Dynamic Modeling of Multivariate Latent Processes and Their Temporal Relationships: Application to Alzheimer's Disease
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Alzheimer's disease gradually affects several components including the cerebral dimension with brain atrophies, the cognitive dimension with a decline in various functions and the functional dimension with impairment in the daily living activities. Understanding how such dimensions interconnect is crucial for AD research. However it requires to simultaneously capture the dynamic and multidimensional aspects, and to explore temporal relationships between dimensions. We propose an original dynamic model that accounts for all these features. The model defines dimensions as latent processes and combines a multivariate linear mixed model and a system of difference equations to model trajectories and temporal relationships between latent processes in finely discrete time. Parameters are estimated in the maximum likelihood framework enjoying a closed form for the likelihood. We demonstrate in a simulation study that this dynamic model in discrete time benefits the same causal interpretation of temporal relationships as mechanistic models defined in continuous time. The model is then applied to the data of the Alzheimer's Disease Neuroimaging Initiative. Three longitudinal dimensions (cerebral anatomy, cognitive ability and functional autonomy) are analyzed and their temporal structure is contrasted between different clinical stages of Alzheimer's disease.
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