Insights on the robust variance estimator under recurrent-events model

Recurrent events are common in medical research for subjects who are followed for the duration of a study. For example, cardiovascular patients with an implantable cardioverter defibrillator (ICD) experience recurrent arrhythmic events that are terminated by shocks or antitachycardia pacing delivered by the device. In a published randomized clinical trial, a recurrent-event model was used to study the effect of a drug therapy in subjects with ICDs, who were experiencing recurrent symptomatic arrhythmic events. Under this model, one expects the robust variance for the estimated treatment effect to diminish when the duration of the trial is extended, due to the additional events observed. However, as shown in this article, that is not always the case. We investigate this phenomenon using large datasets from this arrhythmia trial and from a diabetes study, with some analytical results, as well as through simulations. Some insights are also provided on existing sample size formulae using our results.