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In order to find effective treatments for Alzheimer's disease (AD), we needto identify subjects at risk of AD as early as possible. To this end, recentlydeveloped disease progression models can be used to perform early diagnosis, aswell as predict the subjects' disease stages and future evolution. However,these models have not yet been applied to rare neurodegenerative diseases, arenot suitable to understand the complex dynamics of biomarkers, work only onlarge multimodal datasets, and their predictive performance has not beenobjectively validated. In this work I developed novel models of diseaseprogression and applied them to estimate the progression of Alzheimer's diseaseand Posterior Cortical atrophy, a rare neurodegenerative syndrome causingvisual deficits. My first contribution is a study on the progression ofPosterior Cortical Atrophy, using models already developed: the Event-basedModel (EBM) and the Differential Equation Model (DEM). My second contributionis the development of DIVE, a novel spatio-temporal model of diseaseprogression that estimates fine-grained spatial patterns of pathology,potentially enabling us to understand complex disease mechanisms relating topathology propagation along brain networks. My third contribution is thedevelopment of Disease Knowledge Transfer (DKT), a novel disease progressionmodel that estimates the multimodal progression of rare neurodegenerativediseases from limited, unimodal datasets, by transferring information fromlarger, multimodal datasets of typical neurodegenerative diseases. My fourthcontribution is the development of novel extensions for the EBM and the DEM,and the development of novel measures for performance evaluation of suchmodels. My last contribution is the organization of the TADPOLE challenge, acompetition which aims to identify algorithms and features that best predictthe evolution of AD.

Modelling the Neuroanatomical Progression of Alzheimer's Disease and Posterior Cortical Atrophy