Regression analysis of case K interval‐censored failure time data in the presence of informative 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 (Sun, 2006; Chen, Sun, and Peace, 2012). However, most of the existing approaches assume that the mechanism that yields interval censoring is independent of the failure time of interest and it is clear that this may not be true in practice (Zhang et al., 2007; Ma, Hu, and Sun, 2015). In this article, we consider regression analysis of case K interval‐censored failure time data when the censoring mechanism may be related to the failure time of interest. For the problem, an estimated sieve maximum‐likelihood approach is proposed for the data arising from the proportional hazards frailty model and for estimation, a two‐step procedure is presented. In the addition, the asymptotic properties of the proposed estimators of regression parameters are established and an extensive simulation study suggests that the method works well. Finally, we apply the method to a set of real interval‐censored data that motivated this study.