Prognostic Model Of Mild Cognitive Impairment Based On Functional Joint Model

Background:With the rapid development of aging society,the number of Alzheimer’s Disease(AD)increases year by year,which brings a heavy burden to society and family.AD is an irreversible disease.In the absence of effective treatment,the focus of prevention and treatment of AD has gradually shifted to its early stage--mild cognitive impairment(MCI).MCI is an important transitional stage of AD dementia,and patients with MCI are at high risk of AD.Accurate prediction of the risk and time of MCI progression to AD,and timely individualized prevention and treatment for high-risk MCI patients are very important to reduce the incidence of dementia or delay the onset of dementia.Longitudinal measurements of influencing factors and the time when MCI progressed to AD were obtained from epidemiological follow-up studies,resulting in longitudinal and survival data.Modeling patients’ survival events with longitudinal measurement data has been a hot topic in statistics research.At present,there are two main methods for correlation modeling of longitudinal data and survival data: proportional risk model with time-dependent covariates and joint model based on linear mixed model and survival analysis model.However,the complex characteristics of longitudinal survival data limit the application of these methods to a certain extent.It is still a challenge facing statistics to more effectively model the correlation between complex longitudinal data and survival data and to scientifically evaluate the effects of longitudinal measurement factors on survival events.A new data analysis model is urgently needed to make up for the shortcomings of traditional methods.To better utilize longitudinal survival data in the field of Alzheimer’s disease research to establish a prognostic model of MCI.Objectives:The purpose of this study is to explore a new statistical analysis model of longitudinal survival data based on functional association model,to realize the correlation modeling of complex longitudinal data and survival data,so as to more effectively use longitudinal factors to predict the occurrence of survival events,and to establish a prognosis model of MCI with real follow-up data of Alzheimer’s disease.In order to provide evidence support for clinical decision-making,improve the level of prevention and treatment of patients.Methods:1.On the basis of describing the principle of functional principal component analysis(PACE)method based on conditional expectation,R 4.1.1 software was used to simulate and generate longitudinal data sets of three sparse situations with sample size of 200,and the dimensionality reduction and prediction effect of PACE method were quantitatively evaluated through numerical simulation.2.Construct the functional joint model based on Lasso penalty and SCAD penalty for parameter estimation and variable screening methods,optimize the analysis strategy of the functional joint model.R 4.1.1 software was used to generate two sparse longitudinal survival data sets with different sample sizes.Three modeling methods were set for each case for comparative study.In model 1,multiple functional principal component analysis method based on conditional expectation was directly combined with Cox model without penalty mechanism.Model 2 is a functional association model based on Lasso punishment.Model 3 is a functional association model based on SCAD punishment.Through numerical simulation,the area AUC value under ROC curve,95% confidence interval,AIC value and consistency index were used to quantitatively evaluate the ability of the functional joint model to deal with sparse,irregular and nonlinear longitudinal survival data and the model prediction effect.3.Using the real follow-up data from the Alzheimer’s Disease Collaborating Center in the United States,PACE method was used to process the longitudinal measurement variables: MMSE score of the simple mental state examination scale and the test time of the connected test scale MTT-B,and multivariate functional principal component score was obtained according to the cumulative variance contribution rate FVE.Then these principal component scores and fixed covariates were incorporated into the Cox model to realize the joint modeling of longitudinal data and survival model.Finally,the combined likelihood estimation was carried out by Lasso punishment and SCAD punishment,so as to construct the prognosis model of Alzheimer’s disease progression from MCI to AD,and the fitting effect of the model prediction was evaluated.In this study,R4.1.1 statistical software was used for data analysis.Results:1.Through R software simulation,three longitudinal data sets of different sparse situations with sample size of 200 are generated.On the premise of retaining most of the information of the original data,according to the cumulative variance contribution rate of85%,the number of principal components selected for the longitudinal data sets of three different sparse situations is respectively 4,4 and 3.The prediction results of PACE method have small mean square error(MSE)under different sparse conditions,and the more the number of observation points,the better the prediction effect.2.The results of functional joint model simulation showed that the data loss rate was25%,and the longitudinal survival data sets with sample sizes of 100 and 200 were processed by PACE method respectively.FVE of the former was 93.65%,and FVE of the latter was 95.54%.The final number of principal components selected in the two data sets is 4 and 5 respectively.When the sample size was 100,the AUC values and 95%CI of Model 1,Model 2 and Model 3 were 0.73(0.63-0.83),0.78(0.71-0.88),0.83(0.75-0.90),and AIC values were 398.49,377.94 and 370.86,respectively.The consistency indexes were 0.77,0.79 and 0.84,respectively.When the sample size was 200,the AUC values and 95%CI values of the three models were 0.74(0.64～0.85),0.82(0.75～0.90),0.84(0.77-0.92),and AIC values were 381.27,370.67,327.81,respectively.The consistency indexes were 0.79,0.83 and 0.88,respectively.With the increase of sample size,the prediction effect of functional combination model was better.3.The empirical study results showed that MMSE score and TPT-B test time were selected as longitudinal measurement factors,multivariate functional principal component analysis method based on conditional expectation was used to establish a joint model,and the first four multivariate functional principal component scores were selected according to the cumulative variance contribution rate,and the prognosis model of mild cognitive impairment was constructed by combining with other fixed covariables.The independent prognostic factors screened by the functional combination model based on Lasso punishment were: Marital status,gender,anxiety,age,family history of dementia,APOE e4,MFPC1,MFPC2,MFPC3,MFPC4,the model predicted the progression of MCI patients according to the ROC curve area under the first,third and five-year curves were0.847,0.813,0.798,respectively.The AIC value was 7992.27 and the consistency index was 0.85.Independent prognostic factors of functional combined mode screening based on SCAD punishment are: Marital status,impulsiveness,listlessness,age,APOE e4,MFPC1,MFPC2,MFPC3,MFPC4,the model predicted the progression of MCI patients according to the ROC curve area under the first,third and five-year curves were 0.872,0.845,0.802,respectively.The AIC value was 7977.67 and the consistency index was 0.88.The prediction effect of the two models is better than that of the functional joint model based on SCAD punishment.Conclusions:1.The functional principal component analysis method based on conditional expectation takes full account of the complex characteristics of longitudinal survival data,such as sparsity,irregularity and nonlinearity.It can effectively calculate FPC score and fit individual trajectory,reduce the random trajectory of longitudinal measurement data,and better capture the main mode characteristics of longitudinal data.The estimation of sparse function data is more accurate,and the accuracy improves with the increase of data density.2.By building a functional association model,this study realized the correlation analysis of longitudinal data with complex characteristics and survival data,so as to make more effective use of longitudinal factors to predict the occurrence of survival events.In the joint model parameter estimation,the penalty likelihood can screen the influencing factors more effectively,make the model more concise and achieve better prediction results.3.The prognosis model of mild cognitive dysfunction constructed in this study can accurately predict the risk and time of progression to AD in MCI patients,and can update the prediction results in real time.The prognostic factors screened by the model can be used to dynamically predict individuals with MCI,judge the risk of individuals with MCI,and conduct personalized intervention and treatment for them,which will help clinicians to identify high-risk groups of AD and implement early intervention measures.InnovationThe functional association model proposed in this study solves the problem of the lack of proper statistical methods for longitudinal survival data with complex characteristics to a certain extent,and makes up for the shortcomings of the traditional association model,which has important scientific significance.At the same time,the prognostic model of MCI patients established in this study can accurately predict the risk and time of MCI progression to AD,which has important practical value for improving the prevention and treatment level of MCI patients and preparing for family care.