Quantile Regression Analysis of Length-Biased Survival Data

Analysis of length-biased time-to-event data, which commonly arise in epidemiological cohort studies and cross-sectional surveys, has attracted considerable attention recently. Ignoring length-biased sampling often leads to severe bias in estimating the survival time in the general population. Existing work either completely ignore the covariate effects or use hazard or accelerated failure time regressions, which restrict the covariates to affect only the location of the transformed survival distribution. In this paper, we propose a flexible quantile regression framework for analyzing the covariate effects on the population survival time under both length-biased sampling and random right 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 two estimators, one for covariate-independent censoring and the other for covariate-dependent censoring. We establish the consistency and asymptotic normality theory for both estimators. A lackof-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. By analyzing the CSHA dementia and the Spain unemployment data sets, we demonstrate that the proposed methods are effective in discovering interesting covariate effects at different tails of the target distribution, which were largely overlooked by existing methods in the literature.