A quantile varying-coefficient regression approach to length-biased data modeling

Recent years have seen a growing body of literature on the anal- ysis of length-biased data. Much of this literature adopts the accelerated failure time or proportional hazards models as the basis of study. The over- whelming 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 quan- tiles 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 us- ing a local inverse probability weighted estimating equation approach, and examine these estimators’ asymptotic properties. Moreover, we develop a resampling method for computing the estimators’ covariances. The small sample properties of the proposed methods are investigated in a simulation study. A real data example illustrates the application of the methods in practice.