Analysis of smoking cessation patterns using a stochastic mixed-effects model with a latent cured state

We develop a mixed model to capture the complex stochastic nature of tobacco abuse and dependence. This model describes transition processes among addiction and nonaddiction stages. An important innovation of our model is allowing an unobserved cure state, or permanent quitting, in contrast to transient quitting. This distinction is necessary to model data from situations where censoring prevents unambiguous determination that a person has been "cured." Moreover, the processes that describe transient and permanent quitting are likely to be different and have different policy-making implications. For example, when analyzing factors that influence smoking and can be targeted by interventions, it is more important to target those factors that are associated with permanent quitting rather than transient quitting. We apply our methodology to the Alpha-Tocopherol, Beta-Carotene Cancer Prevention (ATBC) study, a large (29,133 participants) longitudinal cohort study. While ATBC was designed as a cancer prevention study, it contains unique information about the smoking status of each participant during every 4-month period of the study. These data are used to model smoking cessation patterns using a discrete-time stochastic mixed-effects model with three states: smoking, transient cessation, and permanent cessation (absorbent state). Random participant-specific transition probabilities among these states are used to account for participant-to-participant heterogeneity. Another important innovation in our article is to design computationally practical methods for dealing with the size of the dataset and complexity of the models. This is achieved using the marginal likelihood obtained by integrating over the Beta distribution of random effects.