Appears in collection : Statistical Modeling for Shapes and Imaging

In this talk, I propose to present a generic hierarchical spatiotemporal model for longitudinal manifold-valued data, which consists in repeated measurements over time for a group of individuals. This model allows us to estimate a group-average trajectory of evolution, considered as a piece-wise geodesic of a given Riemannian manifold. Individual trajectories of progression are obtained as random variations, which consist in parallel shifting and time reparametrization, of the average trajectory. These spatiotemporal transformations allow us to characterize changes in the direction and in the pace at which trajectories are followed. We propose to estimate the parameters of the model using a stochastic version of the expectation-maximization (EM) algorithm, the Monte Carlo Markov Chain Stochastic Approximation EM (MCMC SAEM) algorithm with tempering schemes. This generic spatiotemporal model is used to analyze the temporal progression of a family of biomarkers. This progression model estimates a normative scenario of the progressive impairments of several cognitive functions, considered here as biomarkers, during the course of Alzheimer’s disease. We also used this model to understand the response to antiangiogenic treatment in metastatic cancers.