  Longitudinal biomedical data are often characterized by a sparse time grid
and individual-specific development patterns. Specifically, in epidemiological
cohort studies and clinical registries we are facing the question of what can
be learned from the data in an early phase of the study, when only a baseline
characterization and one follow-up measurement are available. Inspired by
recent advances that allow to combine deep learning with dynamic modeling, we
investigate whether such approaches can be useful for uncovering complex
structure, in particular for an extreme small data setting with only two
observations time points for each individual. Irregular spacing in time could
then be used to gain more information on individual dynamics by leveraging
similarity of individuals. We provide a brief overview of how variational
autoencoders (VAEs), as a deep learning approach, can be linked to ordinary
differential equations (ODEs) for dynamic modeling, and then specifically
investigate the feasibility of such an approach that infers individual-specific
latent trajectories by including regularity assumptions and individuals'
similarity. We also provide a description of this deep learning approach as a
filtering task to give a statistical perspective. Using simulated data, we show
to what extent the approach can recover individual trajectories from ODE
systems with two and four unknown parameters and infer groups of individuals
with similar trajectories, and where it breaks down. The results show that such
dynamic deep learning approaches can be useful even in extreme small data
settings, but need to be carefully adapted.
