Nonparametric estimate of conditional quantile residual lifetime for right censored data

A nonparametric approach is proposed to estimate the quantile residual lifetime at a given time while considering the effect of covariates. An estimating equation is constructed and a local Kaplan-Meier estimator is employed to incorporate the covariates in the equation while leaving the distribution of survival time unspecified. Asymptotic properties including both consistency and asymptotic normality of the proposed estimator are established and a resampling method is proposed to estimate the asymptotic variance. Simulation studies are conducted to assess the finite-sample performance of the estimator, and an HIV survival data is analyzed using the proposed method.