Smoothed and Corrected Score Approach to Censored Quantile Regression With Measurement Errors

• Published in: Journal of the American Statistical Association Vol. 110; no. 512; pp. 1670 - 1683
• Main Authors: Wu, Yuanshan, Ma, Yanyuan, Yin, Guosheng
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 01.12.2015; Taylor & Francis Group, LLC; Taylor & Francis Ltd
• Subjects: Censored data; Check function; Corrected estimating equation; data analysis; equations; Estimation bias; human diseases; Kernel smoothing; Lung cancer; lung neoplasms; Measurement error; Measurement errors; Regression analysis; Regression quantile; Semiparametric method; Simulation; Statistics; Survival analysis; Theory and Methods
• ISSN: 1537-274X; 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2014.989323

Censored quantile regression is an important alternative to the Cox proportional hazards model in survival analysis. In contrast to the usual central covariate effects, quantile regression can effectively characterize the covariate effects at different quantiles of the survival time. When covariates are measured with errors, it is known that naively treating mismeasured covariates as error-free would result in estimation bias. Under censored quantile regression, we propose smoothed and corrected estimating equations to obtain consistent estimators. We establish consistency and asymptotic normality for the proposed estimators of quantile regression coefficients. Compared with the naive estimator, the proposed method can eliminate the estimation bias under various measurement error distributions and model error distributions. We conduct simulation studies to examine the finite-sample properties of the new method and apply it to a lung cancer study. Supplementary materials for this article are available online.