Dynamic Hidden Markov Structural Equation Model:Application To Alzheimer’s Disease Progression

Nowadays,the incidence of Alzheimer’s disease is gradually increasing which seriously affects the health of the elderly and brings challenges to the society.The traditional diagnosis of Alzheimer’s disease is based on a combination of measurement scales and MRI and FMRI data.The brain image data of Alzheimer’s disease changes with age,and there is currently no satisfactory diagnostic techniques to track the progress of Alzheimer’s disease.Our research mainly focus on tracing changes in Alzheimer’s disease through human brain image data modeling and analytics which shed lights on disease diagnosis techniques.In this dissertation,the dynamic Hidden Markov Structural Equation model is mainly used to analyze the periodical brain MRI image data of Alzheimer’s disease patients.First,in the measurement equation part,we used a dynamic factor model to explore the relationship between manifest variables(gray matter data in different brain regions)and latent variables(brain networks: default network(DMN),FPN network,salience network(SN)).Secondly,in the Structural Equations part,we explored the the connections between the various networks of the brain.In our model construction,we set each clinical examination time t for each person,and a hidden Markov model is constructed based on the hidden state variables of normal person stage,early mild cognitive impairment,late mild cognitive impairment,and Alzheimer’s disease which gradually explored the process of Alzheimer’s disease.Then we set a state transition probability model based on medical background knowledge,and utilized the Kolmogorov forward equations to construct a state transition probability matrix and a state transition rate matrix to form a derived likelihood function based.With the prior knowledge of the parameters distribution,we can have the posterior distribution,then used the MCMC algorithm(Gibbs sampling MH sampling)to implement the Bayesian estimation problem of dynamic hidden Markov structural equation models.Finally,a numerical study was carried out and the model was implemented to a case study of the development process of Alzheimer’s disease which exhibited effectiveness of our proposed research.