Markov-modulated marked Poisson processes for modeling disease dynamics based on medical claims data

We explore Markov-modulated marked Poisson processes (MMMPPs) as a natural framework for modeling 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, that is, driven by unobserved disease levels, as poor health conditions usually lead to more frequent interactions with the health care system. Therefore, we model the observation process as a Markov-modulated Poisson process, where the rate of health care 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 by modeling their drug use and the interval lengths between consecutive physician consultations. The results indicate that MMMPPs are able to detect distinct patterns of health care utilization related to disease processes and reveal interindividual differences in the state-switching dynamics.