  In medicine, comorbidities refer to the presence of multiple, co-occurring
diseases. Due to their co-occurring nature, the course of one comorbidity is
often highly dependent on the course of the other disease and, hence,
treatments can have significant spill-over effects. Despite the prevalence of
comorbidities among patients, a comprehensive statistical framework for
modeling the longitudinal dynamics of comorbidities is missing. In this paper,
we propose a probabilistic model for analyzing comorbidity dynamics over time
in patients. Specifically, we develop a coupled hidden Markov model with a
personalized, non-homogeneous transition mechanism, named Comorbidity-HMM. The
specification of our Comorbidity-HMM is informed by clinical research: (1) It
accounts for different disease states (i. e., acute, stable) in the disease
progression by introducing latent states that are of clinical meaning. (2) It
models a coupling among the trajectories from comorbidities to capture
co-evolution dynamics. (3) It considers between-patient heterogeneity (e. g.,
risk factors, treatments) in the transition mechanism. Based on our model, we
define a spill-over effect that measures the indirect effect of treatments on
patient trajectories through coupling (i. e., through comorbidity
co-evolution). We evaluated our proposed Comorbidity-HMM based on 675 health
trajectories where we investigate the joint progression of diabetes mellitus
and chronic liver disease. Compared to alternative models without coupling, we
find that our Comorbidity-HMM achieves a superior fit. Further, we quantify the
spill-over effect, that is, to what extent diabetes treatments are associated
with a change in the chronic liver disease from an acute to a stable disease
state. To this end, our model is of direct relevance for both treatment
planning and clinical research in the context of comorbidities.
