Joint analysis of stochastic processes with application to smoking patterns and insomnia.

This article proposes a joint modeling framework for longitudinal insomnia measurements and a stochastic smoking cessation process in the presence of a latent permanent quitting state (i.e., 'cure'). We use a generalized linear mixed-effects model and a stochastic mixed-effects model for the longitudinal measurements of insomnia symptom and for the smoking cessation process, respectively. We link these two models together via the latent random effects. We develop a Bayesian framework and Markov Chain Monte Carlo algorithm to obtain the parameter estimates. We formulate and compute the likelihood functions involving time-dependent covariates. We explore the within-subject correlation between insomnia and smoking processes. We apply the proposed methodology to simulation studies and the motivating dataset, that is, the Alpha-Tocopherol, Beta-Carotene Lung Cancer Prevention study, a large longitudinal cohort study of smokers from Finland.