Mixed-effects model for the spatiotemporal analysis of longitudinal manifold-valued data

Jean-Baptiste Schiratti (1, 2) , Stéphanie Allassonnière (1) , Olivier Colliot (2) , Stanley Durrleman (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 ARAMIS - Algorithms, models and methods for images and signals of the human brain = Algorithmes, modèles et méthodes pour les images et les signaux du cerveau humain [ICM Paris]

In this work , we propose a generic hierarchical spatiotem-poral model for longitudinal manifold-valued data , which consist in repeated measurements over time for a group of individuals. This model allows us to estimate a group-average trajectory of progression , considered as a 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 tranformations 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 approximation of the expectation-maximization (EM) algorithm , the Monte Carlo Markov Chain Stochastic Approximation EM (MCMC SAEM) algorithm. 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. The estimated average trajectory provides a normative scenario of disease progression. Random effects provide unique insights into the variations in the ordering and timing of the succession of cognitive impairments across different individuals .

Domaines: Modélisation et simulation; Imagerie médicale

Jean-Baptiste Schiratti, Stéphanie Allassonnière, Olivier Colliot, Stanley Durrleman. Mixed-effects model for the spatiotemporal analysis of longitudinal manifold-valued data. 5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy, Oct 2015, Munich, Germany. ⟨hal-01245905⟩