Nonparametric Estimation For Survival Distribution With Informative Mixed Case Interval Censoring

Interval-censored failure time data occur in many fields such as demography,economics, medical research and reliability and many inference procedures on them have been developed. Mixed case interval-censored data (Schick and Yu (2000)) is a kind of important but complicated interval-censored data. For this data, each subject is observed several times, for which both the number of observations and the observation time points can be random. Because of some limitations, the exact failure time can not be observed and we can only know which interval it falls in. For the complicated structure, there is little research about this kind of data. Furthermore,most of the existing approaches assume that the mechanism that yields mixed case interval censoring is independent of the failure time of interest and it is clear that this may not be true in practice. In this paper, we consider the nonparametric estimation of the survival function for mixed case interval-censored failure time data when the censoring mechanism may be related to the failure time of interest. For the problem,two approaches are proposed. One is based on the conditional likelihood function and the other is based on the generalized estimating equation. The nonparametric estimators of the survival function are proposed, and some simulation studies are conducted to evaluate the performance of the approaches. The simulation results suggest that the methods work well and the proposed estimators possess some good properties.