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Recent years have seen a growing body of literature on the analysis of length-biased data. Much of this literature adopts the accelerated failure time or proportional hazards models as the basis of study. The overwhelming majority of the existing work also assumes independence between the censoring variable and covariates. In this paper, we develop a varying-coefficient quantile regression approach to model length-biased data. Our approach does not only allow the direct estimation of the conditional quantiles of survival times based on a flexible model structure, but also has the important appeal of permitting dependence between the censoring variable and the covariates. We develop local linear estimators of the coefficients using a local inverse probability weighted estimating equation approach, and examine these estimators’ asymptotic properties. Moreover, we develop a resampling method for …