Quantile Regression for Doubly Censored Data with Applications to Cystic Fibrosis Studies

Quantile regression is known for its flexibility to accommodate varying covariate effects and has attracted growing interest in its application to survival analysis. Motivated by Peng and Huang (2008)’s work on quantile regression method with randomly right censored data, we develop a quantile regression method tailored for a double censoring setting that is often encountered in registry studies utilizing the embedded martingale structure. The proposed estimation and inference procedures are computationally simple and stable. We establish the uniform consistency and weak convergence of the resulting estimators. We also provide a sensible solution to address the identifiability issues on regression quantiles at both tails, a unique feature with doubly censored data. The finite-sample performance of our approach is assessed by a series of simulation studies. An application to a registry data on cystic fibrosis illustrates the good practical utility of our method.