Estimation of intervention effects using recurrent event time data in the presence of event dependence and a cured fraction

Recurrent event data with a fraction of subjects having zero event are often seen in randomized clinical trials. Those with zero event may belong to a cured (or non-susceptible) fraction. Event dependence refers to the situation that a person's past event history affects his future event occurrences. In the presence of event dependence, an intervention may have an impact on the event rate in the non-cured through two pathways-a primary effect directly on the outcome event and a secondary effect mediated through event dependence. The primary effect combined with the secondary effect is the total effect. We propose a frailty mixture model and a two-step estimation procedure for the estimation of the effect of an intervention on the probability of cure and the total effect on event rate in the non-cured. A summary measure of intervention effects is derived. The performance of the proposed model is evaluated by simulation. Data on respiratory exacerbations from a randomized, placebo-controlled trial are re-analyzed for illustration.