Presmoothed Kaplan-Meier integrals and the missing censoring indicator model

In Survival Analysis, the lifetimes are often observed under censoring from the right. To cope with this censoring issue, the Kaplan-Meier method is typically used. However, in some instances, some of the censoring indicators are missing, and then the Kaplan- Meier estimator can not be computed. In this work we propose the using of presmoothed Kaplan-Meier integrals (de U~na-Alvarez and Rodrguez-Campos, 2004) for the estimation of important parameters in the presence of covariates and including the possibility of missing censoring indicators. We consider the missing-at-random (MAR) model (Subramanian, 2004). For the presmoothing, we mainly focus on the semiparametric censorship model introduced by Dikta (1998), after proper adaptation to the presence of covariates. We investigate the asymptotic properties of the proposed estimators, as consistency and distributional convergence; as well as their nite sample behavior via simulation studies and real data analysis.