Gui Ping SUN, Mu ZHAO, Yong ZHOU
Residual life is an important quantity to characterize the individual life expectancy. Early studies on the residual life mainly focus on the mean residual life. However, when the potential survival function of population is skewed or heavy-tailed, the mean residual life does not exist. So the statisticians suggest the quantile residual life to characterize the individual life expectancy. With the complete data and the right censored data, the modeling and theoretical properties of the quantile residual life have been established well. However, biased sampling data are often encountered in practical investigations. For example, left truncated data are often encountered in clinical trial, case cohort sampling data frequently occur in epidemiology, length biased sampling data also frequently occur in large medical cohort studies. Ignoring sampling biases will lead to biased estimators and unreasonable inferences. We consider a quantile residual life regression model under the general biased and right censored data. First, we propose a quantile regression model of residual life with the general biased and right censored data. Estimation procedures by using general estimation equation method are proposed. Comparing to the independent assumption of the censored variables and the covariates, which is commonly used in the existing literatures, this paper mainly considers that censored variables depend on the covariates. Second, because the asymptotic variance of the estimator involves the non-parametric density functions, so a bootstrap method is adopted. Finally, the simulation results show that the proposed estimators have good finite sample properties.