Rank-based estimation for semiparametric accelerated failure time model under length-biased sampling

Length-biased sampling appears in many observational studies, including epidemiological studies, labor economics and cancer screening trials. To accommodate sampling bias, which can lead to substantial estimation bias if ignored, we propose a class of doubly-weighted rank-based estimating equations under the accelerated failure time model. The general weighting structures considered in our estimating equations allow great flexibility and include many existing methods as special cases. Different approaches for constructing estimating equations are investigated, and the estimators are shown to be consistent and asymptotically normal. Moreover, we propose efficient computational procedures to solve the estimating equations and to estimate the variances of the estimators. Simulation studies show that the proposed estimators outperform the existing estimators. Moreover, real data from a dementia study and a Spanish unemployment duration study are analyzed to illustrate the proposed method.