Locally Weighted Censored Quantile Regression

Censored quantile regression offers a valuable supplement to Cox propor-tional hazards model for survival analysis. Existing work in the literature of-ten requires stringent assumptions, such as unconditional independence of the survival time and the censoring variable or global linearity at all quantile lev-els. Moreover, some of the work use recursive algorithms making it challeng-ing to derive asymptotic normality. To overcome these drawbacks, we propose a new locally weighted censored quantile regression approach that adopts the redistribution-of-mass 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 im-plemented 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.