Inference on quantile residual life for length-based survival data

Length biased data occurs when a prevalent sampling is used to recruit subject into a study that investigates the time from an initial event to a terminal event. Such data are usually left-truncated and right-censored. While there have been accurate and efficient methods to estimate the survival function, not much work have been done regarding estimation of residual life time distribution or the summary parameters such as the median and quantiles of the residual life. In this paper we propose two ways to estimate the quantiles of the residual life time at fixed time points accounting for the length biased and censored nature of the data. We provide the asymptotic properties of these estimators and investigate them through simulation studies. Considering that the variance of these estimators require density estimation, we suggest an alternate approach to obtain the confidence intervals for the residual function. We apply these methods to a breast cancer dataset from National Surgical Adjuvant Breast and Bowel Project (NSABP).