A semi-parametric estimator of the quantile residual life for heavily censored data

Abstract

The p-quantile residual life function summarizes the lifetime data in a useful and simple concept and in units of time. For uncensored data or when the upper tail of the observations is not censored, this function can be estimated by applying the well-known Kaplan-Meier survival estimator. But, when research terminates in heavy right-censored lifetime data which is the case of many biomedical and survival studies, the p-quantile residual life function is not estimable in this way. In this paper, we propose a novel semi-parametric estimator of the p-quantile residual life function in such cases. It combines the nonparametric Kaplan-Meier survival estimator with an approximated tail model motivated by the extreme value theory. The proposed estimator has been examined by a simulation study and applied to a lifetime data set in the sequel.