Stochastic models for multiple pathways of temporal natural history on co-morbidity of chronic disease

Chronic diseases frequently co-occur in individuals. Susceptibility to co-morbidity, the temporal sequence and the transition rates governing the development of co-morbid diseases are often hidden or partially observable. To tackle these thorny issues we developed a series of co-morbidity stochastic models with latent variables to estimate the true proportions of susceptibility, temporal sequence, and transition rates. We begin with a bivariate co-morbidity model for two chronic diseases, then extend to a trivariate co-morbidity model for three chronic diseases, and to a generalized high-order co-morbidity model to accommodate more than three chronic diseases. To illustrate our approach we fitted the proposed model with data from a population-based health check-up for hypertension, diabetes mellitus (DM), and overweight in Matsu.