Estimating equation methods for quantile regression with length-biased and right-censored data

Abstract

In this paper, we first develop the quantile regression approach for survival data arising from lengthbiased sampling, where the survival times are left-truncated by uniformly distributed random truncated times. As a special case of the left-truncated and right-censored (LTRC) data, length-biased right-censored (LBRC) data supports more information than LTRC data. When we apply the general methods to LBRC data, the resulting estimators may be inefficient because they do not exploit the special structure in LBRC data. In order to improve efficiency, we then develop a composite quantile regression approach for LBRC data, which do not need to estimate the distribution of censoring time. The proposed estimating equations lead to a simple algorithm that involves minimizations of L 1 type convex functions. We establish uniform consistency and weak convergence of the resultant estimators using empirical process and stochastic integral techniques. Simulation studies are conducted to evaluate the finite sample performance of the proposed methods. A real data example is also given.