Nonparametric inference on quantile lost lifespan

In this article, the existing concept of reversed percentile residual life, or percentile inactivity time, is recast to show that it can be used for routine analysis of time-to-event data under right censoring to summarize "life lost," which poses several advantages over the existing methods for survival analysis. An estimating equation approach is adopted to avoid estimation of the probability density function of the underlying time-to-event distribution to estimate the variance of the quantile estimator. Additionally a K-sample test statistic is proposed to test the ratio of the quantile lost lifespans. Simulation studies are performed to assess finite properties of the proposed K-sample statistic in terms of coverage probability and power. The proposed method is illustrated with a real data example from a breast cancer study.