Modeling smoking cessation data with alternating states and a cure fraction using frailty models

We propose a flexible parametric model to describe alternating states recurrent-event data where there is a possibility of cure with each type of event. We begin by introducing a novel cure model in which a common frailty influences both the cure probability and the hazard function given not cured. We then extend our model to data with recurring events of two alternating types. We assume that each type of event has a gamma frailty, and we link the frailties by a Clayton copula. We illustrate the model with an analysis of data from two smoking cessation trials comparing bupropion and placebo, in which each subject potentially experienced a series of lapse and recovery events. Our analysis suggests that bupropion increases the probability of permanent cure and decreases the hazard of lapse, but does not affect the distribution of time to recovery during a lapse. The data suggest a positive but non-significant association between the lapse and recovery frailties. A simulation study suggests that the estimates have little bias and that their 95 per cent confidence intervals have nearly nominal coverage in samples of practical size.