  We explore Markov-modulated marked Poisson processes (MMMPPs) as a natural
framework for modelling patients' disease dynamics over time based on medical
claims data. In claims data, observations do not only occur at random points in
time but are also informative, i.e. driven by unobserved disease levels, as
poor health conditions usually lead to more frequent interactions with the
healthcare system. Therefore, we model the observation process as a
Markov-modulated Poisson process, where the rate of healthcare interactions is
governed by a continuous-time Markov chain. Its states serve as proxies for the
patients' latent disease levels and further determine the distribution of
additional data collected at each observation time, the so-called marks.
Overall, MMMPPs jointly model observations and their informative time points by
comprising two state-dependent processes: the observation process
(corresponding to the event times) and the mark process (corresponding to
event-specific information), which both depend on the underlying states. The
approach is illustrated using claims data from patients diagnosed with chronic
obstructive pulmonary disease (COPD) by modelling their drug use and the
interval lengths between consecutive physician consultations. The results
indicate that MMMPPs are able to detect distinct patterns of healthcare
utilisation related to disease processes and reveal inter-individual
differences in the state-switching dynamics.
