Estimation of the joint distribution function for successive duration times from doubly truncated data with a cure fraction

In prevalent cohort study, interest often focuses on the duration times of successive events. To efficiently sample data, it is common to collect data based on interval sampling, under which subjects are included into a study only if their first events occur within a specific calendar time window. Such sampling scheme leads to double truncation and dependent censoring since both early and late events outside the window are excluded from the sample and the second failure event is observable only if the first event has occurred. In practice, there may exist a fraction of subjects who are nonsusceptible to successive events. In this article, we consider nonparametric estimation of the joint distribution functions of the duration times for doubly truncated successive event data with a cure fraction. Using the inverse-probability-weighted (IPW) method, we propose nonparametric estimators and establish their asymptotic properties. Simulation results demonstrate that the proposed estimators perform well in finite samples.