Quantile regression analysis of length-biased survival data

Length-biased time-to-event data commonly arise in epidemiological cohort studies and cross-sectional surveys. Ignoring length-biased sampling often leads to severe bias in estimating the survival time in the general population. We propose a flexible quantile regression framework for analysing the covariate effects on the population survival time under both length-biased sampling and random censoring. This framework allows for easy interpretation of the statistical model. Furthermore, it allows the covariates to have different impacts at different tails of the survival distribution and thus is able to capture important population heterogeneity. Using an unbiased estimating equation approach, we develop a new estimator that allows the censoring variable to depend on covariates in a non-parametric way. We establish the consistency and asymptotic normality for the proposed estimator. A lack-of-fit test is proposed for diagnosing the adequacy of the population quantile regression model. The finite sample performance of the proposed methods is assessed through a simulation study. We demonstrate that the proposed method is effective in discovering interesting covariate effects by analysing the Canadian Study of Health and Aging dementia data.