Quantile regression adjusting for dependent censoring from semicompeting risks

type="main" xml:id="rssb12063-abs-0001"> We study quantile regression when the response is an event time subject to potentially dependent censoring. We consider the semicompeting risks setting, where the time to censoring remains observable after the occurrence of the event of interest. Although such a scenario frequently arises in biomedical studies, most of current quantile regression methods for censored data are not applicable because they generally require the censoring time and the event time to be independent. By imposing quite mild assumptions on the association structure between the time-to-event response and the censoring time variable, we propose quantile regression procedures, which allow us to garner a comprehensive view of the covariate effects on the event time outcome as well as to examine the informativeness of censoring. An efficient and stable algorithm is provided for implementing the new method. We establish the asymptotic properties of the resulting estimators including uniform consistency and weak convergence. The theoretical development may serve as a useful template for addressing estimating settings that involve stochastic integrals. Extensive simulation studies suggest that the method proposed performs well with moderate sample sizes. We illustrate the practical utility of our proposals through an application to a bone marrow transplant trial.