Censored quantile regression offers a valuable supplement to Cox proportional hazards model for survival analysis. Existing work in the literature often requires stringent assumptions, such as unconditional independence of the survival time and the censoring variable or global linearity at all quantile levels. Moreover, some of the work uses recursive algorithms, making it challenging to derive asymptotic normality. To overcome these drawbacks, we propose a new locally weighted censored quantile regression approach that adopts the redistribution-ofmass idea and employs a local reweighting scheme. Its validity only requires conditional independence of the survival time and the censoring variable given the covariates, and linearity at the particular quantile level of interest. Our method leads to a simple algorithm that can be conveniently implemented with R software. Applying recent theory of M-estimation with infinite dimensional parameters, we establish the consistency and asymptotic normality of the proposed estimator. The proposed method is studied via simulations and is illustrated with the analysis of an acute myocardial infarction dataset.
Bibliographical noteFunding Information:
Huixia Judy Wang is Assistant Professor, Department of Statistics, North Carolina State University, Raleigh, NC 27695 (E-mail: email@example.com). Lan Wang is Associate Professor, Department of Statistics, University of Minnesota, Minneapolis, MN 55455 (E-mail: firstname.lastname@example.org). The research is partially supported by the NSF awards DMS-07-06963 and DMS-07-06842. The authors thank two referees, an Associate Editor, the Editor, and Professor Dennis D. Boos for helpful comments and suggestions, and Professors Xuming He, Wenbin Lu, and Tereza Neocleous for inspiring discussions.
- Kaplan-meier estimator
- Quantile regression
- Random censoring
- Survival analysis