In incident cohort studies, survival data often include subjects who havehad an initiate event at recruitment and may potentially experience twosuccessive events (first and second) during the follow-up period. Since the second durationprocess becomes observable only if the first event has occurred, left-truncationand dependent censoring arise if the two duration times are correlated.To confront the two potential sampling biases, weprovide two inverse-probability-weighted (IPW) approaches for estimatingthe joint survival function of successive duration times.One of them is similar to the estimator proposed by Chang and Tzeng (2006).The other is the extension of thenonparametric estimatorproposed by Wang and Wells (1998).A simulation study isconducted to compare the two IPW approaches.Besides, the delete-one jackknife variance estimate is used to constructconfidence intervals for both estimators.
