MCI cognitive trajectory and bidirectional outcome dynamic prediction method based on joint model

Abstract

The invention relates to the technical field of medical informatization, in particular to an MCI cognitive trajectory and bidirectional outcome dynamic prediction method based on a joint model. The method comprises the following specific steps: firstly, constructing a univariate joint model, then constructing a multivariate joint model, and then constructing a function type multivariate joint model; performing parameter estimation and statistical inference on the model; fitting evaluation is carried out on the function type multivariable joint model based on multi-longitudinal cognition and multi-state outcome; and finally, carrying out individualized dynamic prediction. According to the method, a baseline or longitudinal nerve image is processed by using a function type data analysis technology, and a change track is reconstructed; a plurality of cognitive assessments are used as longitudinal measurement indexes, covariants such as age and gender and functional nerve images are used as predictive factors, two-way outcome of MCI and occurrence time of the two-way outcome are set as survival outcomes, a joint model based on multi-longitudinal cognitive multi-state outcomes is constructed, early screening of high-risk groups is assisted, and the survival outcomes of the high-risk groups are determined. And powerful support is provided for optimal distribution of medical and medical and health resources.

Description

Technical Field

[0001] This invention belongs to the field of medical information technology, and specifically relates to a dynamic prediction method for MCI cognitive trajectory and bidirectional outcome based on a joint model. Background Technology

[0002] Alzheimer's disease (AD) exhibits a continuous disease spectrum, with mild cognitive impairment (MCI) representing a transitional state between normal cognition (NC) and AD. This intermediate state is of great significance, as it represents a critical window for ultra-early intervention in AD and a crucial period for implementing effective treatment. The risk of MCI patients progressing to AD remains consistently high. Therefore, if a simple and easily implemented method could be used to conduct preliminary screening of an individual's cognitive function and daily living abilities, identifying high-risk individuals with potential AD risk, and enabling accurate diagnosis and timely treatment to prevent further cognitive deterioration, it would undoubtedly have extremely important practical value and significance.

[0003] However, many problems remain to be solved in the field of MCI. On the one hand, the explanation for the reversal of MCI to NC is still inconclusive. Due to the questionable reliability of MCI diagnosis, MCI patients with good cognitive trajectories may benefit little from anti-dementia treatment but have to bear the adverse effects of drugs and higher economic costs. On the other hand, if the reversal of MCI is not given enough attention, the elderly and their families will face a series of potential adverse consequences, such as anxiety. These factors are interconnected and may further trigger a chain reaction, leading to cognitive deterioration. Therefore, it is urgent to explore the heterogeneous trajectory of MCI. In existing research, researchers are committed to constructing AD joint models based on a combination of factors such as cognitive assessment and neuroimaging to achieve dynamic monitoring of disease progression in high-risk individuals. Although the introduction of multiple candidate factors has enhanced the predictive value of the model for MCI prognosis to some extent, these predictions currently have obvious limitations. They are either qualitative (only judging whether MCI will progress to AD as a binary response variable) or quantitative (only providing cognitive scores), but they ignore the key factor of heterogeneity in the bidirectional outcome of MCI.

[0004] From a theoretical perspective, joint models possess the ability to effectively analyze longitudinal survival data of cognitive impairment. However, in practical applications, they still face many significant limitations. For example, in the longitudinal sub-models of joint models, cognitive trajectories do not always exhibit linearity or a specific fixed shape, making it extremely difficult to predetermine the pattern of cognitive trajectories. Secondly, there is a high correlation between repeated measurements of individuals at different time points. When the observation time is sparse and irregular, linear mixed models struggle to effectively handle the correlation problem between different observation time points, and a limited number of longitudinal measurements can also lead to difficulties in estimating model parameters.

[0005] In view of this, the present invention proposes a dynamic prediction method for MCI cognitive trajectory and bidirectional regress based on a joint model to solve the problems existing in the prior art. Summary of the Invention

[0006] In view of this, the main objective of this invention is to provide a dynamic prediction method for MCI cognitive trajectory and bidirectional outcome based on a joint model, which aims to solve the problems of limited prediction results, difficulty in clarifying cognitive trajectory patterns, difficulty in processing observation data, and difficulty in estimating model parameters in the process of constructing AD joint models based on multi-factor combinations for dynamic monitoring of disease progression in high-risk individuals in existing technologies.

[0007] The technical solution of this invention is implemented as follows:

[0008] A joint model-based dynamic prediction method for MCI cognitive trajectories and bidirectional outcomes includes:

[0009] Step 1: Construct a univariate joint model;

[0010] Step 2: Construct a multivariate joint model based on the univariate joint model;

[0011] Step 3: Based on the multivariate joint model, construct a functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes;

[0012] Step 4: Perform parameter estimation and statistical inference on the functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes established in Step 3;

[0013] Step 5: Evaluate the goodness of fit of the functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes established in Step 3 based on the parameter estimation and statistical inference results of Step 4.

[0014] Step 6: Perform individualized dynamic prediction based on a functional multivariate joint model;

[0015] Based on individual longitudinal cognitive assessment and neuroimaging, the risk and longitudinal cognitive trajectory of bidirectional MCI outcome are dynamically updated to provide an individual's instantaneous risk assessment.

[0016] In a preferred embodiment of the present invention, the process of constructing the univariate joint model in step 1 includes:

[0017] Step 1.1: Construct the vertical sub-model;

[0018] ;

[0019] in, For individuals exist Cognitive assessment value at any given moment; For fixed effects dimensional vector; For random effects dimensional vector; For connection With fixed factors for longitudinal measurements 3D design matrix; For connection With longitudinal measurement of random factors 3D design matrix; residual This includes measurement error and sequence correlation. For individuals of 3D positive definite variance-covariance matrix express 3D identity matrix ;

[0020] Step 1.2: Construct the survival sub-model;

[0021] The survival process was fitted using a multi-state Markov model, and the results were obtained. The transition intensity when MCI reverses to NC The transfer intensity of MCI to AD They are respectively:

[0022] ;

[0023] in, and As the benchmark risk function, and As covariates, and These are the corresponding regression coefficients; and This is a parameter vector used to quantize the cutoff time. The association between potential longitudinal cognitive processes and bidirectional MCI outcomes;

[0024] Step 1.3: Establish the relationship structure between the longitudinal sub-model and the survival sub-model;

[0025] Step 1.4: Calculate the area under the longitudinal trajectory;

[0026] Set time point Survival risks and deadlines The longitudinal measurement trajectory is correlated with the area, and the correlation strength is determined by the parameters. To measure, we get:

[0027] ;

[0028] in, The trajectory of individual i's cognitive function over time; Let be the set of all longitudinal measurements of cognitive function for individual i up to time t. And its potential true trajectory, i.e. All the information contained therein; For individual i, the random effect; For the set of associated parameter vectors; for A specific component; Given a cutoff time t, the instantaneous risk of an event occurring at time t based on covariates and the longitudinal process individual i. Used as the benchmark risk function; These are covariates that may affect survival risk; covariates The corresponding coefficient vector;

[0029] Step 1.5: Establish a model relating the current value to the area under the vertical trajectory;

[0030] Set time point Survival risks and deadlines Current value of longitudinal measurement Related to the area under the trajectory, the correlation strength is determined by the parameters. and To measure:

[0031] .

[0032] In a preferred embodiment of the present invention, the process of establishing the association structure between the longitudinal sub-model and the survival sub-model in step 1.3 includes:

[0033] Step 1.3.1: Set the current value;

[0034] Set time point Survival risk at the same point in time Current value of longitudinal measurement Correlation, the strength of the correlation is determined by parameters To measure:

[0035] ;

[0036] in, The trajectory of individual i's cognitive function over time; Let be the set of all longitudinal measurements of cognitive function for individual i up to time t. And its potential true trajectory; For individual i, the random effect; For the set of associated parameter vectors; for A specific component; Given a cutoff time t, the instantaneous risk of an event occurring at time t based on covariates and the longitudinal process individual i. The baseline risk function represents the survival risk when all covariates and longitudinal processes are equal to 0. These are covariates that may affect survival risk; covariates The corresponding coefficient vector represents the impact of these covariates on survival risk;

[0037] Step 1.3.2: Set the current slope;

[0038] Set time point Survival risk at the same point in time The current slope of the longitudinal measurement Correlation, the strength of the correlation is determined by parameters To measure:

[0039] ;

[0040] in, For the set of associated parameter vectors; For individual i's potential longitudinal cognitive trajectory The instantaneous rate of change or slope at time point t; This is a slope-related parameter;

[0041] Step 1.3.3: Establish the relationship between the current value and the current slope;

[0042] Set time point Survival risk at the same point in time Current value of longitudinal measurement With the current slope Correlation, the strength of the correlation is determined by parameters and To measure:

[0043] .

[0044] In a preferred embodiment of the present invention, the process of constructing the multivariate joint model in step 2 includes:

[0045] Step 2.1: Construct a multivariate longitudinal sub-model;

[0046] Let individuals have A longitudinal cognitive assessment, For different longitudinal measurements of cognitive assessment, the longitudinal cognitive process is as follows:

[0047] ;

[0048] in, The expected mean or potential true value of individual i's cognitive assessment at time t at the p-th time excludes random measurement error; For individual i, the actual observed value of the p-th cognitive assessment at time t; Let i be the vector of fixed-effects covariates related to the p-th cognitive assessment at time t; For covariates The corresponding fixed effects coefficient vector; Let be the vector of random effects of individual i at time t related to the p-th cognitive assessment; For individual i, the random effect on the p-th cognitive dimension; It is the inverse function of the connection function of the p-th cognitive assessment;

[0049] Suppose a random effect with a multivariate normal distribution It can capture the correlation between multiple longitudinal cognitive assessments:

[0050] ;

[0051] Using a multiple linear mixed-effects model for the same individual At different times Multiple longitudinal cognitive assessments Modeling:

[0052] ;

[0053] in, For individuals exist Cognitive assessment of time Longitudinal measurement value For connection fixed effect With cognitive assessment The covariate matrix of longitudinal measurements, To connect random effects With cognitive assessment Design matrix of random factors for longitudinal measurements, residuals ;

[0054] Step 2.2: Construct a multivariate survival sub-model;

[0055] A Markov model was used to fit the transition time. The transition intensity when MCI reverses to NC The transfer intensity of MCI to AD They are respectively:

[0056] ;

[0057] Among them, multivariable functions For the first The longitudinal trajectory of cognitive assessment; and For parameters.

[0058] In a preferred embodiment of the present invention, step 3, the process of establishing a functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes, includes:

[0059] Step 3.1: Construct the longitudinal sub-model of the functional multivariate joint module;

[0060] Using a multiple linear mixed-effects model for the same individual At different times Multiple longitudinal cognitive assessments Modeling was performed; baseline neuroimaging functional predictors based on the brain spatial continuum were incorporated, and the model was expanded to:

[0061] ;

[0062] in, This is the random error term; As a functional predictor of baseline neuroimaging, It is a continuous variable; It is a functional covariate of individual i; It is a set of basis functions used to approximate unknown coefficient functions; the integral of S is expressed as a summation over the entire field S.

[0063] By incorporating longitudinal neuroimaging functional predictors based on the two-dimensional continuous domains of brain space and time, the model is expanded to:

[0064] ;

[0065] in, A functional predictor of baseline neuroimaging; As a predictor of longitudinal neuroimaging;

[0066] Step 3.2: Construct a survival sub-model of the functional multivariate joint module;

[0067] By incorporating baseline neuroimaging functional predictors based on the brain spatial continuum, the model is expanded to:

[0068] ;

[0069] By incorporating longitudinal neuroimaging functional predictors based on the two-dimensional continuous domains of brain space and time, the model is expanded to:

[0070] (17);

[0071] in, A functional predictor of baseline neuroimaging; It is a longitudinal neuroimaging predictor for a two-dimensional continuous domain of time and brain structure.

[0072] In a preferred embodiment of the present invention, step 4, the process of parameter estimation and statistical inference for the functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes, includes:

[0073] Step 4.1: Perform Gibbs sampling;

[0074] Let the distribution of the parameters of interest be... , Each element It is a scalar, vector, or matrix, and is sampled using the Gibbs sampling method;

[0075] Step 4.2: Perform model convergence diagnosis for the functional multivariate joint model.

[0076] In a preferred embodiment of the present invention, the fitting evaluation process of the functional multivariate joint model in step 5 includes:

[0077] Step 5.1: Set the evaluation metrics for the survival sub-model;

[0078] The evaluation indicators include a consistency index and a global test.

[0079] Step 5.2: Set the evaluation index for the joint model.

[0080] In a preferred embodiment of the present invention, the process of establishing the joint model evaluation index includes:

[0081] Step 5.2.1: Deviation Information Criteria;

[0082] DIC is the sum of penalty terms based on the number of effective parameters, which is a measure of both the goodness of fit and the complexity of the model.

[0083] ;

[0084] in, It is a deviation function; , where is the number of valid parameters; and They are respectively and The posterior mean;

[0085] Step 5.2.2: Modify DIC and establish WAIC criteria:

[0086] ;

[0087] in, , , This represents the sample variance.

[0088] Step 5.2.3: Log-pseudo-marginal likelihood:

[0089] ;

[0090] in, The conditional prediction order / ordinate.

[0091] In a preferred embodiment of the present invention, step 6, the process of performing individualized dynamic prediction based on a functional multivariate joint model, includes:

[0092] Step 6.1: Predict the conditional survival probability of MCI bidirectional reversion;

[0093] Set up a new individual At the point of time No endpoint event occurred, i.e., no bidirectional MCI outcome occurred, and multiple longitudinal cognitive assessments are known. Predict its timing The conditional survival probability of the bidirectional reversal is:

[0094]

[0095] ;

[0096] Step 6.2: Perform longitudinal trajectory prediction.

[0097] In a preferred embodiment of the present invention, the longitudinal trajectory prediction process in step 6.2 includes:

[0098] Known longitudinal measurement trajectory of a new individual Predict its timing Longitudinal measurement values: ;

[0099] in, , Samples for fitting the joint model.

[0100] Compared with existing technologies, this invention provides a dynamic prediction method for MCI cognitive trajectory and bidirectional outcome based on a joint model, which has the following beneficial effects:

[0101] 1. This method uses repeatedly measured cognitive indicators as longitudinal data inputs and combines them with survival outcomes to dynamically update risk predictions, which significantly improves the efficiency of real-time data fusion.

[0102] 2. This method employs functional data analysis to process baseline or longitudinal neuroimaging and reconstruct its trajectory. Multiple cognitive assessments are used as longitudinal measures, with age and gender as covariates and functional neuroimaging as predictive factors. The bidirectional outcome of MCI and its onset time are used as survival outcomes. A joint model based on multiple longitudinal cognitive and multi-state outcomes is established, and relevant model parameters are estimated. An individualized dynamic prediction framework for MCI cognitive trajectories and bidirectional outcomes is constructed, which facilitates early screening of high-risk populations and supports precision medicine and the optimal allocation of limited medical and health resources.

[0103] 3. The predictive model established by this method helps to identify high-risk individuals with cognitive decline in a timely manner, reduce the burden on social service systems, provide reliable epidemiological evaluation and important information for public health management for individualized prevention guidance and early intervention of cognitive impairment in the elderly, and provide strong statistical decision support for disease surveillance. Attached Figure Description

[0104] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0105] Figure 1 The flowchart shows the dynamic prediction method for MCI cognitive trajectory and bidirectional outcome based on the joint model of the present invention.

[0106] Figure 2 This is a structural diagram of the functional joint model based on multiple longitudinal cognitions and multiple state outcomes of the present invention;

[0107] Figure 3This is a schematic diagram of the correlation structure of Embodiment 1 of the present invention based on the current value, current slope, and area under the longitudinal trajectory;

[0108] Figure 4 This is the individualized dynamic prediction diagram of ADAS11 based on a multi-longitudinal cognitive assessment multi-state joint model in Embodiment 3 of the present invention.

[0109] Figure 5 This is the individualized dynamic prediction diagram of ADAS13 based on a multi-longitudinal cognitive assessment multi-state joint model in Embodiment 3 of the present invention.

[0110] Figure 6 This is the individualized dynamic prediction diagram of ADASQ4 based on a multi-longitudinal cognitive assessment multi-state joint model in Embodiment 3 of the present invention.

[0111] Figure 7 This is the individualized dynamic prediction diagram of the FAQ based on the multi-longitudinal cognitive assessment multi-state joint model of the present invention in Embodiment 3 of the present invention;

[0112] Figure 8 This is the individualized dynamic prediction graph of RAVLT_immediate based on the multi-longitudinal cognitive assessment multi-state joint model of the present invention in Embodiment 3 of the present invention;

[0113] Figure 9 This is the individualized dynamic prediction diagram of RAVLT_learning based on a multi-longitudinal cognitive assessment multi-state joint model in Embodiment 3 of the present invention;

[0114] Figure 10 This is the individualized dynamic prediction graph of RAVLT_forgetting based on the multi-longitudinal cognitive assessment multi-state joint model in Embodiment 3 of the present invention.

[0115] Figure 11 This is the individualized dynamic prediction graph of RAVLT_perc_forgetting based on the multi-longitudinal cognitive assessment multi-state joint model in Embodiment 3 of the present invention.

[0116] Figure 12 This is the individualized dynamic prediction diagram of TRABSCOR based on the multi-longitudinal cognitive assessment multi-state joint model of the present invention in Embodiment 3 of the present invention;

[0117] Figure 13 This is the individualized dynamic prediction graph of mPACCdigit based on the multi-longitudinal cognitive assessment multi-state joint model in Embodiment 3 of the present invention.

[0118] Figure 14 This is the individualized dynamic prediction diagram of mPACCtrailsB based on the multi-longitudinal cognitive assessment multi-state joint model in Embodiment 3 of the present invention.

[0119] Figure 15 This is an individualized dynamic prediction graph of the bidirectional outcome of longitudinal cognitive assessment and survival information over a 5-year period from baseline, as known in Embodiment 3 of the present invention.

[0120] Figure 16 This is an individualized dynamic prediction graph of the bidirectional outcome of longitudinal cognitive assessment and survival information over a 6-year period from baseline, as known in Embodiment 3 of the present invention.

[0121] Figure 17 This is an individualized dynamic forecast of the bidirectional evolution of longitudinal cognitive assessment and survival information over 8 years from baseline, as known in Embodiment 3 of the present invention.

[0122] Figure 18 This is an individualized dynamic prediction graph of the bidirectional outcome of longitudinal cognitive assessment and survival information over a known 10-year period from baseline, as described in Embodiment 3 of the present invention.

[0123] Figure 19 This is an individualized dynamic prediction graph of the bidirectional regression of longitudinal cognitive assessment and survival information over a known 12-year period from baseline, as described in Embodiment 3 of the present invention.

[0124] Among them: Figure 4 In the figure, Figure (a) is the individualized dynamic prediction of ADAS11 based on the multi-longitudinal cognitive assessment multi-state joint model over 3 years, Figure (b) is the individualized dynamic prediction of ADAS11 based on the multi-longitudinal cognitive assessment multi-state joint model over 5 years, Figure (c) is the individualized dynamic prediction of ADAS11 based on the multi-longitudinal cognitive assessment multi-state joint model over 7 years, Figure (d) is the individualized dynamic prediction of ADAS11 based on the multi-longitudinal cognitive assessment multi-state joint model over 9 years, and Figure (e) is the individualized dynamic prediction of ADAS11 based on the multi-longitudinal cognitive assessment multi-state joint model over 10 years.

[0125] exist Figure 5 In the figure, Figure (a) is the individualized dynamic prediction of ADAS13 based on the multi-longitudinal cognitive assessment multi-state joint model over 3 years, Figure (b) is the individualized dynamic prediction of ADAS13 based on the multi-longitudinal cognitive assessment multi-state joint model over 5 years, Figure (c) is the individualized dynamic prediction of ADAS13 based on the multi-longitudinal cognitive assessment multi-state joint model over 7 years, Figure (d) is the individualized dynamic prediction of ADAS13 based on the multi-longitudinal cognitive assessment multi-state joint model over 9 years, and Figure (e) is the individualized dynamic prediction of ADAS13 based on the multi-longitudinal cognitive assessment multi-state joint model over 10 years.

[0126] exist Figure 6In the figure, Figure (a) is the individualized dynamic prediction of ADASQ4 based on the multi-longitudinal cognitive assessment multi-state joint model within 3 years, Figure (b) is the individualized dynamic prediction of ADASQ4 based on the multi-longitudinal cognitive assessment multi-state joint model within 5 years, Figure (c) is the individualized dynamic prediction of ADASQ4 based on the multi-longitudinal cognitive assessment multi-state joint model within 7 years, Figure (d) is the individualized dynamic prediction of ADASQ4 based on the multi-longitudinal cognitive assessment multi-state joint model within 9 years, and Figure (e) is the individualized dynamic prediction of ADASQ4 based on the multi-longitudinal cognitive assessment multi-state joint model within 10 years.

[0127] exist Figure 7 In the figure, Figure (a) is the individualized dynamic prediction diagram of the FAQ based on the multi-longitudinal cognitive assessment multi-state joint model within 3 years, Figure (b) is the individualized dynamic prediction diagram of the FAQ based on the multi-longitudinal cognitive assessment multi-state joint model within 5 years, Figure (c) is the individualized dynamic prediction diagram of the FAQ based on the multi-longitudinal cognitive assessment multi-state joint model within 7 years, Figure (d) is the individualized dynamic prediction diagram of the FAQ based on the multi-longitudinal cognitive assessment multi-state joint model within 9 years, and Figure (e) is the individualized dynamic prediction diagram of the FAQ based on the multi-longitudinal cognitive assessment multi-state joint model within 10 years.

[0128] exist Figure 8 In the figure, Figure (a) is the individualized dynamic prediction of RAVLT_immediate based on the multi-longitudinal cognitive assessment multi-state joint model over 3 years, Figure (b) is the individualized dynamic prediction of RAVLT_immediate based on the multi-longitudinal cognitive assessment multi-state joint model over 5 years, Figure (c) is the individualized dynamic prediction of RAVLT_immediate based on the multi-longitudinal cognitive assessment multi-state joint model over 7 years, Figure (d) is the individualized dynamic prediction of RAVLT_immediate based on the multi-longitudinal cognitive assessment multi-state joint model over 9 years, and Figure (e) is the individualized dynamic prediction of RAVLT_immediate based on the multi-longitudinal cognitive assessment multi-state joint model over 10 years.

[0129] exist Figure 9In the figure, Figure (a) is the individualized dynamic prediction of RAVLT_learning based on the multi-longitudinal cognitive assessment multi-state joint model over 3 years, Figure (b) is the individualized dynamic prediction of RAVLT_learning based on the multi-longitudinal cognitive assessment multi-state joint model over 5 years, Figure (c) is the individualized dynamic prediction of RAVLT_learning based on the multi-longitudinal cognitive assessment multi-state joint model over 7 years, Figure (d) is the individualized dynamic prediction of RAVLT_learning based on the multi-longitudinal cognitive assessment multi-state joint model over 9 years, and Figure (e) is the individualized dynamic prediction of RAVLT_learning based on the multi-longitudinal cognitive assessment multi-state joint model over 10 years.

[0130] exist Figure 10 In the figure, Figure (a) is the individualized dynamic prediction of RAVLT_forgetting based on the multi-longitudinal cognitive assessment multi-state joint model over 3 years, Figure (b) is the individualized dynamic prediction of RAVLT_forgetting based on the multi-longitudinal cognitive assessment multi-state joint model over 5 years, Figure (c) is the individualized dynamic prediction of RAVLT_forgetting based on the multi-longitudinal cognitive assessment multi-state joint model over 7 years, Figure (d) is the individualized dynamic prediction of RAVLT_forgetting based on the multi-longitudinal cognitive assessment multi-state joint model over 9 years, and Figure (e) is the individualized dynamic prediction of RAVLT_forgetting based on the multi-longitudinal cognitive assessment multi-state joint model over 10 years.

[0131] exist Figure 11 In the figure, Figure (a) is the individualized dynamic prediction of RAVLT_perc_forgetting based on the multi-longitudinal cognitive assessment multi-state joint model over 3 years, Figure (b) is the individualized dynamic prediction of RAVLT_perc_forgetting based on the multi-longitudinal cognitive assessment multi-state joint model over 5 years, Figure (c) is the individualized dynamic prediction of RAVLT_perc_forgetting based on the multi-longitudinal cognitive assessment multi-state joint model over 7 years, Figure (d) is the individualized dynamic prediction of RAVLT_perc_forgetting based on the multi-longitudinal cognitive assessment multi-state joint model over 9 years, and Figure (e) is the individualized dynamic prediction of RAVLT_perc_forgetting based on the multi-longitudinal cognitive assessment multi-state joint model over 10 years.

[0132] exist Figure 12In the figure, Figure (a) is the individualized dynamic prediction of TRABSCOR based on the multi-longitudinal cognitive assessment multi-state joint model over 3 years, Figure (b) is the individualized dynamic prediction of TRABSCOR based on the multi-longitudinal cognitive assessment multi-state joint model over 5 years, Figure (c) is the individualized dynamic prediction of TRABSCOR based on the multi-longitudinal cognitive assessment multi-state joint model over 7 years, Figure (d) is the individualized dynamic prediction of TRABSCOR based on the multi-longitudinal cognitive assessment multi-state joint model over 9 years, and Figure (e) is the individualized dynamic prediction of TRABSCOR based on the multi-longitudinal cognitive assessment multi-state joint model over 10 years.

[0133] exist Figure 13 In the figure, Figure (a) is the individualized dynamic prediction of mPACCdigit based on the multi-longitudinal cognitive assessment multi-state joint model over 3 years, Figure (b) is the individualized dynamic prediction of mPACCdigit based on the multi-longitudinal cognitive assessment multi-state joint model over 5 years, Figure (c) is the individualized dynamic prediction of mPACCdigit based on the multi-longitudinal cognitive assessment multi-state joint model over 7 years, Figure (d) is the individualized dynamic prediction of mPACCdigit based on the multi-longitudinal cognitive assessment multi-state joint model over 9 years, and Figure (e) is the individualized dynamic prediction of mPACCdigit based on the multi-longitudinal cognitive assessment multi-state joint model over 10 years.

[0134] exist Figure 14 In the figure, Figure (a) is the individualized dynamic prediction of mPACCtrailsB based on the multi-longitudinal cognitive assessment multi-state joint model over 3 years, Figure (b) is the individualized dynamic prediction of mPACCtrailsB based on the multi-longitudinal cognitive assessment multi-state joint model over 5 years, Figure (c) is the individualized dynamic prediction of mPACCtrailsB based on the multi-longitudinal cognitive assessment multi-state joint model over 7 years, Figure (d) is the individualized dynamic prediction of mPACCtrailsB based on the multi-longitudinal cognitive assessment multi-state joint model over 9 years, and Figure (e) is the individualized dynamic prediction of mPACCtrailsB based on the multi-longitudinal cognitive assessment multi-state joint model over 10 years.

[0135] And in the above Figures 4-14 In Figures (a)-(e), the blue dots to the left of the dashed line represent known longitudinal assessment values, while the solid blue lines and bars represent predicted values ​​and their confidence intervals.

[0136] exist Figure 15 In the figure, Figure (a) is an individualized dynamic prediction map of longitudinal cognitive assessments within 5 years from baseline, and Figure (b) is an individualized dynamic prediction map of survival information within 5 years from baseline.

[0137] exist Figure 16In the figure, Figure (a) is an individualized dynamic prediction plot of longitudinal cognitive assessments over a 6-year period from baseline, and Figure (b) is an individualized dynamic prediction plot of survival information over a 6-year period from baseline.

[0138] exist Figure 17 In the figure, Figure (a) is an individualized dynamic prediction plot of longitudinal cognitive assessments known over 8 years from baseline, and Figure (b) is an individualized dynamic prediction plot of survival information known over 8 years from baseline.

[0139] exist Figure 18 In the figure, Figure (a) is an individualized dynamic prediction of longitudinal cognitive assessments over a 10-year period from baseline, and Figure (b) is an individualized dynamic prediction of survival information over a 10-year period from baseline.

[0140] exist Figure 19 In the figure, Figure (a) is an individualized dynamic prediction of longitudinal cognitive assessments over a 12-year period from baseline, and Figure (b) is an individualized dynamic prediction of survival information over a 12-year period from baseline.

[0141] And in the above Figures 15-19 In Figures (a) and (b), the solid line and bars to the right of the dashed line represent the predicted values ​​and their confidence intervals. Green indicates MCI reversal to NC, and red indicates MCI progression to AD. Detailed Implementation

[0142] The following description, in conjunction with the accompanying drawings and embodiments of the present invention, provides a more detailed explanation of the dynamic prediction method for MCI cognitive trajectory and bidirectional regress based on a joint model.

[0143] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0144] Example 1:

[0145] The following is in conjunction with the instruction manual appendix. Figure 1 -Appendix Figure 3 This invention describes a dynamic prediction method for MCI cognitive trajectories and bidirectional outcomes based on a joint model. This method primarily constructs a functional joint model based on multiple longitudinal cognitions and multiple state outcomes, and then uses this joint model to dynamically predict MCI cognitive trajectories and bidirectional outcomes. The specific process includes:

[0146] Step 1: Construct a univariate joint model;

[0147] set up For a sample in the target population, For individuals Actual survival time The censoring time is the observed lifetime. , As an indicator variable for survival outcome, when The value is 1 if the condition is met, and 0 otherwise. For different time points The longitudinal measurement value.

[0148] Step 1.1: Construct the vertical sub-model;

[0149] Based on one-to-one monotonic join function The longitudinal process is fitted using a generalized linear mixed-effects model:

[0150] (2);

[0151] Using a linear mixture model for individuals Modeling longitudinal cognitive assessments at different time points;

[0152] (3);

[0153] in, For individuals exist Cognitive assessment value at any given moment For fixed effects dimensional vector, For random effects dimensional vector, ; For connection With fixed factors for longitudinal measurements 3D design matrix, For connection With longitudinal measurement of random factors 3D design matrix, residual This includes measurement error and serial correlation. For individuals of A positive definite variance-covariance matrix, where express 3D identity matrix .

[0154] Step 1.2: Construct the survival sub-model;

[0155] set up For a finite state space The multi-state process in the model is assumed to be a continuous Markov process.

[0156] set up For individuals Transition time between different states , That is, each transfer time is longer than the previous transfer time.

[0157] set up For individuals Transition indicator vectors between different states, if Observe the state at all times The direct transfer, then ,otherwise .

[0158] A multi-state Markov model with proportional risk is used to fit the survival process. The results are... The transition intensity when MCI reverses to NC The transfer intensity of MCI to AD They are respectively:

[0159] (4);

[0160] in, and As the benchmark risk function, and As covariates, and For the corresponding regression coefficients; parameter vector and Used to quantify the cutoff time point The association between potential longitudinal cognitive processes and bidirectional MCI outcomes.

[0161] Step 1.3: Establish the association structures between the longitudinal sub-model and the survival sub-model.

[0162] Step 1.3.1: Set the current value;

[0163] Set time point Survival risk at the same point in time Current value of longitudinal measurement Correlation, the strength of the correlation is determined by parameters To measure:

[0164] (5);

[0165] in, The trajectory of cognitive function change of individual i over time, i.e., the expected mean or potential true longitudinal process value of individual i at time t (excluding measurement error). Let be the set of all longitudinal measurements of cognitive function for individual i up to time t. And its potential true trajectory, i.e. All the information contained therein; For individual i, the random effect is used to capture the unique changes in an individual's trajectory that deviate from the population mean. For the set of associated parameter vectors; for One specific component, the current value-related parameter, is used to quantify the strength of the impact of cognitive function on survival risk at the current moment in a longitudinal process; that is, at the same time point t, the longitudinal measurement value For each additional unit, the resulting change in the logarithmic risk rate is... A value greater than 0 indicates that the higher the current value, the greater the risk. Given a cutoff time t, the instantaneous risk of an event occurring at time t based on covariates and the longitudinal process individual i. The baseline risk function represents the survival risk when all covariates and longitudinal processes are equal to 0. Covariates that may affect survival risk (e.g., gender, etc.); covariates The corresponding coefficient vector represents the impact of these covariates on survival risk.

[0166] Step 1.3.2: Set the current slope;

[0167] Set time point Survival risk at the same point in time The current slope of the longitudinal measurement Correlation, the strength of the correlation is determined by parameters To measure:

[0168] (6);

[0169] in, For the set of associated parameter vectors; For individual i's potential longitudinal cognitive trajectory The instantaneous rate of change or slope at time point t; The slope correlation parameter is used to quantify the impact of the instantaneous rate of change of the longitudinal trajectory on survival risk. >0 indicates the slope of the upward trajectory; other values ​​are the same as above.

[0170] Step 1.3.3: Establish the relationship between the current value and the current slope (current value + current slope):

[0171] Set time point Survival risk at the same point in time Current value of longitudinal measurement With the current slope Correlation, the strength of the correlation is determined by parameters and To measure,

[0172] (7);

[0173] in: For the set of associated parameter vectors; Associate parameters with the current value; This is the slope-related parameter; others are the same as above.

[0174] Step 1.3.4: Calculate the cumulative effects area under the longitudinal trajectory.

[0175] Set time point Survival risks and deadlines The longitudinal measurement trajectory is correlated with the area, and the correlation strength is determined by the parameters. To measure:

[0176] (8);

[0177] in: For the set of associated parameter vectors; This is a parameter associated with the cumulative effect, used to quantify the strength of the cumulative effect of cognitive function on survival risk; The sum or cognitive reserve of all longitudinal cognitive measurements experienced by individual i from the start of the study (time 0) to the current time t; other parameters are the same as above.

[0178] Step 1.4: Establish a relationship model between the current value and the area under the longitudinal trajectory (current value + cumulative effects / area);

[0179] Set time point Survival risks and deadlines Current value of longitudinal measurement Related to the area under the trajectory, the correlation strength is determined by the parameters. and To measure:

[0180] (9);

[0181] The physical meaning of the parameters in this formula is the same as above.

[0182] A schematic diagram of the associated structure based on the current value, current slope, and area under the vertical trajectory is obtained. Figure 3 As shown.

[0183] Step 2: Construct a multivariate joint model based on the univariate joint model;

[0184] Step 2.1: Construct a multivariate longitudinal sub-model;

[0185] Assuming individual have A longitudinal cognitive assessment, For different longitudinal measurements of cognitive assessment, the longitudinal cognitive process is as follows:

[0186] (10);

[0187] in, The expected mean or potential true value of individual i's cognitive assessment at time t at the p-th time excludes random measurement error and reflects the "true" level of the individual's cognitive function. For individual i, the actual observed value of the p-th cognitive assessment at time t; Let i be the vector of fixed-effects covariates related to the p-th cognitive assessment at time t; For covariates The corresponding fixed effects coefficient vector; Let be the vector of random effects of individual i at time t related to the p-th cognitive assessment; This represents the random effect of individual i on the p-th cognitive dimension, used to capture the individual-specific portion of the individual's cognitive trajectory that deviates from the overall average trajectory; It is the inverse function of the connection function for the p-th cognitive assessment (also known as the mean function), which maps the value of the linear predictor to a reasonable mean.

[0188] Suppose a random effect with a multivariate normal distribution It can capture the correlation between multiple longitudinal cognitive assessments:

[0189] (11);

[0190] Using a multiple linear mixed-effects model for the same individual At different times Multiple longitudinal cognitive assessments Modeling:

[0191] (12);

[0192] in, For individuals exist Cognitive assessment of time Longitudinal measurement value For connection fixed effect With cognitive assessment The covariate matrix of longitudinal measurements, To connect random effects With cognitive assessment Design matrix of random factors for longitudinal measurements, residuals .

[0193] Step 2.2: Construct a multivariate survival sub-model;

[0194] A multi-state Markov model with proportional risk is used to fit the transition time. The transition intensity when MCI reverses to NC The transfer intensity of MCI to AD They are respectively:

[0195] (13);

[0196] Among them, multivariable functions For the first A longitudinal trajectory of cognitive assessment. Parameters and Quantitative First The deadline for each longitudinal cognitive assessment The association between potential longitudinal cognitive processes and bidirectional MCI regression. Similar to univariate joint models, different association structures can be used to fit the bidirectional MCI regression.

[0197] Step 3: Based on the multivariate joint model, construct a functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes;

[0198] Step 3.1: Construct the longitudinal sub-model of the functional multivariate joint module;

[0199] Using a multiple linear mixed-effects model for the same individual At different times Multiple longitudinal cognitive assessments Modeling is performed.

[0200] By incorporating baseline neuroimaging functional predictors based on the brain spatial continuum, the model is expanded to:

[0201] (14);

[0202] in, This is the random error term; As a functional predictor of baseline neuroimaging, It is a continuous variable defined on the domain S (space), that is, the brain region coordinates; It is a functional covariate of individual i (such as baseline brain imaging data), and it is a function of s; It is a set of basis functions (such as B-spline basis) used to approximate unknown coefficient functions; the integral of S represents the summation over the entire domain S, representing the functional predictor pair. The cumulative effect.

[0203] By incorporating longitudinal neuroimaging functional predictors based on the two-dimensional continuous domains of brain space and time, the model is expanded to:

[0204] (15);

[0205] in, It is a longitudinal neuroimaging predictor that can simultaneously take into account the two-dimensional continuous domain of time and brain structure.

[0206] Step 3.2: Construct a survival sub-model of the functional multivariate joint module;

[0207] A multi-state Markov model with proportional risk is used to fit the transition time.

[0208] By incorporating baseline neuroimaging functional predictors based on the brain spatial continuum, the model is expanded to:

[0209] (16);

[0210] By incorporating longitudinal neuroimaging functional predictors based on the two-dimensional continuous domains of brain space and time, the model is expanded to:

[0211] (17);

[0212] in, A functional predictor of baseline neuroimaging; Longitudinal neuroimaging predictors refer to the two-dimensional continuous domain of time and brain structure.

[0213] Step 4: Perform parameter estimation and statistical inference on the functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes established in Step 3;

[0214] Step 4.1: Perform Gibbs sampling;

[0215] Bayesian estimation integrates prior information through the prior distribution of parameters. It combines prior information about unknown parameters with sample information and infers unknown parameters by estimating the joint posterior distribution of the model based on the Bayesian formula.

[0216] Joint prior distributions can provide prior information for unknown parameters in a joint model.

[0217] individual The complete joint log-likelihood of the longitudinal survival data is as follows:

[0218] (18);

[0219] in, For the parameter set in the model, For survival function, This is prior information.

[0220] Obtaining the posterior distribution using Bayesian methods typically requires integrating a high-dimensional function, which limits the widespread implementation of Bayesian methods due to the difficulty of computational integration. Furthermore, the joint likelihood function of longitudinal and survival data integrates all information from both datasets, resulting in a complex structure that makes it difficult to obtain an analytical solution for the posterior probability.

[0221] Markov Chain Monte Carlo (MCMC) algorithms are often used to estimate the posterior distribution or the likelihood function of the parameter of interest. They directly draw samples from some complex distributions of the parameter of interest, and then use these samples to randomly generate the next sample, thus forming a Markov chain. That is, the transition probability between two samples is a function of the probability between the two most recent samples. This can solve the integration problem caused by high-dimensional features when estimating parameters of functional data.

[0222] Gibbs sampling is a case of MCMC (Multi-Dimensional Computational-Conditional) sampling, constructed using a full-conditional distribution. It is typically used when the target distribution is multi-dimensional, effectively addressing issues such as high computational cost, slow convergence speed, and long runtime associated with high dimensionality. Assume the distribution of the parameters of interest is... , Each element It can be a scalar, vector, or matrix. The specific method for Gibbs sampling is as follows:

[0223] Step 1: Set the initial values ​​of the parameters ;

[0224] (19);

[0225] Step 2: Update the obtained new value ;

[0226] (5-20);

[0227] Step 3: Repeat step 2 until convergence. After several iterations, the Gibbs sample chain is obtained.

[0228] (twenty one);

[0229] Finally, the mean and variance of the parameters can be directly estimated using the MCMC method through the sample chain;

[0230] (twenty two);

[0231] in, For parameters The posterior mean estimate, when the sample size is large enough, the sample mean converges to the true posterior expectation; For parameters The posterior variance estimate is used to measure the uncertainty of the parameter estimate; , where is the total number of Gibbs sampling iterations, i.e., the total length of the sample chain generated in Formula 21; ∑ is the summation symbol, indicating that all sample values ​​from the first iteration (d=1) to the Dth iteration (d=D) are summed; For parameters The sample value generated in the d-th iteration is that, given the current values ​​of other parameters, it is sampled from the fully conditional distribution of that parameter.

[0232] This embodiment proposes to use the Gibbs sampling-based MCMC algorithm to perform 6500 iterations on three different chains; statistical inference is performed using individual random effects samples generated by the full posterior distribution to obtain posterior mean estimates (regression coefficients and HR) and 95% CI, and then these samples are used to make individualized predictions of the longitudinal trajectory of cognitive assessment and the bidirectional outcome of MCI.

[0233] Step 4.2: Perform model convergence diagnosis on the functional multivariate joint model;

[0234] Before a given MCMC analysis reaches its stationary distribution, the empirical results of the generated Markov chains may be unreliable. Therefore, monitoring the convergence of the algorithm is essential for producing results from the posterior distribution of interest to determine whether the algorithm has reached its stable target distribution. Time series plots and posterior density plots are the most commonly used convergence evaluation methods. Summary statistics include the posterior mean and 95% CI of the parameters of interest, and finally, the significance of each independent variable is assessed by statistically testing the regression coefficients (posterior mean) against the 95% CI.

[0235] Step 5: Evaluate the goodness of fit of the functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes established in Step 3 based on the parameter estimation and statistical inference results of Step 4.

[0236] Step 5.1: Set the evaluation metrics for the survival sub-model;

[0237] Step 5.1.1: Consistency Index;

[0238] The concordance index (C-index) is used to evaluate the discriminatory power between the predicted and actual values ​​of a survival sub-model, ranging from 0.5 to 1. A C-index of 0.5 indicates that the predicted and actual values ​​are completely inconsistent, meaning the survival sub-model has extremely low discriminatory power; a C-index of 1 indicates that the predicted and actual values ​​are completely consistent, meaning the survival sub-model has extremely high discriminatory power. A C-index between 0.5 and 0.7 represents low discriminatory power; a C-index between 0.71 and 0.9 represents moderate discriminatory power; and a C-index above 0.9 represents high discriminatory power.

[0239] Step 5.1.2: Global check;

[0240] The global significance of the survival sub-model was evaluated using the likelihood ratio test, Wald test, and score test, and the p-values ​​of the three tests for the overall significance of the survival sub-model were output.

[0241] Step 5.2: Define the evaluation metrics for the joint model;

[0242] Step 5.2.1: Deviation Information Criterion (DIC);

[0243] DIC is the sum of penalty terms based on bias metric and model complexity, representing a comprehensive measure of both goodness of fit and complexity of the model.

[0244] (twenty three);

[0245] in, The bias function measures the goodness of fit of the model. The number of valid parameters measures the complexity of the model. and They are respectively and The posterior mean of the model. The smaller the DIC value, the better the model fit.

[0246] Step 5.2.2: WAIC (Widely Applicable Information Criterion): Improvements to DIC:

[0247] (twenty four);

[0248] in, , , This represents the sample variance. The smaller the WAIC value, the better the model fit.

[0249] Step 5.2.3: Logarithm of the pseudo marginal likelihood (LPML):

[0250] (25);

[0251] in, This is the conditional predictive ordinate. A higher LPML value indicates a better model fit.

[0252] Step 6: Perform individualized dynamic prediction based on a functional multivariate joint model;

[0253] Based on individual longitudinal cognitive assessment and neuroimaging, the risk and longitudinal cognitive trajectory of bidirectional MCI outcome are dynamically updated to provide an individual's instantaneous risk assessment.

[0254] Step 6.1: Predict the conditional survival probability of MCI bidirectional reversion;

[0255] Assuming a new individual At the point of time No endpoint event occurred, i.e., no bidirectional MCI outcome occurred, and multiple longitudinal cognitive assessments are known. Predict its timing The conditional survival probability of bidirectional reversal:

[0256]

[0257] (26);

[0258] in, Given the longitudinal cognitive measurement data of a new individual new before time t, and assuming that no event has occurred at time t, the probability that the individual survives (i.e. no event has occurred) until a future time u. The actual survival time of an individual's "new" state, that is, the actual point in time when cognitive regression occurs, is a potential variable that cannot be directly observed. The complete longitudinal cognitive assessment measurement history of the new individual up to time t; The sample used to fit the joint model contains complete longitudinal and survival data of n subjects; It is the complete set of parameters for the joint model, including all model parameters that need to be estimated, such as the fixed effects coefficients, the variance and covariance matrix parameters of the random effects, and the baseline risk parameters of the survival model. Model parameters The posterior distribution is used to reflect the observed training data. Then, the probability distribution of the model parameters taking various possible values.

[0259] The first part of the integrand takes the following form:

[0260]

[0261] (27);

[0262]

[0263] (28);

[0264] in, Let be the posterior distribution of the random effect parameters.

[0265] Individual random effects are used to capture unique patterns in which an individual's cognitive trajectory deviates from the overall average trajectory. For the cutoff time t, based on individual random effects and model parameters The constructed individualized longitudinal process history is used to represent the true history of an individual's cognitive trajectory given individual specificity and model parameters; To provide a given model parameter Given that no event has occurred for the individual by time t and that the individual has a longitudinal measurement history, the random effects of the event are as follows: The posterior distribution of; In order to provide a history of individualized longitudinal processes Under these conditions, the individual's actual survival time Exceeding time The probability of; Let be the risk function of an individual, that is, the probability that an event will occur at a given moment in time s, given its historical information.

[0266] The following simulation scheme was used to obtain the conditional survival probability. Monte Carlo estimation:

[0267] The first step is to calculate the empirical Bayesian estimate. ;

[0268] The second step, from Extract ;

[0269] (29);

[0270] The third step, from Extract ;

[0271] (30);

[0272] Step 4, Calculation ;

[0273] (31);

[0274] Repeat the above steps Next, among them The number of Monte Carlo samples.

[0275] Step 6.2: Perform longitudinal trajectory prediction;

[0276] Known longitudinal measurement trajectory of a new individual Predict its timing longitudinal measurement value ,in , Samples for fitting the joint model.

[0277] Adopting a similar Method estimation ,

[0278]

[0279] (32);

[0280] The first part of the integrand takes the following form:

[0281]

[0282] (33);

[0283] Similar Monte Carlo estimation,

[0284] The first step, from Extract ;

[0285] (34);

[0286] The second step, from Extract ;

[0287] (35);

[0288] The third step is to calculate.

[0289] (36);

[0290] Repeat the above steps, Next, among them The number of Monte Carlo samples.

[0291] Then calculate 95% CI.

[0292] (37).

[0293] Example 2:

[0294] Unlike Embodiment 1 described above, a functional joint model based on multiple longitudinal cognitions and multiple state outcomes is established based on the method described in Embodiment 1. In this functional joint model, longitudinal survival data is processed by combining functional data analysis with the joint model. Its model framework is as follows: Figure 2 As shown. In Figure 2 middle:

[0295] The longitudinal sub-model employs a linear mixture model to model longitudinal multi-cognition, including fixed and random effects such as age, gender, years of education, marital status, APOEε4 carrier status, and functional neuroimaging.

[0296] The survival sub-model uses a multi-state model with proportional hazards to explain the bidirectional outcome of MCI. It incorporates predictive factors such as age, gender, years of education, marital status, APOEε4 carrier status, and functional neuroimaging, and considers five different association structures: current value, current slope, area under the longitudinal trajectory, current value and current slope, and current value and area under the longitudinal trajectory.

[0297] Its specific model structure is as follows: Let and These are two possible outcomes for the individual. and The data types are longitudinal measurements or survival outcomes, constructed based on random effects models. joint density :

[0298] (1);

[0299] in, As a random effect, used to explain and The relationship between them.

[0300] Example 3:

[0301] Unlike the above embodiments, in order to verify the effectiveness of the joint model-based MCI cognitive trajectory and bidirectional outcome dynamic prediction method described in Embodiment 1, in this embodiment:

[0302] Step 7: Validate the process through individualized dynamic prediction of MCI cognitive trajectory and bidirectional regress.

[0303] For example, a 69-year-old female with 8 years of education and a baseline diagnosis of MCI was identified. She was married and carried one APOE ε4 allele. Her longitudinal cognitive assessments during the 12-year follow-up period from baseline are shown in Table 1. Her cognitive status remained stable during the 12 years, with no reversal from MCI to NC or progression to AD.

[0304] Table 1: Longitudinal cognitive assessment of an individual during a 12-year follow-up period from baseline.

[0305] Cognitive assessment Baseline 0.5 years 1 year 1.5 years 4 years 5 years ADAS11 11 13 8 9 12 7 ADAS13 17 21 12 14 18 16 ADASQ4 6 7 4 5 5 8 FAQ 0 0 0 0 0 6 RAVLT_immediate 29 33 31 38 34 13 RAVLT_learning 3 3 4 1 5 5 RAVLT_forgetting 6 4 5 4 3 3 RAVLT_perc_forgetting 86 57 63 50 33 108 TRABSCOR 171 97 152 129 250 65 mPACCdigit -8 -6 -6 -6 -7 -14 mPACCtrailsB -10 -5 -6 -6 -9 -10 Cognitive assessment 6 years 8 years 10 years 11 years 12 years ADAS11 12 10 9 9 9 ADAS13 19 17 13 19 18 ADASQ4 6 6 3 5 7 FAQ 1 5 5 6 7 RAVLT_immediate 29 36 30 31 37 RAVLT_learning 6 4 6 1 3 RAVLT_forgetting 8 7 4 6 4 RAVLT_perc_forgetting 100 88 50 100 50 TRABSCOR 300 278 256 217 74 mPACCdigit -11 -14 -6 -5 -8 mPACCtrailsB -12 -14 -7 -6 -6

[0306] Based on a multi-state outcome joint model of multiple longitudinal cognitive assessments, different scenarios are set up where the individual's longitudinal cognitive assessments and survival information are known over 5, 6, 8, 10 and 12 years from baseline. Individualized dynamic predictions of the individual's cognitive trajectory and bidirectional outcome over the next 10, 9, 7, 5 and 3 years are made respectively.

[0307] Step 7.1: Individualized dynamic prediction of MCI cognitive trajectory;

[0308] Step 7.1.1: Individualized dynamic prediction of ADAS11;

[0309] The individualized dynamic prediction of ADAS11 for this individual can be found in [link to relevant documentation]. Figure 4 The ADAS11 prediction score has remained around 10 over time. The confidence interval gradually narrows as the known information period increases.

[0310] Step 7.1.2: Individualized dynamic prediction of ADAS13;

[0311] The individualized dynamic prediction of ADAS13 for this individual can be found in [link to relevant documentation]. Figure 5 The ADAS13 prediction score has remained around 20 over time. The confidence interval gradually narrows as the known information period increases.

[0312] Step 7.1.3: Individualized dynamic prediction for ADASQ4;

[0313] The individualized dynamic prediction of ADASQ4 for this individual can be found in [link to relevant documentation]. Figure 6 In the three scenarios where longitudinal cognitive assessment and survival information from baseline is known for 5, 6, and 8 years, the ADASQ4 predictive value shows an upward trend over time; in the scenario where longitudinal cognitive assessment and survival information from baseline is known for 10 years, the ADASQ4 predictive value shows a downward trend over time; and in the scenario where longitudinal cognitive assessment and survival information from baseline is known for 12 years, the ADASQ4 predictive value shows a stable trend over time. Furthermore, the confidence interval for the ADASQ4 predictive value gradually narrows as the known information period increases.

[0314] Step 7.1.4: Individualized dynamic prediction of FAQs;

[0315] Individualized dynamic prediction of the FAQ for this individual can be found in [link to individual FAQ]. Figure 7 The FAQ has shown an increasing trend year by year over time. As the number of known longitudinal assessment values ​​increases, the confidence interval for the predicted FAQ values ​​gradually narrows.

[0316] Step 7.1.5: Individualized dynamic prediction of RAVLT_immediate;

[0317] The individualized dynamic prediction of RAVLT_immediate for this individual is shown in [link to individual dynamic prediction]. Figure 8 In the three scenarios where longitudinal cognitive assessment and survival information from baseline is known for 5, 6, and 8 years, the RAVLT_immediate predictive value shows a decreasing trend over time; in the scenarios where longitudinal cognitive assessment and survival information from baseline is known for 10 and 12 years, the RAVLT_immediate predictive value shows a stable trend over time. Furthermore, the confidence interval for the RAVLT_immediate predictive value gradually narrows as the known information period increases.

[0318] Step 7.1.6: Individualized dynamic prediction of RAVLT_learning;

[0319] The individualized dynamic prediction of RAVLT_learning for this individual is shown in [link to data]. Figure 9In scenarios where longitudinal cognitive assessment and survival information over 5 years from baseline is known, the RAVLT_learning predictive value shows a decreasing trend over time. In four scenarios where longitudinal cognitive assessment and survival information over 6, 8, 10, and 12 years from baseline is known, the RAVLT_learning predictive value shows a gradual increasing trend over time. Furthermore, the confidence interval of the RAVLT_learning predictive value gradually narrows as the known information period increases.

[0320] Step 7.1.7: Individualized dynamic prediction of RAVLT_forgetting;

[0321] The individualized dynamic prediction of RAVLT_forgetting for this individual is shown in [link to individual dynamic prediction]. Figure 10 In five scenarios where longitudinal cognitive assessment and survival information was known over 5, 6, 8, 10, and 12 years from baseline, the RAVLT_forgetting predictor values ​​showed a stable trend over time. Furthermore, the confidence interval for the RAVLT_forgetting predictor values ​​gradually narrowed as the known information duration increased.

[0322] Step 7.1.8: Individualized dynamic prediction of RAVLT_perc_forgetting;

[0323] The individualized dynamic prediction of RAVLT_perc_forgetting for this individual is shown in [link to individual dynamic prediction]. Figure 11 In five scenarios where longitudinal cognitive assessment and survival information were known over 5, 6, 8, 10, and 12 years from baseline, the predicted value of RAVLT_perc_forgetting showed a stable trend over time.

[0324] Step 7.1.9: Individualized dynamic predictions by TRABSCOR;

[0325] The individualized dynamic prediction of the TRABSCOR for this individual is shown in [link to TRABSCOR prediction]. Figure 12 In five scenarios where longitudinal cognitive assessment and survival information was available for 5, 6, 8, 10, and 12 years from baseline, the TRABSCOR predictive values ​​showed an increasing trend over time. Furthermore, the confidence interval for the TRABSCOR predictive values ​​gradually narrowed as the number of years of available information increased.

[0326] Step 7.1.10: Individualized dynamic prediction of mPACCdigit;

[0327] The individualized dynamic prediction of this individual mPACCdigit is shown below. Figure 13In four scenarios where longitudinal cognitive assessment and survival information from baseline is known for 5, 6, 8, and 10 years, the mPACCdigit predictive value shows a decreasing trend over time. In the scenario where longitudinal cognitive assessment and survival information from baseline is known for 12 years, the mPACCdigit predictive value shows a stable trend over time. Furthermore, the confidence interval for the mPACCdigit predictive value gradually narrows as the known information period increases.

[0328] Step 7.1.11: Individualized dynamic prediction of mPACCtrailsB;

[0329] The individualized dynamic prediction of this individual mPACCtrailsB is shown in [link to documentation]. Figure 14 In four scenarios where longitudinal cognitive assessment and survival information from baseline is known for 5, 6, 8, and 10 years, the mPACCtrailsB predictive value shows a decreasing trend over time. In the scenario where longitudinal cognitive assessment and survival information from baseline is known for 12 years, the mPACCtrailsB predictive value shows a stable trend over time. Furthermore, the confidence interval for the mPACCtrailsB predictive value gradually narrows as the known information period increases.

[0330] Step 7.2: Individualized dynamic prediction of MCI bidirectional reversion;

[0331] Given longitudinal cognitive assessment and survival information over 5 years from baseline, the probabilities of reversing to non-cognitive impairment (NC) and progressing to acute dementia (AD) in year 6 are 0.01% and 0.76%, respectively; in year 8, the probabilities are 0.03% and 2.47%, respectively; in year 10, the probabilities are 0.15% and 5.29%, respectively; in year 12, the probabilities are 0.52% and 10.76%, respectively; and in year 15, the probabilities are 0.98% and 29.25%, respectively. Individualized dynamic predictions are available in [link to individualized dynamic predictions]. Figure 15 .

[0332] Given longitudinal cognitive assessment and survival information over 6 years from baseline, the probabilities of reversing to non-cognitive impairment (NC) and progressing to acute dementia (AD) in year 8 are 0.02% and 1.76%, respectively; in year 10, the probabilities are 0.05% and 4.53%, respectively; in year 12, the probabilities are 0.12% and 9.87%, respectively; and in year 15, the probabilities are 0.47% and 28.14%, respectively. Individualized dynamic predictions can be found in [link to individualized dynamic predictions]. Figure 16 .

[0333] Given longitudinal cognitive assessment and survival information over 8 years from baseline, the probability of reversing to non-cognitive impairment (NC) at years 10, 12, and 15 is less than 0.01%; the probabilities of progression to acute dementia (AD) at years 10, 12, and 15 are 2.60%, 7.40%, and 23.90%, respectively. See individualized dynamic prediction. Figure 17 .

[0334] It is known that the probability of longitudinal cognitive assessment and survival information reversing to non-competent state (NC) in years 12 and 15 from baseline is less than 0.01%; the probability of progression to acute dementia (AD) in years 12 and 15 is 3.04% and 12.51%, respectively. See individualized dynamic prediction. Figure 18 .

[0335] Given longitudinal cognitive assessment and survival information over 12 years from baseline, the probability of reversing to non-cognitive impairment (NC) in year 15 is less than 0.01%, and the probability of progression to acute dementia (AD) is 6.74%. See individualized dynamic prediction. Figure 19 .

[0336] The results above demonstrate the significant effectiveness of the joint model-based dynamic prediction method for MCI cognitive trajectory and bidirectional outcome described in Embodiment 1 of this invention. By performing individualized dynamic predictions of the cognitive trajectory and bidirectional outcome of a specific MCI individual under different known longitudinal cognitive assessment years and survival information scenarios, it was found that the predicted values ​​of various cognitive indicators (such as ADAS11, ADAS13, etc.) showed a reasonable trend over time, and the confidence interval gradually narrowed with the increase of known information years, thus improving prediction accuracy. Furthermore, in the bidirectional outcome prediction, the changes in the probability of an individual reversing from MCI to NC or progressing to AD over time were clearly presented. These results indicate that this method can accurately and meticulously characterize the cognitive trajectory and bidirectional outcome dynamics of MCI individuals, providing strong evidence for clinical decision-making and individualized intervention, and possessing high application value.

[0337] The above-described embodiments are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A dynamic prediction method for MCI cognitive trajectory and bidirectional outcome based on a joint model, characterized in that, include: Step 1: Construct a univariate joint model; Step 2: Construct a multivariate joint model based on the univariate joint model; Step 3: Based on the multivariate joint model, construct a functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes; Step 4: Perform parameter estimation and statistical inference on the functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes established in Step 3; Step 5: Evaluate the goodness of fit of the functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes established in Step 3 based on the parameter estimation and statistical inference results of Step 4. Step 6: Perform individualized dynamic prediction based on a functional multivariate joint model; Based on individual longitudinal cognitive assessment and neuroimaging, the risk and longitudinal cognitive trajectory of bidirectional MCI outcome are dynamically updated to provide an individual's instantaneous risk assessment.

2. The method for dynamic prediction of MCI cognitive trajectory and bidirectional outcome based on a joint model as described in claim 1, characterized in that, The construction process of the univariate joint model described in step 1 includes: Step 1.1: Construct the vertical sub-model; ； in, For individuals exist Cognitive assessment value at any given moment; For fixed effects dimensional vector; For random effects dimensional vector; For connection With fixed factors for longitudinal measurements 3D design matrix; For connection With longitudinal measurement of random factors 3D design matrix; residual This includes measurement error and sequence correlation. For individuals of 3D positive definite variance-covariance matrix express 3D identity matrix ; Step 1.2: Construct the survival sub-model; The survival process was fitted using a multi-state Markov model, and the results were obtained. The transition intensity when MCI reverses to NC The transfer intensity of MCI to AD They are respectively: ； in, and As the benchmark risk function, and As covariates, and These are the corresponding regression coefficients; and This is a parameter vector used to quantize the cutoff time. The association between potential longitudinal cognitive processes and bidirectional MCI outcomes; Step 1.3: Establish the relationship structure between the longitudinal sub-model and the survival sub-model; Step 1.4: Calculate the area under the longitudinal trajectory; Set time point Survival risks and deadlines The longitudinal measurement trajectory is correlated with the area, and the correlation strength is determined by the parameters. To measure, we get: ； in, The trajectory of individual i's cognitive function over time; Let be the set of all longitudinal measurements of cognitive function for individual i up to time t. And its potential true trajectory, i.e. All the information contained therein; For individual i, the random effect; For the set of associated parameter vectors; for A specific component; Given a cutoff time t, the instantaneous risk of an event occurring at time t based on covariates and the longitudinal process individual i. Used as the benchmark risk function; These are covariates that may affect survival risk; covariates The corresponding coefficient vector; Step 1.5: Establish a model relating the current value to the area under the vertical trajectory; Set time point Survival risks and deadlines Current value of longitudinal measurement Related to the area under the trajectory, the correlation strength is determined by the parameters. and To measure: 。 3. The method for dynamic prediction of MCI cognitive trajectory and bidirectional outcome based on a joint model as described in claim 2, characterized in that, Step 1.3 describes the process of establishing the association structure between the longitudinal sub-model and the survival sub-model, which includes: Step 1.3.1: Set the current value; Set time point Survival risk at the same point in time Current value of longitudinal measurement Correlation, the strength of the correlation is determined by parameters To measure: ； in, The trajectory of individual i's cognitive function over time; Let be the set of all longitudinal measurements of cognitive function for individual i up to time t. And its potential true trajectory; For individual i, the random effect; For the set of associated parameter vectors; for A specific component; Given a cutoff time t, the instantaneous risk of an event occurring at time t based on covariates and the longitudinal process individual i. The baseline risk function represents the survival risk when all covariates and longitudinal processes are equal to 0. These are covariates that may affect survival risk; covariates The corresponding coefficient vector; Step 1.3.2: Set the current slope; Set time point Survival risk at the same point in time The current slope of the longitudinal measurement Correlation, the strength of the correlation is determined by parameters To measure: ； in, For the set of associated parameter vectors; For individual i's potential longitudinal cognitive trajectory The instantaneous rate of change or slope at time point t; This is a slope-related parameter; Step 1.3.3: Establish the relationship between the current value and the current slope; Set time point Survival risk at the same point in time Current value of longitudinal measurement With the current slope Correlation, the strength of the correlation is determined by parameters and To measure: 。 4. The method for dynamic prediction of MCI cognitive trajectory and bidirectional outcome based on a joint model as described in claim 1, characterized in that, Step 2 describes the process of constructing the multivariate joint model, which includes: Step 2.1: Construct a multivariate longitudinal sub-model; Let individuals have A longitudinal cognitive assessment, For different longitudinal measurements of cognitive assessment, the longitudinal cognitive process is as follows: ； in, The expected mean or potential true value of individual i's cognitive assessment at time t at the p-th time excludes random measurement error; For individual i, the actual observed value of the p-th cognitive assessment at time t; Let i be the vector of fixed-effects covariates related to the p-th cognitive assessment at time t; For covariates The corresponding fixed effects coefficient vector; Let be the vector of random effects of individual i at time t related to the p-th cognitive assessment; For individual i, the random effect on the p-th cognitive dimension; It is the inverse function of the connection function of the p-th cognitive assessment; Suppose a random effect with a multivariate normal distribution It can capture the correlation between multiple longitudinal cognitive assessments: ； Using a multiple linear mixed-effects model for the same individual At different times Multiple longitudinal cognitive assessments Modeling: ； in, For individuals exist Cognitive assessment at any moment Longitudinal measurement value For connection fixed effect With cognitive assessment The covariate matrix of longitudinal measurements, To connect random effects With cognitive assessment Design matrix of random factors for longitudinal measurements, residuals ; Step 2.2: Construct a multivariate survival sub-model; A Markov model was used to fit the transition time. The transition intensity when MCI reverses to NC The transfer intensity of MCI to AD They are respectively: ； Among them, multivariable functions For the first The longitudinal trajectory of cognitive assessment; and For parameters.

5. The method for dynamic prediction of MCI cognitive trajectory and bidirectional outcome based on a joint model as described in claim 1, characterized in that, Step 3 describes the process of establishing a functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes, which includes: Step 3.1: Construct the longitudinal sub-model of the functional multivariate joint module; Using a multiple linear mixed-effects model for the same individual At different times Multiple longitudinal cognitive assessments Modeling was performed; baseline neuroimaging functional predictors based on the brain spatial continuum were incorporated, and the model was expanded to: ； in, This is the random error term; As a functional predictor of baseline neuroimaging, It is a continuous variable; It is a functional covariate of individual i; It is a set of basis functions used to approximate unknown coefficient functions; the integral of S is expressed as a summation over the entire field S; By incorporating longitudinal neuroimaging functional predictors based on the two-dimensional continuous domains of brain space and time, the model is expanded to: ； in, A functional predictor of baseline neuroimaging; As a predictor of longitudinal neuroimaging; Step 3.2: Construct a survival sub-model of the functional multivariate joint module; By incorporating baseline neuroimaging functional predictors based on the brain spatial continuum, the model is expanded to: ； By incorporating longitudinal neuroimaging functional predictors based on the two-dimensional continuous domains of brain space and time, the model is expanded to: （17）； in, A functional predictor of baseline neuroimaging; It is a longitudinal neuroimaging predictor for a two-dimensional continuous domain of time and brain structure.

6. The method for dynamic prediction of MCI cognitive trajectory and bidirectional outcome based on a joint model as described in claim 1, characterized in that, Step 4 describes the parameter estimation and statistical inference process for the functional multivariate joint model based on multiple longitudinal cognitions and multiple state outcomes, which includes: Step 4.1: Perform Gibbs sampling; Let the distribution of the parameters of interest be... , Each element It is a scalar, vector, or matrix, and is sampled using the Gibbs sampling method; Step 4.2: Perform model convergence diagnosis for the functional multivariate joint model.

7. The method for dynamic prediction of MCI cognitive trajectory and bidirectional outcome based on a joint model as described in claim 1, characterized in that, Step 5 describes the process of evaluating the fit of the functional multivariate joint model, which includes: Step 5.1: Set the evaluation metrics for the survival sub-model; The evaluation indicators include a consistency index and a global test. Step 5.2: Set the evaluation index for the joint model.

8. The method for dynamic prediction of MCI cognitive trajectory and bidirectional outcome based on a joint model as described in claim 7, characterized in that, The process of establishing the evaluation index for the joint model includes: Step 5.2.1: Deviation Information Criteria; DIC is the sum of penalty terms based on the number of effective parameters, which is a measure of both the goodness of fit and the complexity of the model. ； in, It is a deviation function; , where is the number of valid parameters; and They are respectively and The posterior mean; Step 5.2.2: Modify DIC and establish WAIC criteria: ； in, , , This represents the sample variance. Step 5.2.3: Log-pseudo-marginal likelihood: ； in, The conditional prediction order / ordinate.

9. The method for dynamic prediction of MCI cognitive trajectory and bidirectional outcome based on a joint model as described in claim 1, characterized in that, Step 6 describes the process of individualized dynamic prediction based on a functional multivariate joint model, which includes: Step 6.1: Predict the conditional survival probability of MCI bidirectional reversion; Set up a new individual At the point of time No endpoint event occurred, i.e., no bidirectional MCI outcome occurred, and multiple longitudinal cognitive assessments are known. Predict its timing The conditional survival probability of the bidirectional reversal is: ； Step 6.2: Perform longitudinal trajectory prediction.

10. The method for dynamic prediction of MCI cognitive trajectory and bidirectional outcome based on a joint model as described in claim 9, characterized in that, Step 6.2 describes the longitudinal trajectory prediction process, which includes: Known longitudinal measurement trajectory of a new individual Predict its timing Longitudinal measurement values: ; in, , Samples for fitting the joint model.

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