Nonparametric estimation of successive duration times under dependent censoring

This paper considers nonparametric inference for duration times of two successive events. Since the second duration process becomes observable only if the first event has occurred, the length of the first duration affects the probability of the second duration being censored. Dependent censoring arises if the two duration times are correlated, which is often the case. Standard approaches to this problem fail because of dependent censoring mechanism. A new product-limit estimator for the second duration variable and a pathdependent joint survival function estimator are proposed, both modified for the dependent censoring. Properties of the estimators are discussed. An example from Lawless (1982) is studied for illustrative purposes as well as a simulation study.