  When modeling longitudinal biomedical data, often dimensionality reduction as
well as dynamic modeling in the resulting latent representation is needed. This
can be achieved by artificial neural networks for dimension reduction, and
differential equations for dynamic modeling of individual-level trajectories.
However, such approaches so far assume that parameters of individual-level
dynamics are constant throughout the observation period. Motivated by an
application from psychological resilience research, we propose an extension
where different sets of differential equation parameters are allowed for
observation sub-periods. Still, estimation for intra-individual sub-periods is
coupled for being able to fit the model also with a relatively small dataset.
We subsequently derive prediction targets from individual dynamic models of
resilience in the application. These serve as interpretable resilience-related
outcomes, to be predicted from characteristics of individuals, measured at
baseline and a follow-up time point, and selecting a small set of important
predictors. Our approach is seen to successfully identify individual-level
parameters of dynamic models that allows us to stably select predictors, i.e.,
resilience factors. Furthermore, we can identify those characteristics of
individuals that are the most promising for updates at follow-up, which might
inform future study design. This underlines the usefulness of our proposed deep
dynamic modeling approach with changes in parameters between observation
sub-periods.
