Censored quantile regression model with time-varying covariates under length-biased sampling

Quantile regression is a flexible and effective tool for modeling survival data and its relationship with important covariates, which often vary over time. Informative right censoring of data from the prevalent cohort within the population often results in length-biased observations. We propose an estimating equation-based approach to obtain consistent estimators of the regression coefficients of interest based on length-biased observations with time-dependent covariates. In addition, inspired by Zeng and Lin 2008, we also develop a more numerically stable procedure for variance estimation. Large sample properties including consistency and asymptotic normality of the proposed estimator are established. Numerical studies presented demonstrate convincing performance of the proposed estimator under various settings. The application of the proposed method is demonstrated using the Oscar dataset.