Semiparametric Quantile Regression Analysis of Right-censored and Length-biased Failure Time Data with Partially Linear Varying Effects

Right-censored and length-biased failure time data arise in many fields including cross-sectional prevalent cohort studies, and their analysis has recently attracted a great deal of attention. It is well-known that for regression analysis of failure time data, two commonly used approaches are hazard-based and quantile-based procedures, and most of the existing methods are the hazard-based ones. In this paper, we consider quantile regression analysis of right-censored and length-biased data and present a semiparametric varying-coefficient partially linear model. For estimation of regression parameters, a three-stage procedure that makes use of the inverse probability weighted technique is developed, and the asymptotic properties of the resulting estimators are established. In addition, the approach allows the dependence of the censoring variable on covariates, while most of the existing methods assume the independence between censoring variables and covariates. A simulation study is conducted and suggests that the proposed approach works well in practical situations. Also, an illustrative example is provided.