Comorbidities refer to the existence of numerous, co-occurring diseases in medicine. The course of one comorbidity is typically extremely dependent on the course of the other condition due to their co-occurrence, and therapies can have major spill-over effects. Despite the high occurrence of comorbidities among patients, there is no complete statistical framework for modelling comorbidity longitudinal dynamics. We propose a probabilistic approach for studying comorbidity dynamics in patients over time in this paper. This approach is a non-homogenous transition technique/mechanism using Hidden Markov Model called as coupled-HMM. Clinical research influenced the design of our coupled-HMM: (1) It accounts for different disease stages (acute, stable) in disease progression by providing clinically meaningful latent phases. (2) It simulates a relationship between the trajectories of comorbidities and the dynamics of capturing co-evolution. (3) The transition mechanism takes into account between-patient heterogeneity (e.g., risk factors, treatments). Based on 675 health trajectories, we assessed our proposed Coupled-HMM, which investigates the concomitant evolution of diabetes mellitus and chronic liver disease. We find that our Coupled-HMM provides a superior fit when compared to competing models without coupling. We also assess the spill-over impact, or the amount to which diabetic therapies are linked to a shift in chronic liver disease from an acute to a stable condition. Immediate application in treatment planning and clinical research becomes possible as a result of our approach in context of comorbidities.
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