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Project

Quantile Regression for Censored Data

One of the statistical challenges in survival analysis is the study of the relationship between a time-to-event response T and a set covariates X. This can be done using a wide variety of regression techniques like, for example, linear, AFT or Cox models. A robust and flexible alternative to these classical models is quantile regression, which has gained considerable popularity and interest in recent years. Many methods have been developed for quantile regression with completely observed data. But when data are subject to censoring, statistical estimation and inference become more difficult, and the literature is sparse. The existing work focuses on the case of i.i.d. data with a right-censored response, but in practice censoring mechanisms can be quite complicated (e.g. interval censoring) and may concern both the response and the covariates. The objective of this project is to develop and study consistent and computationally efficient procedures to conduct estimation and inference in quantile regression models with complicated censoring mechanisms. To this end, an enriched asymmetric Laplace distribution will be proposed and studied. Once studied, this distribution will be used to investigate the case of quantile regression with (1) censored response, (2) censored covariates and (3) censored response and censored covariates.

Date:21 Sep 2020 →  Today
Keywords:Survival analysis, mathematical statistics, semiparametric regression, right censoring, interval censoring
Disciplines:Statistics, Biostatistics
Project type:PhD project