Censored quantile regression with covariate measurement errors

Abstract

We study censored quantile regression with covariates measured with errors. We propose a composite quantile objective function based on inverse censoringprobability weighting, and an averaging estimator to improve estimation efficiency. Our procedure can eliminate the bias in the naive estimator that is obtained by treating mismeasured covariates as error-free. Using a combination of martingale and quantile regression techniques, we show that the proposed estimators for the regression coefficients are consistent and asymptotically normal. We conducted simulation studies to examine the finite-sample properties of the new method, and demonstrated efficiency gain of the averaging estimator over the single quantile regression estimator. For illustration, we applied our model to a lung cancer study.