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

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 func-tion 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. (c) 2020 The Author(s). Published by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).