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. Compared with 3.93% of co-morbidity directly estimated from empirical data, approximately 12% (10%-14%) of participants have the potential of developing both hypertension and DM from the underlying population. Hypertension prior to DM was 74% (54.10%-93.77%) of these subjects susceptible to co-morbidity. Those who developed DM first had a higher likelihood of having hypertension (65.85 per 100 person-years; 95% CI: 15.61-116.09) compared with those with hypertension first and DM later (36.37 cases per 100 person-years; 95% CI: 14.57-58.18). Gender, smoking, and alcohol drinking modeled by incorporating them as covariates with proportional hazards form had impacts on different parameters of interest. The deviance statistics, indicating a lack of statistical significance (p values were 0.26 for the bivariate model) for the model without covariates and for the model with covariates (all p values >0.05), suggest a satisfactory model fit. However, the trivariate co-morbidity model had poorer fit than the bivariate co-morbidity model. Our proposed co-morbidity stochastic latent variable models can tackle the problem of underestimating the proportion of susceptibility to co-morbidity, giving a clue to the temporal sequence of a constellation of co-morbid diseases, and quantifying the incidence rates of each disease and the corresponding transitions rates between co-morbid diseases. The generalized high-order co-morbidity model can be extended to model the complex pathway of high dimension of chronic diseases in the clinical field provided the dataset is sufficiently large.