A bayesian disease risk high-precision mapping method and system

Abstract

The application provides a kind of bayesian disease risk high-precision mapping method and system, it is related to spatial statistical analysis technical field.The application collects multiple source covariates, constructs integrated covariate sub-model and generates out-of-sample prediction and in-sample prediction;establishes bayesian regional spatio-temporal hierarchical correlation model, takes sub-model prediction result as covariate, expresses prevalence rate as covariate linear combination by logit function, residual error uses three-dimensional Gaussian process and utilizes random partial differential equation approximation;high-resolution grid risk map is generated by posterior sampling, and is population-weighted to administrative unit.The application can realize multi-factor driven disease risk high-precision spatio-temporal estimation and mapping, and is suitable for public health monitoring, disease early warning and precise intervention.

Description

Technical Field

[0001] This invention relates to the field of spatial statistical analysis technology, specifically to a Bayesian method and system for high-precision disease risk mapping. Background Technology

[0002] The core purpose of disease risk mapping is to obtain risk estimates for different regions and express them in map form by spatially or spatiotemporally modeling disease occurrence data and related influencing factors, providing technical support for disease surveillance, resource allocation, and precision intervention. With the improvement of regional disease surveillance and multi-source data acquisition capabilities, disease risk mapping technology has become an important foundational technology for disease early warning systems, risk assessment systems, and spatial epidemiological analysis.

[0003] Among existing disease risk mapping techniques, Bayesian inference methods have gradually become the mainstream approach in practical applications due to their advantages in smoothing estimations of small sample data and modeling spatial correlations. A typical Bayesian risk mapping technique usually includes the following three layers of technical structure: Data observation layer: establishing a probability distribution model for disease occurrence data within the region to describe the data generation process; Potential risk layer: using methods such as spatial autoregressive structures, spatial random effects, or spatial conditional association structures to express spatial dependencies between regions; Prior knowledge layer: constraining parameters through prior distributions to enable the model to handle small sample scenarios and obtain smooth risk estimates.

[0004] Bayesian disease risk mapping techniques typically employ Markov chain Monte Carlo methods or ensemble nested Laplace approximation methods to perform posterior calculations of model parameters and potential risks, thereby obtaining stable regional disease risk estimates. However, with the continuous enrichment of disease data, existing Bayesian disease risk mapping techniques have gradually revealed several technical shortcomings in practical applications, primarily including:

[0005] (1) Lack of effective multi-factor comprehensive modeling capabilities.

[0006] Traditional disease risk mapping models are mostly based on single or a few factors, typically modeling different influencing factors separately or simply adding them together, making it difficult to simultaneously integrate multi-source heterogeneous information such as air pollution, socioeconomic characteristics, meteorological environment, and demographic characteristics. Due to the lack of technical mechanisms that can describe the nonlinear relationships, interactions, and complex combined effects between variables, existing technologies are not well-suited for multi-factor driven disease risk modeling.

[0007] (2) Limited ability to model complex spatial structures.

[0008] Existing techniques typically employ simple spatial dependency structures based on adjacency relationships, such as conditional autoregressive (CAR) or spatial stochastic effects, and primarily rely on administrative boundary demarcation or regular grids as modeling units. These spatial structures have limited descriptive power and struggle to characterize common irregular spatial morphologies, multi-scale spatial structures, spatial clustering relationships, and cross-regional diffusion patterns in the real world. When data exhibits strong spatial heterogeneity, existing techniques are prone to problems such as risk oversmoothing or loss of spatial detail.

[0009] (3) Insufficient expression of spatiotemporal correlation.

[0010] Many existing technologies only support static spatial models. While some methods incorporate temporal trends, they often model time and space separately, lacking a systematic technical framework that can simultaneously express temporal changes, spatial structure, and their interactions. When dealing with diseases that change dynamically over time (such as cognitive decline, chronic diseases, and the spread of infectious diseases), relying solely on spatial or temporal modeling is insufficient to accurately describe the risk evolution process.

[0011] (4) Insufficient high-resolution mapping capabilities.

[0012] As disease surveillance data evolves towards higher precision, gridded structures, and multi-source data, existing technologies that model using administrative regions or coarse grids are no longer sufficient to meet the demands of high-resolution disease risk assessment. Because they cannot simultaneously integrate multidimensional factors and complex spatial dependencies, existing models lack the ability to characterize risk changes within small-scale regions, making it difficult to generate fine-grained, high-precision risk distribution maps.

[0013] (5) There is a lack of modeling frameworks specifically designed for complex disease mechanisms.

[0014] In chronic disease scenarios such as cognitive decline, the effects are influenced by the coupling of multiple factors, including air pollution exposure, meteorological elements, living environment, socioeconomic level, and individual characteristics, with nonlinear relationships and interactions among these factors. Existing Bayesian models are typically only applicable to simple structures and lack a general technical framework to support complex causal relationships, multi-level spatial structures, and the simultaneous effects of multiple factors.

[0015] In summary, while existing Bayesian disease risk mapping techniques have become an important method for regional disease risk analysis, there is still a lack of novel, high-precision mapping techniques capable of simultaneously handling multi-factor influences, complex spatial distribution structures, and dynamic spatiotemporal correlations. There is an urgent need for a new technical solution to construct a Bayesian disease risk mapping method suitable for complex disease mechanisms, multi-source data fusion, and high-precision risk assessment, in order to improve the accuracy and resolution of spatial disease risk assessment and meet the technical needs of public health monitoring and refined intervention. Summary of the Invention

[0016] Purpose of the invention: The first purpose of this invention is to provide a high-precision Bayesian disease risk mapping method that integrates multiple factors and takes into account spatiotemporal hierarchical correlations. The second purpose is to provide a high-precision Bayesian disease risk mapping system.

[0017] Technical solution: In a first aspect, the present invention provides a Bayesian method for high-precision disease risk mapping, comprising the following steps:

[0018] S1. Collect raw data within the study area, including disease surveillance data, covariate data, population grid data, and administrative unit data, and perform preprocessing.

[0019] S2. Divide the disease surveillance data into a training set according to the proportion, use all covariates as prediction variables, fit multiple sub-models on the training set and test them with five-fold cross-validation to obtain multiple corresponding out-of-sample predictions, compile them to obtain a comprehensive prediction set, input all disease surveillance data into the sub-models to obtain in-sample predictions.

[0020] S3. Threshold determination is performed on multiple disease outcome data in the disease surveillance data, and the corresponding disease surveillance objects are marked as having disease risk or no disease risk. Spatial cluster analysis is performed on the disease outcome data of all disease surveillance objects to obtain multiple disease outcome data clusters. A finite element mesh is constructed, and the disease outcome data clusters are mapped to the mesh cells. The disease outcome data is used as the response variable and input into the Bayesian regional spatiotemporal hierarchical correlation model. The comprehensive prediction set is used as the covariate of the Bayesian regional spatiotemporal hierarchical correlation model. The logit connection function is used to model the prevalence rate as a linear combination of covariates, spatiotemporal correlation error terms, and nugget error terms. The Bayesian regional spatiotemporal hierarchical correlation model is fitted to simulate the change of prevalence rate in the study area.

[0021] S4. Using the in-sample prediction as a covariate in the Bayesian regional spatiotemporal hierarchical correlation model, a posterior distribution is generated after running the model. Samples are extracted from the posterior distribution and mapped to grid cells within the study area. The posterior mean of each grid cell is calculated by continuously sampling a set number of times. The estimated value of the grid cell is obtained by weighting it according to the population grid data and then summarized to the corresponding administrative unit to generate a high-resolution disease risk map.

[0022] Specifically, step S1 includes: collecting disease surveillance data, covariate data, population grid data, and administrative unit data within the study area; calculating statistics for each monitored individual or data observation point in the raw data according to a predetermined time window for the covariate; using a unified coordinate reference system for the raw data and mapping the point data in the raw data to the corresponding geographical location within the study area; and finally standardizing the raw data.

[0023] Preferably, step S1 further includes: for missing short sequence data in the covariate data, linear interpolation or spline interpolation is used to supplement them; for missing spatial data in the covariate data, spatial interpolation or nearest neighbor imputation is used to supplement them.

[0024] Specifically, the sub-models include the generalized additive model, the enhanced regression tree, lasso regression, least squares linear regression, and ridge regression.

[0025] Specifically, disease outcome data includes continuous and discrete outcome data. Continuous outcome data includes numerical disease surveillance data, while discrete outcome data includes data on whether an individual has a disease, their survival status, their mortality events, and their abnormal diagnostic events. For continuous outcome data, the data is compared with the corresponding clinical reference range. Individuals who do not meet the clinical reference range are marked as having a disease risk, otherwise they are marked as having no disease risk. For discrete outcome data, individuals are directly classified and coded based on whether they are in an abnormal state, and marked as having a disease risk or having no disease risk.

[0026] Specifically, the formula for the Bayesian regional spatiotemporal hierarchical correlation model is as follows:

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034] In the formula: Indicates that there is a grid cell inside A cluster of disease outcome data, This indicates the number of individuals monitored within a grid cell who pose a disease risk. express Total number of samples within each disease outcome data cluster This indicates the disease prevalence rate within the grid cell. This is the logit join function. The intercept term represents the baseline disease prevalence level. As covariates, For spatiotemporal correlation error terms, For the spatiotemporal correlation error term within the grid cell, This is an independent error term for nuggets. The prediction weights are for the five sub-models. For the variance of the gold nugget, For spatial covariance, For time covariance, For Gaussian processes, The distance between two points. For scale parameters, These are joint parameters used to define how the spatial covariance varies with distance. This is a modified Bessel function of the second kind. For the Gamma function, For smoothing parameters, For accuracy parameters, The time autocorrelation coefficient, For the k-th time step, Let j be the j-th time step.

[0035] Preferably, step S3 further includes: in the Bayesian regional spatiotemporal hierarchical correlation model, the spatiotemporal correlation error term is approximated as a sparse precision matrix based on triangular finite element method using stochastic partial differential equation method, and when constructing the finite element mesh, the maximum side length is set for the land and the buffer respectively.

[0036] Preferably, step S4 further includes: evaluating the Bayesian regional spatiotemporal hierarchical association model using spatial blocking cross-validation, calculating the root mean square error and log score, and performing sensitivity analysis on the hyperparameters of the Bayesian regional spatiotemporal hierarchical association model and recording the results.

[0037] Specifically, step S4 includes: drawing samples multiple times from the posterior distribution to obtain the prevalence rate for each sampling; for each grid cell, mapping the posterior sample at that location to the grid resolution through spatial interpolation; calculating the posterior mean of each grid cell; weighting the values ​​according to population grid data; and summing the estimated values ​​of the grid cells to the administrative unit, as shown in the following formula:

[0038]

[0039]

[0040] In the formula: For the incidence rate within an administrative unit, For weighted weights, The posterior mean is... Represents grid cells Belongs to an administrative unit. Represents grid cells Population grid data within the area.

[0041] Secondly, the present invention also provides a Bayesian disease risk high-precision mapping system, comprising:

[0042] Data acquisition module: used to collect raw data within the study area, including disease surveillance data, covariate data, population grid data, and administrative unit data, and to perform preprocessing.

[0043] Sub-model training module: This module is used to divide the disease surveillance data into training sets according to a certain proportion, use all covariates as prediction variables, fit multiple sub-models on the training set and test them using five-fold cross-validation to obtain multiple corresponding out-of-sample predictions. After compilation, a comprehensive prediction set is obtained. All disease surveillance data are then input into the sub-models to obtain in-sample predictions.

[0044] The main model training module is used to determine thresholds for various disease outcome data in disease surveillance data, marking the corresponding disease surveillance objects as having disease risk or no disease risk. It performs spatial clustering analysis on the disease outcome data of all disease surveillance objects to obtain multiple disease outcome data clusters, constructs a finite element mesh, maps the disease outcome data clusters to the mesh cells, uses the disease outcome data as a response variable, inputs it into the Bayesian regional spatiotemporal hierarchical correlation model, uses the comprehensive prediction set as a covariate of the Bayesian regional spatiotemporal hierarchical correlation model, uses the logit connection function to model the prevalence as a linear combination of covariates, spatiotemporal correlation error terms, and nugget error terms, fits the Bayesian regional spatiotemporal hierarchical correlation model, and simulates the change of prevalence within the study area.

[0045] Map generation module: Used to use in-sample predictions as covariates in Bayesian regional spatiotemporal hierarchical correlation model. After running, it generates a posterior distribution, extracts samples from the posterior distribution and maps them to grid cells within the study area. It calculates the posterior mean of each grid cell by continuously sampling a set number of times, weights the values ​​of the grid cells according to the population grid data, and summarizes them to the corresponding administrative units to generate a high-resolution disease risk map.

[0046] Beneficial effects: Compared with the prior art, the significant effects of the present invention are:

[0047] 1. Improved Spatial and Temporal Accuracy of Disease Risk Estimation: This invention constructs a spatiotemporal hierarchical model based on a Bayesian framework, introducing spatial random effects, temporal random effects, and their interaction structure to jointly characterize the correlation of disease risk in spatial and temporal dimensions. This effectively reduces the instability of risk estimation in small sample areas and low-incidence areas. Experimental tests show that in remote or low-incidence areas with extremely small sample sizes, compared to the traditional conditional autoregressive (CAR) model, the stability of the posterior estimate (characterized by the coefficient of variation, CV) is improved by more than 30%. This method effectively solves the problem of estimation bias or extreme outliers that traditional models easily produce in areas of data sparsity, making the disease risk map more consistent with biological distribution characteristics in terms of spatial continuity. This provides a reliable basis for precise intervention in low-prevalence areas and improves the overall accuracy and reliability of disease risk estimation results.

[0048] 2. Enhanced modeling capability for complex covariate relationships: This invention adopts an integrated covariate modeling strategy to uniformly model multi-source, multi-scale environmental factors, socioeconomic factors, and demographic characteristics, thereby achieving nonlinear characterization and uncertainty quantification of covariate effects and overcoming the problem that traditional linear or single model methods cannot accurately reflect complex influence mechanisms.

[0049] 3. Robust prediction for unknown areas and future time periods: By introducing in-sample and out-of-sample prediction mechanisms in the Bayesian inference process, this invention can make reasonable inferences about disease risk in areas with missing observation data or sparse monitoring points, and predict the risk level for future time periods, significantly improving the applicability of the model in practical public health applications.

[0050] 4. Effectively quantify the uncertainty information of disease risk: This invention not only outputs the point estimation results of disease risk, but also simultaneously generates uncertainty indicators such as risk distribution, confidence interval and posterior probability, providing more comprehensive and interpretable technical support for disease risk assessment and decision-making, and avoiding decision bias caused by a single deterministic result.

[0051] 5. Improved automation and consistency of disease risk mapping: This invention combines Bayesian modeling results with post-processing and mapping modules to achieve streamlined processing of disease risk from raw data input to risk map output, reducing manual intervention and ensuring the consistency and repeatability of risk mapping results in different regions and at different time scales.

[0052] 6. Enhanced versatility and scalability: The technical solution of this invention is applicable to data scenarios of various disease types and different spatial scales. The model structure and parameter settings can be flexibly adjusted according to application needs. It has good versatility and scalability, and is easy to promote and apply in disease monitoring, risk warning and public health decision support systems. Attached Figure Description

[0053] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention.

[0054] Figure 2 This is a flowchart of integrated covariate modeling in Embodiment 1 of the present invention. Detailed Implementation

[0055] A preferred embodiment of the present invention will be further described below with reference to the accompanying drawings.

[0056] Example 1

[0057] Please see Figure 1 As shown, this embodiment provides a Bayesian method for high-precision disease risk mapping, including the following steps:

[0058] S1. Collect raw data within the study area, including disease surveillance data, covariate data, population grid data, and administrative unit data, and perform preprocessing.

[0059] In this embodiment, disease surveillance data within the study area is first collected, including basic information of monitored individuals (ID, gender, age, etc.), latitude and longitude coordinates of data collection, data collection time, and disease outcome data. Then, relevant covariate data (air pollution data, meteorological data, socioeconomic data, land use data, etc.), population grid data, and administrative unit data are collected. Next, time alignment is performed. For each monitored individual or data observation point in the original data, statistics (mean, median, volatility index, etc.) are calculated for the covariates according to a predetermined time window (e.g., 365 days before the detection date, 30 days before, etc.). Finally, the original data is spatially aligned using a unified coordinate reference system (WGS84). (or national coordinate system), and map the point data in the original data to the corresponding geographical locations within the study area; for short-sequence data missing in the covariate data, linear interpolation or spline interpolation is used to supplement them; for spatial data missing in the covariate data, spatial interpolation or nearest neighbor imputation is used to supplement them; for data that cannot be interpolated or imputed, missing support is allowed in the sub-model (tree model, etc.) or missing indicator variables are introduced in the subsequent Bayesian model; finally, the original data is standardized, and logarithmic transformation or z-score standardization is performed for continuous variables; one-hot encoding is used for categorical variables; outliers are handled by truncation or Winsorize.

[0060] S2. Divide the disease surveillance data proportionally to obtain a training set, use all covariates as prediction variables, fit multiple sub-models on the training set and test them using five-fold cross-validation to obtain multiple corresponding out-of-sample predictions, compile them to obtain a comprehensive prediction set, input all disease surveillance data into the sub-models to obtain in-sample predictions.

[0061] In this embodiment, please refer to Figure 2 As shown, the sub-models include a generalized additive model (GAM, used to fit smooth nonlinear effects), enhanced regression trees (e.g., XGBoost / GBM, used to automatically capture nonlinearity and higher-order interactions), Lasso regression (LASSO, used for variable selection and sparsification), least squares linear regression (OLS, used to provide an explanatory linear baseline), and ridge regression (used to stabilize linear estimates and mitigate collinearity). The predictive performance of each sub-model was tested using five-fold cross-validation to avoid overfitting, creating five out-of-sample predictions, which were then compiled into a comprehensive prediction set for the model. Furthermore, the sub-models were run using 100% disease surveillance data to create complete in-sample predictions. When fitting the subsequent Bayesian regional spatiotemporal hierarchical association model, the five out-of-sample sub-model predictions were input as explanatory covariates into the complete Bayesian regional spatiotemporal hierarchical association model. When using the fitted complete Bayesian regional spatiotemporal hierarchical association model to generate predictions, the in-sample predictions of the sub-models were used as covariates. This integrated covariate modeling method, which integrates the influence of different factors, achieves higher predictive accuracy compared to a single model.

[0062] S3. Threshold determination is performed on multiple disease outcome data in the disease surveillance data, and the corresponding disease surveillance objects are marked as having disease risk or no disease risk. Spatial cluster analysis is performed on the disease outcome data of all disease surveillance objects to obtain multiple disease outcome data clusters. A finite element mesh is constructed, and the disease outcome data clusters are mapped to the mesh cells. The disease outcome data is used as the response variable and input into the Bayesian regional spatiotemporal hierarchical correlation model. The comprehensive prediction set is used as the covariate of the Bayesian regional spatiotemporal hierarchical correlation model. The logit connection function is used to model the prevalence as a linear combination of covariates, spatiotemporal correlation error terms, and nugget error terms. The Bayesian regional spatiotemporal hierarchical correlation model is fitted to simulate the change of prevalence in the study area.

[0063] In this embodiment, the disease outcome variables are first categorized based on their value format. These variables are classified into two types: continuous and discrete. Correspondingly, disease outcome data are divided into continuous and discrete outcome data. Continuous outcome data includes numerical disease monitoring data (including but not limited to physiological function measurements, laboratory test values, and scale scores). Discrete outcome data includes data on the occurrence of individual diseases, individual survival status, individual mortality events, and individual diagnostic abnormalities; the results are represented in a binary or multi-category format. For each type of outcome variable, a corresponding standardization method is applied to uniformly convert them into risk characterization variables suitable for subsequent spatial statistical modeling.

[0064] For continuous outcome data, the continuous outcome data are compared with the corresponding clinical reference range (in the absence of clinical reference values, the population mean or population median can be used as a substitute). Individuals who do not meet the clinical reference values ​​are marked as having disease risk, and others are marked as having no disease risk. In this way, the continuous outcome variable is converted into a binary indicator reflecting the disease risk status.

[0065] For discrete outcome data, individuals are directly classified and coded based on whether they are in an abnormal state. Individuals in an abnormal state (death, disease event, or survival status meeting the abnormality criteria) are marked as having disease risk, while individuals in a normal state are marked as having no disease risk.

[0066] After completing the risk labeling of outcome variables, spatial clustering analysis was performed on the disease outcome data of all monitored individuals. Based on the geographical coordinates and observation time information of the monitored individuals, individuals with similar spatial locations and disease outcome characteristics were aggregated into several disease data clusters. These disease data clusters were then mapped to pre-constructed grid cells, and individual-level disease outcome data were folded and aggregated into referable grid cells. For each grid cell, the number of data clusters falling within that grid cell was counted, denoted as . Within each disease data cluster, the number of monitored individuals marked as having disease risk and the number marked as having no disease risk are counted separately to construct a binary indicator set for disease outcomes. These binary indicator sets are used to uniformly characterize the occurrence of disease risk at specific spatial locations and time points for different types of disease outcome variables, ensuring consistency in the statistical expression of continuous and discrete disease outcome variables. Through this general processing method for multiple types of disease outcome variables, risk labeling, spatial aggregation, and probabilistic modeling of different types of disease monitoring data can be completed within the same technical framework, thus providing a consistent and stable data foundation for subsequent high-precision disease risk mapping and regional risk assessment.

[0067] Next, disease outcome data is used as the response variable and input into the Bayesian regional spatiotemporal hierarchical association model. The comprehensive prediction set is used as the covariate of the Bayesian regional spatiotemporal hierarchical association model. Through a unified risk modeling interface, unified spatiotemporal risk modeling and prediction of continuous and discrete disease outcome variables are achieved. Within the integrated modeling framework, a Bayesian regional spatiotemporal hierarchical association model that takes into account complex spatial distributions is constructed to simulate the changes in disease risk throughout the region.

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] In the formula: Indicates that there is a grid cell inside A cluster of disease outcome data, This indicates the number of individuals monitored within a grid cell who pose a disease risk. express Total number of samples within each disease outcome data cluster This indicates the disease prevalence rate within the grid cell. This is the logit join function. The intercept term represents the baseline disease prevalence level. As covariates, This is the spatiotemporal correlation error term, used in 3D Gaussian process modeling to capture the spatial autocorrelation component that cannot be explained by covariates. The spatiotemporal correlation error term within the grid cell represents the residual spatiotemporal autocorrelation between individual data points after considering the predictive effects of the sub-model covariates, modeled as a zero-centered spatiotemporal three-dimensional Gaussian process. (Gaussian Process), simulated using a covariance matrix constructed from the Kronnecker product of spatial and temporal covariance kernels; For nugget independent error terms, each nugget independent error term is an independent error term for each data point, representing the irreducible error for each data point; The prediction weights are set to the five sub-models, and the sum of the five weights is set to 1. For the variance of the gold nugget, Spatial covariance is modeled using an isotropic and stationary Matérn function. For time covariance, an annual autoregressive function is used for modeling. This is a modified Bessel function of the second kind. For the Gamma function, For smoothing parameters, For scale parameters, The distance between two points. It is used as a joint parameter in the calculation to define how spatial covariance changes with distance. For accuracy parameters, The time autocorrelation coefficient, For the k-th time step, Let j be the j-th time step.

[0076] The model described above utilizes the residual correlation structure of the data to more accurately predict the prevalence estimate in areas without data points, in order to predict and calculate the prevalence estimate for each grid cell each year.

[0077] To improve the computational feasibility and achieve large-scale inference, the stochastic partial differential equation (SPDE) method is used in the Bayesian regional spatiotemporal hierarchical correlation model to approximate the Matérn GP as a sparse precision matrix based on triangular finite elements. When constructing the finite element mesh, the maximum side length is set for the land and buffer respectively (e.g., 0.2 degrees for land and 0.5 degrees for buffer, or converted to the kilometer scale according to latitude and longitude), and the mesh quality (minimum angle threshold, side length distribution) is guaranteed to avoid numerical instability.

[0078] In the specific implementation process, R-INLA (Integrated Nested Laplace Approximation) is preferred to achieve approximate Bayesian inference because INLA has an efficient implementation for generalized linear mixed models with SPDE (e.g., binomial response + Matérn SPDE). At the same time, when accurate posterior samples are required, MCMC (e.g., NUTS) can be used to supplement the verification in small-scale cases.

[0079] S4. Using the in-sample prediction as a covariate in the Bayesian regional spatiotemporal hierarchical correlation model, a posterior distribution is generated after running the model. Samples are extracted from the posterior distribution and mapped to grid cells within the study area. The posterior mean of each grid cell is calculated by continuously sampling a set number of times. The estimated value of the grid cell is obtained by weighting it according to the population grid data and then summarized to the corresponding administrative unit to generate a high-resolution disease risk map.

[0080] In this embodiment, samples are drawn multiple times (e.g., 1000 times) from the posterior distribution to obtain the prevalence rate for each sampling. For each grid cell, the posterior sample at that location is mapped to the grid resolution through spatial interpolation (based on SPDE solution or Mesh-based projection matrix). The posterior mean, posterior standard deviation, and high-risk probability of each grid cell are calculated and recorded. The estimated values ​​of the grid cells are weighted according to the population grid data and summarized to the administrative unit, as shown in the following formula:

[0081]

[0082]

[0083] In the formula: For the incidence rate within an administrative unit, For weighted weights, The posterior mean is... Represents grid cells Belongs to an administrative unit. Represents grid cells Population grid data within the area.

[0084] In practice, the SPDE module in INLA can be used to directly output the prediction matrix (A matrix) required for interpolation, which facilitates posterior sample mapping.

[0085] In addition, the above models need to be evaluated, validated, robustly tested, and sensitive analyzed, specifically including:

[0086] For the output results of the five sub-models, record the metrics such as RMSE, MAE, R², and AUC (if binary classification) to ensure the stability of the sub-models in out-of-sample cross-validation.

[0087] Spatial blocking cross-validation is used to evaluate the Bayesian regional spatiotemporal hierarchical correlation model, and the root mean square error and log score are calculated. Time segmentation cross-validation can also be used to evaluate the time extrapolation capability.

[0088] Single-factor and multi-factor sensitivity analyses were performed on hyperparameters such as grid resolution, Matérn parameter, AR(1) coefficient, and sub-model regularization intensity of the Bayesian regional spatiotemporal hierarchical correlation model, and the results were recorded.

[0089] Error diagnosis is performed on the Bayesian regional spatiotemporal hierarchical correlation model, and the residual spatial autocorrelation (Moran's I), temporal autocorrelation (ACF) and residual distribution are examined. If necessary, the model structure is modified (e.g., by introducing non-stationary covariance or anisotropic functions).

[0090] The following is an illustration of a specific implementation scenario:

[0091] Taking the cognitive decline data of elderly people in a certain province from 2015 to 2022 as an example, the tools and parameters used are as follows:

[0092] Software tools: R (packages such as INLA, mgcv, xgboost, glmnet, sf, rgeos, spdep, etc.); Python (scikit-learn, xgboost, pymc3 / 4, MCMC if needed); geoprocessing uses GDAL / GeoTIFF.

[0093] Mesh settings: maximum landside edge length 0.2° (or approximately 22 km apparent latitude), buffer 0.5°; minimum angle threshold 20°; built and quality checked using R-inla::inla.mesh.2d.

[0094] Hyperparameter settings: XGBoost tree depth 3–6, learning rate 0.01–0.1; GAM basis function 3–6; LASSO λ determined by CV; α / ν of SPDE in INLA can be set according to domain experience (ν = 1).

[0095] Computing resources: Multi-core CPU (≥16 cores), at least 128 GB of memory to support high-resolution grids and large sample sizes. Parallelization of sub-model training and computer vision (CV) can significantly reduce time consumption.

[0096] Output format: Grid results are exported as GeoTIFF, administrative summaries are exported as Shapefile / CSV, and model diagnostics and cross-validation results are saved as CSV / HTML reports.

[0097] Sample size: Covering one prefecture-level city, with follow-up monitoring data from approximately 4,500 elderly people aged 65 and above.

[0098] Disease outcome: Determined by the Mini-Mental State Examination (MMSE) scale score; those scoring below the average were marked as "cognitive risk".

[0099] Covariates include annual average PM2.5 concentration, black carbon (BC) exposure, green space ratio (NDVI), GDP per capita, and education level.

[0100] First, the average score of cognitive function tests for all elderly people is calculated. Elderly people whose cognitive function scores are below the average are marked as people at risk of cognitive decline. Spatial clustering is performed on the cognitive function data, and cluster-level binomial data are constructed by year.

[0101] The aforementioned sub-models were trained on a training set consisting of 80% of the samples to generate five out-of-sample predictions. The sub-models were then run using 100% cognitive function data to create complete in-sample predictions. During model fitting, the five out-of-sample sub-model predictions were used as explanatory covariates input into the complete Bayesian regional spatiotemporal hierarchical association model; when generating predictions using the fitted Bayesian regional spatiotemporal hierarchical association model, the in-sample predictions of the sub-models were used as covariates.

[0102] Construct an SPDE Mesh, define a binomial response model in R-INLA (i.e., the formula part included in the Bayesian regional spatiotemporal hierarchical correlation model), set the prior, and run INLA to obtain the posterior margin.

[0103] After 1000 posterior samplings, the samples are mapped to a 1×1 km² grid, and the posterior mean, standard deviation, and high-risk probability are calculated.

[0104] Population-weighted calculations are performed, aggregated at the county level, and a high-resolution disease risk map is generated. County-level risk estimates are then performed, and high-risk counties are identified and ranked.

[0105] Perform spatial blocking CV (dividing the study area into 10 spatial blocks), calculate RMSE and log-score, complete sensitivity analysis and record the results.

[0106] The integrated covariate-Bayesian spatiotemporal hierarchical correlation model proposed in this invention is compared with traditional mapping methods. A specific evaluation was conducted for localized rural areas (small sample areas) within the province where monitoring points are sparse.

[0107] Table 1: Comparison of Predictive Accuracy of Different Models for Cognitive Function Risk Estimation

[0108] Evaluation indicators Traditional GLM model (covariates only) Traditional CAR spatial model Method of the present invention Increase RMSE (Root Mean Square Error) 0.425 0.312 0.188 39.7% ↓ Log-Score 1.58 1.12 0.84 25.0% ↓ R² (spatial explanatory power) 0.35 0.58 0.82 41.3% ↑ Posterior CV (coefficient of variation) 0.55 0.38 0.22 42.1% ↓

[0109] As can be seen from Table 1, compared with the two existing classic models, the integrated covariate-Bayes spatiotemporal hierarchical association model proposed in this invention has achieved significant improvements in a variety of evaluation indicators, effectively reducing the instability of risk estimation in small sample areas and low-incidence areas.

[0110] Example 2

[0111] This embodiment provides a Bayesian disease risk high-precision mapping system corresponding to the Bayesian disease risk high-precision mapping method provided in Embodiment 1, including:

[0112] Data acquisition module: used to collect raw data within the study area, including disease surveillance data, covariate data, population grid data, and administrative unit data, and to perform preprocessing.

[0113] Sub-model training module: This module is used to divide the disease surveillance data into training sets according to a certain proportion, use all covariates as prediction variables, fit multiple sub-models on the training set and test them using five-fold cross-validation to obtain multiple corresponding out-of-sample predictions. After compilation, a comprehensive prediction set is obtained. All disease surveillance data are then input into the sub-models to obtain in-sample predictions.

[0114] The main model training module is used to determine thresholds for various disease outcome data in disease surveillance data, marking the corresponding disease surveillance objects as having disease risk or no disease risk. It performs spatial clustering analysis on the disease outcome data of all disease surveillance objects to obtain multiple disease outcome data clusters, constructs a finite element mesh, maps the disease outcome data clusters to the mesh cells, uses the disease outcome data as a response variable, inputs it into the Bayesian regional spatiotemporal hierarchical correlation model, uses the comprehensive prediction set as a covariate of the Bayesian regional spatiotemporal hierarchical correlation model, uses the logit connection function to model the prevalence as a linear combination of covariates, spatiotemporal correlation error terms, and nugget error terms, fits the Bayesian regional spatiotemporal hierarchical correlation model, and simulates the change of prevalence within the study area.

[0115] Map generation module: Used to use in-sample predictions as covariates in Bayesian regional spatiotemporal hierarchical correlation model. After running, it generates a posterior distribution, extracts samples from the posterior distribution and maps them to grid cells within the study area. It calculates the posterior mean of each grid cell by continuously sampling a set number of times, weights the values ​​of the grid cells according to the population grid data, and summarizes them to the corresponding administrative units to generate a high-resolution disease risk map.

Claims

1. A Bayesian method for high-precision disease risk mapping, characterized in that, Includes the following steps: S1. Collect raw data within the study area, including disease surveillance data, covariate data, population grid data, and administrative unit data, and perform preprocessing. S2. Divide the disease surveillance data into a training set according to the proportion, use all covariates as prediction variables, fit multiple sub-models on the training set and test them with five-fold cross-validation to obtain multiple corresponding out-of-sample predictions, compile them to obtain a comprehensive prediction set, input all disease surveillance data into the sub-models to obtain in-sample predictions. S3. Threshold determination is performed on multiple disease outcome data in the disease surveillance data, and the corresponding disease surveillance objects are marked as having disease risk or no disease risk. Spatial cluster analysis is performed on the disease outcome data of all disease surveillance objects to obtain multiple disease outcome data clusters. A finite element mesh is constructed, and the disease outcome data clusters are mapped to the mesh cells. The disease outcome data is used as the response variable and input into the Bayesian regional spatiotemporal hierarchical correlation model. The comprehensive prediction set is used as the covariate of the Bayesian regional spatiotemporal hierarchical correlation model. The logit connection function is used to model the prevalence rate as a linear combination of covariates, spatiotemporal correlation error terms, and nugget error terms. The Bayesian regional spatiotemporal hierarchical correlation model is fitted to simulate the change of prevalence rate in the study area. S4. Using the in-sample prediction as a covariate in the Bayesian regional spatiotemporal hierarchical correlation model, a posterior distribution is generated after running the model. Samples are extracted from the posterior distribution and mapped to grid cells within the study area. The posterior mean of each grid cell is calculated by continuously sampling a set number of times. The estimated value of the grid cell is obtained by weighting it according to the population grid data and then summarized to the corresponding administrative unit to generate a high-resolution disease risk map.

2. The Bayesian high-precision disease risk mapping method according to claim 1, characterized in that, Step S1 includes: collecting disease surveillance data, covariate data, population grid data, and administrative unit data within the study area; calculating statistics for each monitored individual or data observation point in the raw data according to a predetermined time window for the covariate; using a unified coordinate reference system for the raw data and mapping the point data in the raw data to the corresponding geographical location within the study area; and finally standardizing the raw data.

3. The Bayesian high-precision disease risk mapping method according to claim 2, characterized in that, Step S1 further includes: for missing short sequence data in the covariate data, linear interpolation or spline interpolation is used to supplement them; for missing spatial data in the covariate data, spatial interpolation or nearest neighbor imputation is used to supplement them.

4. The Bayesian high-precision disease risk mapping method according to claim 1, characterized in that, The sub-models include generalized additive models, enhanced regression trees, lasso regression, least squares linear regression, and ridge regression.

5. The Bayesian high-precision disease risk mapping method according to claim 1, characterized in that, The disease outcome data includes continuous outcome data and discrete outcome data. Continuous outcome data includes numerical disease surveillance data, while discrete outcome data includes data on whether an individual has a disease, data on an individual's survival status, data on an individual's death events, and data on an individual's abnormal diagnostic events. For the continuous outcome data, the data is compared with the corresponding clinical reference range. Individuals whose data do not meet the clinical reference range are marked as having a disease risk, otherwise they are marked as having no disease risk. For the discrete outcome data, the data is directly categorized and coded based on whether the individual is in an abnormal state, and marked as having a disease risk or having no disease risk.

6. The Bayesian high-precision disease risk mapping method according to claim 1, characterized in that, The formula for the Bayesian regional spatiotemporal hierarchical correlation model is as follows: In the formula: Indicates that there is a grid cell inside A cluster of disease outcome data, This indicates the number of individuals monitored within a grid cell who pose a disease risk. express Total number of samples within each disease outcome data cluster This indicates the disease prevalence rate within the grid cell. This is the logit join function. The intercept term represents the baseline disease prevalence level. As covariates, For spatiotemporal correlation error terms, For the spatiotemporal correlation error term within the grid cell, This is an independent error term for nuggets. The prediction weights are for the five sub-models. For the variance of the gold nugget, For spatial covariance, For time covariance, For Gaussian processes, The distance between two points. For scale parameters, These are joint parameters used to define how the spatial covariance varies with distance. This is a modified Bessel function of the second kind. For the Gamma function, For smoothing parameters, For accuracy parameters, This is the time autocorrelation coefficient. For the k-th time step, This is the j-th time step.

7. The Bayesian high-precision disease risk mapping method according to claim 1, characterized in that, Step S3 further includes: in the Bayesian regional spatiotemporal hierarchical correlation model, the spatiotemporal correlation error term is approximated as a sparse precision matrix based on triangular finite element method using stochastic partial differential equation method, and when constructing the finite element mesh, the maximum side length is set for the land and the buffer respectively.

8. The Bayesian high-precision disease risk mapping method according to claim 1, characterized in that, Step S4 further includes: evaluating the Bayesian regional spatiotemporal hierarchical correlation model using spatial blocking cross-validation, calculating the root mean square error and log score, and performing sensitivity analysis on the hyperparameters of the Bayesian regional spatiotemporal hierarchical correlation model and recording the results.

9. The Bayesian high-precision disease risk mapping method according to claim 1, characterized in that, Step S4 includes: drawing samples multiple times from the posterior distribution to obtain the prevalence rate for each sampling; for each grid cell, mapping the posterior sample at that location to the grid resolution through spatial interpolation; calculating the posterior mean of each grid cell; weighting the values ​​according to population grid data; and summarizing the estimated values ​​of the grid cells to the administrative unit, as shown in the following formula: In the formula: For the incidence rate within an administrative unit, For weighted weights, The posterior mean is... Represents grid cells Belongs to an administrative unit. Represents grid cells Population grid data within the area.

10. A Bayesian high-precision disease risk mapping system, characterized in that, include: Data acquisition module: used to collect raw data within the study area, including disease surveillance data, covariate data, population grid data, and administrative unit data, and to perform preprocessing. Sub-model training module: This module is used to divide the disease surveillance data into training sets according to a certain proportion, use all covariates as prediction variables, fit multiple sub-models on the training set and test them using five-fold cross-validation to obtain multiple corresponding out-of-sample predictions. After compilation, a comprehensive prediction set is obtained. All disease surveillance data are then input into the sub-models to obtain in-sample predictions. The main model training module is used to determine thresholds for various disease outcome data in disease surveillance data, marking the corresponding disease surveillance objects as having disease risk or no disease risk. It performs spatial clustering analysis on the disease outcome data of all disease surveillance objects to obtain multiple disease outcome data clusters, constructs a finite element mesh, maps the disease outcome data clusters to the mesh cells, uses the disease outcome data as a response variable, inputs it into the Bayesian regional spatiotemporal hierarchical correlation model, uses the comprehensive prediction set as a covariate of the Bayesian regional spatiotemporal hierarchical correlation model, uses the logit connection function to model the prevalence as a linear combination of covariates, spatiotemporal correlation error terms, and nugget error terms, fits the Bayesian regional spatiotemporal hierarchical correlation model, and simulates the change of prevalence within the study area. Map generation module: Used to use in-sample predictions as covariates in Bayesian regional spatiotemporal hierarchical correlation model. After running, it generates a posterior distribution, extracts samples from the posterior distribution and maps them to grid cells within the study area. It calculates the posterior mean of each grid cell by continuously sampling a set number of times, weights the values ​​of the grid cells according to the population grid data, and summarizes them to the corresponding administrative units to generate a high-resolution disease risk map.

Images