Nonparametric Estimation Time Data in the Presence of Interval-censored Failure of Informative Censoring

Nonparametric estimation of a survival function is one of the most commonly asked questions in the analysis of failure time data and for this, a number of procedures have been developed under various types of censoring structures （Kalbfleisch and Prentice, 2002）. In particular, several algorithms are available for interval-censored failure time data with independent censoring mechanism （Sun, 2006; Turnbull, 1976）. In this paper, we consider the interval-censored data where the censoring mechanism may be related to the failure time of interest, for which there does not seem to exist a nonparametric estimation procedure. It is well-known that with informative censoring, the estimation is possible only under some assumptions. To attack the problem, we take a copula model approach to model the relationship between the failure time of interest and censoring variables and present a simple nonparametric estimation procedure. The method allows one to conduct a sensitivity analysis among others.