Longitudinal modelling is of pivotal interest for the study of neurodegenerative diseases. The Disease Course Mapping is a multivariate Bayesian mixed-effect progression model that is able to recover the course of a disease from a cohort with multimodal longitudinal observations (imaging variables, cognitive and clinical scores) and to extract interpretable parameters to describe each patient. It has been validated on multiple diseases and on multiple applications settings (cohort study, trial enrichment, data simulation, ...) However, its statistical formulation relies only on time-dependent observations. It thus fail to integrate time-independent information (gender, education levels, genetic factors, ...) in its modelling, even though such covariates are known to modulate clinical disease courses. We propose a mixed-effect formulation that captures the influence of such covariates over the dynamic of the disease.