In medical research, especially in longitudinal epidemiological studies and when monitoring patients with chronic diseases, participants repeatedly undergo a large set of examinations. The data recorded on one participant over time can be modelled as a multivariate time series or as a high-dimensional trajectory, where the dimensions are the variables to be recorded according to the examinations' protocol. Prediction of future recordings and of the labels of given variables (outcomes) is essential for winning insights from medical data. However, research on prediction in time series and in trajectories has not paid yet enough attention to some challenges that emerge when collecting epidemiological data over time: (i) the examination protocol may change from one time point to the next one, so that the set of dimensions changes; (ii) some examinations are not performed on all participants, e.g. because they depend on sex. This means that the data may be systematically incomplete. Moreover, participation is voluntary, which means that participants of an epidemiological study may exit it, while participants of a patient monitoring programme may respond irregularly: this leads to trajectories of different lengths, implying that a lot of data is available for some participants, and only few data for others. The goal of this work is to extend stream mining methods towards new solutions for the robust prediction of a patient's trajectory development which overcome the aforementioned challenges in order to facilitate diagnosis and treatment. Special focus will be placed on the prediction of the development of hepatic steatosis (fatty liver) which is reversible and the prediction of goitre which is not reversible using data from the Study of Health in Pomerania (SHIP).