Learning Disease Progression Models With Longitudinal Data and Missing Values

Statistical methods have been developed for the analysis of longitunal data in neurodegenerative diseases. To cope with the lack of temporal markers - i.e. to account for subject-specific disease progression in regard to age - a common strategy consists in realigning the individual sequence data in time. Patient's specific trajectories can indeed be seen as spatiotemporal perturbations of the same normative disease trajectory. However, these models do not easily allow one to account for multimodal data, which more than often include missing values. Indeed, it is rare that imaging and clinical examinations for instance are performed at the same frequency in clinical protocols. Multimodal models also need to allow a different profile of progression for data with different structure and representation.We propose to use a generative mixed effect model that considers the progression trajectories as curves on a Riemannian Manifold. We use the concept of product manifold to handle multimodal data, and leverage the generative aspect of our model to handle missing values. We assess the robusteness of our methods toward missing values frequency on both synthetic and real data. Finally we apply our model on a real-world dataset to model Parkinson's disease progression from data derived from clinical examination and imaging.