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