute scaling error characterizes whether the model prediction is better than the basic variation level of the sequence itself by comparing the error with the random walk benchmark.

[0031] This invention provides a method for predicting the category structure of elderly people in disease populations based on gray component prediction modeling, which has the following beneficial effects:

[0032] 1. This invention introduces a time elasticity mechanism to construct a non-equidistant gray component modeling framework and a novel gray component prediction model, breaking through the dependence of component data on equidistant data, enabling high-precision modeling of structured data, and effectively addressing the problem of modeling component data with inconsistent time intervals in actual observations.

[0033] 2. The structural curves obtained by the gray component prediction model in this invention can effectively characterize the structural dynamic evolution trend of the elderly population with diseases, realize the analysis of health data of the structural elderly population, and support refined resource allocation.

[0034] 3. This invention solves the problem of difficulty in making high-precision dynamic predictions of the disability structure within the elderly population under conditions of sparse and irregular data by solving parameters based on a gray component prediction model and estimating the structural evolution of each component. This improves the ability of health management departments to grasp the changing trends of the disease burden of the elderly population. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the method flow proposed in this invention;

[0036] Figure 2 A flowchart for predicting the structural components of the elderly category in a disease population;

[0037] Figure 3To assess the predictive performance of different models on the category structure of cardiovascular diseases in the middle-aged and elderly populations;

[0038] Figure 4 A diagram showing the predicted evolution of cardiovascular disease categories in the elderly. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0040] Although the steps in this invention are arranged by reference numerals, this is not intended to limit the order of the steps. Unless the order of the steps is explicitly stated or the execution of a step requires other steps as a basis, the relative order of the steps can be adjusted. It is understood that the term "and / or" as used herein refers to and covers any and all possible combinations of one or more of the associated listed items.

[0041] Please refer to Figures 1 to 4 A specific implementation method of this embodiment is given:

[0042] like Figure 1 As shown, this invention presents a method for predicting the category structure of elderly populations in disease populations based on grey component prediction modeling, as proposed in this paper. Figure 2 As shown, this method comprises two parts: a modeling framework for component structure analysis and the construction of a novel dynamic gray component prediction model; specifically, it includes the following steps:

[0043] S1. Collect multi-component elderly population structure data affected by specific diseases and analyze the characteristics of the component data;

[0044] As a preferred embodiment of step S1, it specifically includes:

[0045] Data on the multi-component elderly population structure affected by diseases were collected and organized. Based on the degree and status of disability, elderly people with diseases were divided into four categories: healthy elderly, mildly disabled elderly, moderately disabled elderly, and severely disabled elderly. The number of elderly people with cardiovascular diseases under different disability conditions in different years nationwide was statistically analyzed, and their proportions were calculated as follows: ,satisfy:

[0046] ;

[0047] ;

[0048] in, The sequence is non-equally spaced, representing the percentage of elderly people in different years under different disability conditions. Each group must satisfy the constraint that the sum is 1 in a specific year.

[0049] S2. Based on the data characteristics, construct a modeling framework that integrates time elasticity mechanism and component structure analysis;

[0050] As a preferred embodiment of step S2, it specifically includes:

[0051] S21. Based on the original data obtained in S1, perform an asymmetric transformation (alr) on the component data to obtain the modeling sequence: ,and The formula is expressed as:

[0052] ;

[0053] S22. Use 85% of the transformed component structure data as the modeling sequence and 15% as the simulation prediction sequence to construct a non-equidistant gray dynamic component model.

[0054] S3. Based on the modeling framework, establish a non-equidistant gray dynamic component prediction model that is adapted to irregular time series component data. Optimize and mine the implicit cumulative rules, background value coefficients and nonlinear characteristics through parameter combination. Its expression includes the optimizable order, exponent, background value and fixed and dynamic parameters to be solved.

[0055] As a preferred embodiment of step S3, it specifically includes:

[0056] The elderly component data in disease populations reflects the structural characteristics of the system and exhibits different changing patterns at different times due to interference from the entire system and its individual components. For non-equidistant component data, considering the differences in component data trends and the irregularity of data spacing at different times, a novel nonlinear non-equidistant grey component prediction model is constructed by optimizing parameter combinations and using an intelligent optimization algorithm to uncover the magnitude of implicit cumulative patterns, the magnitude of background value coefficients, and nonlinear characteristics. The formula expression is as follows:

[0057] ;

[0058] in, , For the number of components, The sum of the number of points contained in each sequence. This represents a specific point in time corresponding to the sequence. The order of the operator that applies the processing to the original sequence is used to characterize the strength of the gray operator during generation; it is defined as a real number, i.e. , For index, The background value is the value immediately adjacent to the generated sequence, and the parameter is the dynamic parameter to be solved. Let be the fixed parameters to be solved, where This is called the development coefficient, and its magnitude and sign indicate the development trend of the original sequence. This represents the amount of gray action, the magnitude of which is related to the time point. Related; parameters This is a random disturbance term, used to represent information influenced by chance or weak factors; and For the new sequence, It satisfies the formula:

[0059] ;

[0060] , indicating time point With time point The spacing between them , and Same meaning, among which The summation index is used to represent the sum from time 1 to time 2. Each historical data point.

[0061] S4. Solve the parameters of the gray component prediction model based on logarithmic transformation and perform anti-logarithmic transformation to estimate the structural evolution of each component of the elderly disease population. This includes: solving the fixed parameters of the model using the least squares method; using the particle swarm optimization algorithm to globally combine and optimize the dynamic parameters to minimize the global average relative simulation error; obtaining the cumulative sequence prediction value of each sequence based on the solved parameters and restoring it to the original sequence prediction value through cumulative subtraction; finally obtaining the simulation or prediction result of the original proportion sequence through anti-logarithmic transformation; and connecting the prediction values ​​at each discrete time point to obtain the component evolution curves of different categories of the elderly population in the disease population.

[0062] As a preferred embodiment of step S4, it specifically includes:

[0063] S41. Based on steps S21 and S22, obtain the modeling sequence and the corresponding sequence grouping for simulation and prediction;

[0064] S42. A novel nonlinear, non-equidistant gray component model includes fixed and dynamic parameters, with the objective function being the minimum sum of squared errors. First, the estimation matrix of the fixed parameters is obtained using the least squares method. The specific calculation formula is as follows:

[0065] ;

[0066] in, The specific formula is:

[0067] ;

[0068] ;

[0069] in, The distance between time point j in the time series and the previous time point can be used to solve for the estimates of the four parameters. ;

[0070] S43. The Particle Swarm Optimization (PSO) algorithm is used to perform global combination optimization of the given parameters. Specifically, based on the common parameter combination optimization principle selected by different model groups and the condition of minimizing the global average relative simulation error, the optimal parameter combination of the model is sought, satisfying the formula:

[0071] ;

[0072] S44. Substitute the parameters obtained in steps S41 and S42 into the constructed gray component prediction model to obtain... The predicted values ​​of the cumulative R-order sequence at each time point are as follows:

[0073] ;

[0074] in, These parameters are not additional parameters, but rather a combination rewrite of the model parameters obtained from the solution, so that the prediction update formula can be presented in a more concise form. Used as an index variable in the summation process, it does not have a specific physical or model meaning; its function is to iterate through historical data item by item.

[0075] S45. Using the R-order cumulative decrease operator as the recurrence relation, we obtain... The predicted values ​​of each sequence at time point are expressed by the formula:

[0076] ;

[0077] S46. Based on the sequences obtained in step S45, perform asymmetric antilogarithmic transformation (Realr) component data transformation to obtain the simulated / predicted sequences of the original sequences. The formula is expressed as:

[0078] ;

[0079] S47. Using the mean relative percentage error (MRPE), the standard deviation of the relative percentage error (STD), and the mean absolute scaling error (MASE) as evaluation criteria, the accuracy of the prediction curves of the elderly category structure in the disease population obtained by the proposed novel grey component prediction model is evaluated. The specific formula is as follows:

[0080] ;

[0081] ;

[0082] ;

[0083] in, For the number of components, The sum of the number of points contained in each sequence. and They have the same meaning, representing the specific position in the sequence at a particular point in time. This represents a specific point in time corresponding to the sequence. , indicating time point With time point The spacing between them; Representative modeling sequence corresponding time point The corresponding original value, This represents the value predicted by the model at the corresponding point in time.

[0084] In this embodiment, based on the CLHLS database, structural data on cardiovascular diseases among the elderly nationwide were extracted and processed as the research object in actual experiments. Simultaneously, based on the database data, more refined classification structural data of cardiovascular diseases was obtained, categorized into four groups according to disability status and degree: no disability, mild disability, moderate disability, and severe disability. To compare the advantages of the proposed model, the model of this invention is abbreviated as NLUGM. Advanced non-equidistant grey component models were selected, including the non-equidistant GM(1,1) model (UGM), the non-equidistant fractional GM(1,1) model (UFGM), the non-equidistant GM(1,1) power model (UPGM), the exponential nonlinear regression model (ENLR), and the support vector regression model (SVR), which are feature-friendly for this type of data and robust to time intervals and proportions, for modeling and prediction.

[0085] Using 85% of the transformed structural data as the modeling sequence and 15% as the simulation prediction sequence, the structural simulation results of cardiovascular diseases among the elderly in China are as follows: Figure 3 As shown in Table 1, its accuracy evaluation is as follows.

[0086] Table 1. Evaluation of the Prediction Accuracy of Cardiovascular Disease Category Structure in the Elderly

[0087]

[0088] The results show that, among the six models and under different component data transformation methods, the NLUGM model exhibits the best fitting and prediction performance for each component. Furthermore, the results of each model under different scenarios were calculated using three model validation methods: MAPE, STD, and MASE. The results for each component were calculated, and the corresponding comprehensive results were obtained. The results show that, among all component data models, the NLUGM model proposed in this invention has the lowest comprehensive MAPE and comprehensive STD, with a MAPE of 4.167%, below 5%, belonging to Level 1 accuracy (>95%). Based on the performance of the prediction model, such accuracy meets the requirements, reflecting the effectiveness and rationality of the proposed method. Furthermore, using… Figure 4 The prediction results were displayed.

[0089] In summary, the method proposed in this invention constructs a novel grey component prediction model targeting the structural component characteristics of elderly populations with specific diseases. Based on small sample data, the new model can effectively capture the trends of each sequence and achieve high prediction accuracy. The grey prediction model does not require prior knowledge of the disease's internal evolutionary history, nor does it require making assumptions about patterns or choosing a specific model form.

[0090] Based on the evolution curve obtained from the grey component prediction model, a new technical path and specific numerical analysis results are provided for the modeling and prediction of the cardiovascular disease prevalence structure in China's elderly population, utilizing health resource allocation.

[0091] In this specification, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to at least one embodiment or example described in connection with a specific feature, structure, material, or characteristic. These specific features, structures, materials, or characteristics may be combined in a suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples and their features described in this specification.

[0092] The logic and / or steps shown in the flowchart or otherwise described can be viewed as a sequence of executable instructions for implementing logical functions. These instructions may be implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device. Such systems, apparatus, or devices include processor systems or other systems capable of receiving and executing instructions.

[0093] The above embodiments detail the principles and implementation methods of the present invention, and illustrate its working principle using specific examples. These examples are only used to help understand the method and core ideas of the present invention. Furthermore, based on the ideas of the present invention, actual implementation methods and application scope may vary. Therefore, the content of this specification should not be construed as limiting the present invention.

Claims

1. A method for predicting the category structure of elderly populations in disease populations based on grey component prediction modeling, characterized in that, Includes the following steps: S1. Collect multi-component elderly population structure data affected by a certain type of disease and analyze the characteristics of the component data; Specifically, it includes: Data on the impact of a certain type of disease on the structure of the elderly population was collected. The data came from a database containing multiple rounds of surveys, and the survey time points formed a non-equidistant time series. The elderly with the disease were divided into four distinct component categories according to their disability status and degree. After obtaining the original proportion sequence of the four categories, the core features of the sequence were identified and quantified, namely the non-equidistant time interval and the constraint of the component structure. By calculating the actual interval length between consecutive time points in the sequence and analyzing the coefficient of variation of these interval lengths, the degree of non-uniformity of the time series is numerically characterized. At the same time, the summation consistency verification is performed on the proportion data of all categories at each time point. The change pattern of each component sequence over time is analyzed. By calculating the absolute change and direction of the proportion of each component between adjacent time points, the heterogeneity of the evolution trend of the proportion of different disability categories is identified, that is, some categories show monotonic changes while other categories show fluctuations or turning points. S2. Based on data characteristics, construct a modeling framework that integrates time elasticity mechanisms and component structure analysis; specifically including: An asymmetric logarithmic ratio transformation is performed on the collected original multi-component elderly population structure data to convert the original proportion sequence into a modeling sequence. The transformation process is achieved by calculating the natural logarithm of the ratio of each component proportion to the reference component proportion, thereby eliminating the constancy and constraints of the component data and making the transformed sequence suitable for grey modeling. The transformed component structure data is used as a modeling sequence to construct a gray dynamic component prediction model. By processing irregular time intervals and integrating component structure analysis, the dynamic evolution characteristics of multi-component systems can be captured. An asymmetric anti-logarithmic transformation is performed on the output simulated and predicted sequences to restore the sequences to the original proportion sequences. The inverse transformation process uses exponential operations and normalization to ensure that the restored sequences satisfy the constraint that the sum of the proportions of all components is 1. The accuracy of the prediction curves for the elderly category structure of the disease population obtained by the grey component model is evaluated using the mean relative percentage error, the standard deviation of the relative percentage error, and the mean absolute scaling error as evaluation criteria. The mean relative percentage error is calculated as the average of the absolute values ​​of the relative errors between the predicted and actual values ​​at each time point. The standard deviation of the relative percentage error is calculated as the dispersion index of these relative errors. The mean absolute scaling error is calculated as the ratio of the prediction error to the mean absolute value of the first-order difference of the sequence. S3. Based on the modeling framework, establish a non-equidistant gray dynamic component prediction model that is adapted to irregular time series component data. Optimize and mine the implicit cumulative rules, background value coefficients and nonlinear characteristics through parameter combination. Its expression includes the optimizable order, exponent, background value and fixed and dynamic parameters to be solved. S4. Solve the parameters of the gray component prediction model based on logarithmic transformation and perform anti-logarithmic transformation to estimate the structural evolution of each component of the elderly disease population. This includes: solving the fixed parameters of the model using the least squares method; using the particle swarm optimization algorithm to globally combine and optimize the dynamic parameters to minimize the global average relative simulation error; obtaining the cumulative sequence prediction value of each sequence based on the solved parameters and restoring it to the original sequence prediction value through cumulative subtraction; finally obtaining the simulation or prediction result of the original proportion sequence through anti-logarithmic transformation; and connecting the prediction values ​​at each discrete time point to obtain the component evolution curves of different categories of the elderly population in the disease population.

2. The method for predicting the elderly category structure in a disease population based on grey component prediction modeling according to claim 1, characterized in that: In S3, based on the modeling framework, a non-equidistant gray dynamic component prediction model is constructed to address the system structural characteristics reflected by the elderly category component data in the disease population, as well as the differences in the changing patterns of the data at different times due to interference from the system as a whole and its components. The grey dynamic component prediction model uses a parameter combination optimization process, which includes optimizable order parameters, exponential parameters, and background value parameters of adjacent generated sequences, and simultaneously includes fixed parameters and dynamic parameters to be solved. In the specific model construction process, based on the non-uniformity of time intervals in non-equally spaced sequences, a new sequence is defined as the cumulative generation sequence of the original sequence. The cumulative order is dynamically determined by an intelligent optimization algorithm to capture the implicit cumulative pattern of the data. Secondly, the coefficients of the background values ​​of the gray dynamic component prediction model are adjusted by exponential parameters to reflect the nonlinear characteristics of the sequence, and dynamic parameters are used to characterize the uncertainty of its evolution over time. The grey dynamic component prediction model integrates fixed parameters to describe the basic trend of the system and dynamic parameters to adapt to the variability of the component structure. It also optimizes the parameter combination to mine the magnitude of the cumulative regularity, the magnitude of the background value coefficient, and the nonlinear characteristics hidden in the non-equal interval component data, thereby forming a grey prediction model structure that is suitable for irregular time series component data.

3. The method for predicting the elderly category structure in a disease population based on grey component prediction modeling according to claim 2, characterized in that: The intelligent optimization algorithm mines the implicit cumulative patterns, background coefficients, and nonlinear characteristics to construct a gray component prediction model with non-equidistant spacing. The formula expression is as follows: ； in, , For the number of components, The sum of the number of points contained in each sequence. This represents a specific point in time corresponding to the sequence. The order of the operator that applies the processing to the original sequence is used to characterize the strength of the gray operator during generation; it is defined as a real number, i.e. , For index, The background value is the value immediately adjacent to the generated sequence, and the parameter is the dynamic parameter to be solved. Let be the fixed parameters to be solved, where This is called the development coefficient, and its magnitude and sign indicate the development trend of the original sequence. This represents the amount of gray action, the magnitude of which is related to the time point. Related; parameters This is a random disturbance term, used to represent information influenced by chance or weak factors; and For the new sequence, It satisfies the formula: ； ； , indicating time point With time point The spacing between them , and Same meaning, among which The summation index is used to represent the sum from time 1 to time 2. Each historical data point.

4. The method for predicting the category structure of elderly people in a disease population based on grey component prediction modeling according to claim 1, characterized in that: In S4, based on the gray dynamic component prediction model with non-equal intervals, the least squares method is used to solve the fixed parameter estimation matrix in the model. This solution process is achieved by constructing a matrix operation that includes non-equal interval time intervals. Subsequently, the particle swarm optimization algorithm was used to perform global combination optimization of the dynamic parameters in the gray dynamic component prediction model. The optimization process takes minimizing the global average relative simulation error as the objective function and determines the optimal parameter combination through iterative optimization. After obtaining the fixed and dynamic parameters, they are substituted into the gray dynamic component prediction model to calculate the cumulative sequence prediction value of each sequence at the prediction time. Next, the cumulative subtraction operator is used as the recursive formula to restore the cumulative sequence prediction value to the original sequence prediction value. This restoration process is achieved through successive difference operations.

5. The method for predicting the elderly category structure in a disease population based on grey component prediction modeling according to claim 4, characterized in that: An asymmetric anti-logarithmic transformation is performed on the original sequence prediction values ​​obtained by cumulative subtraction to convert the modeled sequence back to the original proportion sequence. This transformation process ensures that the sum of the proportions of each component meets the unit constraint through exponential operation and normalization. By connecting the predicted values ​​at discrete time points, component evolution curves of different elderly categories in the disease population are formed. The accuracy of the prediction results is quantitatively evaluated using mean relative percentage error, standard deviation of relative percentage error, and mean absolute scaling error as evaluation indicators. The mean relative percentage error reflects the average accuracy of the prediction, the standard deviation of relative percentage error characterizes the stability of the prediction, and the mean absolute scaling error characterizes whether the model prediction is better than the basic variation level of the sequence itself by comparing the error with the random walk benchmark.

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