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

Abstract

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.

• Censored data
• Check function
• Corrected estimating equation
• Kernel smoothing
• Measurement error
• Regression quantile
• Semiparametric method
• Survival analysis

Additional information

Notes on contributors

Yuanshan Wu

Yuanshan Wu is Assistant Professor, School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China (E-mail: [email protected]). Yanyuan Ma is Professor, Department of Statistics, University of South Carolina, Columbia, SC 29208. (E-mail: [email protected]). Guosheng Yin, the corresponding author, is Professor, Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong (E-mail: [email protected]). We thank two referees, the associate editor, and editor for their many constructive comments that have led to significant improvements in the article. Wu’s research was partially supported by the National Natural Science Foundation of China, Ma’s research by the National Science Foundation and National Institute of Neurological Disorder and Stroke, and Yin’s research by the Research Grants Council of Hong Kong.

Yanyuan Ma

Yuanshan Wu is Assistant Professor, School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China (E-mail: [email protected]). Yanyuan Ma is Professor, Department of Statistics, University of South Carolina, Columbia, SC 29208. (E-mail: [email protected]). Guosheng Yin, the corresponding author, is Professor, Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong (E-mail: [email protected]). We thank two referees, the associate editor, and editor for their many constructive comments that have led to significant improvements in the article. Wu’s research was partially supported by the National Natural Science Foundation of China, Ma’s research by the National Science Foundation and National Institute of Neurological Disorder and Stroke, and Yin’s research by the Research Grants Council of Hong Kong.

Guosheng Yin

Yuanshan Wu is Assistant Professor, School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China (E-mail: [email protected]). Yanyuan Ma is Professor, Department of Statistics, University of South Carolina, Columbia, SC 29208. (E-mail: [email protected]). Guosheng Yin, the corresponding author, is Professor, Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong (E-mail: [email protected]). We thank two referees, the associate editor, and editor for their many constructive comments that have led to significant improvements in the article. Wu’s research was partially supported by the National Natural Science Foundation of China, Ma’s research by the National Science Foundation and National Institute of Neurological Disorder and Stroke, and Yin’s research by the Research Grants Council of Hong Kong.