  Electronic health records contain valuable information for monitoring
patients' health trajectories over time. Disease progression models have been
developed to understand the underlying patterns and dynamics of diseases using
these data as sequences. However, analyzing temporal data from EHRs is
challenging due to the variability and irregularities present in medical
records. We propose a Markovian generative model of treatments developed to (i)
model the irregular time intervals between medical events; (ii) classify
treatments into subtypes based on the patient sequence of medical events and
the time intervals between them; and (iii) segment treatments into subsequences
of disease progression patterns. We assume that sequences have an associated
structure of latent variables: a latent class representing the different
subtypes of treatments; and a set of latent stages indicating the phase of
progression of the treatments. We use the Expectation-Maximization algorithm to
learn the model, which is efficiently solved with a dynamic programming-based
method. Various parametric models have been employed to model the time
intervals between medical events during the learning process, including the
geometric, exponential, and Weibull distributions. The results demonstrate the
effectiveness of our model in recovering the underlying model from data and
accurately modeling the irregular time intervals between medical actions.
