This project aims at developing quantile regression methodology for time-to-event data with random censoring. As a primary statistical tool to assess functional covariate effects, quantile regression has been extensively developed for uncensored data and for data with fixed censoring. However,time-to-event data are often subject to random censoring where the censoring time is observed only for censored individuals but not for uncensored ones. Such censoring poses substantial challenges for the estimation and inference, particularly under the standard conditional independence censoring mechanism that the censoring time and survival time are conditionally independent given the covariates. Building on recent advances, the investigator will pursue three important research directions. First, the model will be generalized to accommodate time-dependent covariates, which are common in survival studies. Second, two-stage sampling, including case-cohort and case-control designs, will be accommodated for censored quantile regression. These designs may have tremendous cost savings in large-scale studies. Finally, data-driven transformations of the survival time will be incorporated in the model for further flexibility. Statistical and computational methods will be developed for the resulting nonlinear quantile regression model. The proposed work will significantly advance the existing censored quantile regression methodology.
Time-to-event data arise in survival studies from a wide range of fields including biomedical sciences, engineering, economics, sociology, public health, and demography. Scientific questions of interest are often concerned with how survival time might be affected by covariates, i.e., predictors; for instance, whether HIV-infected individuals may survive longer with a new intervention. Standard survival analysis techniques, as routinely adopted, presume constant effects of covariates over time. Such a practice has contributed to many scientific controversies in circumstances where effects of interest may evolve over time. This research tackles the problem by adopting censored quantile regression, which accommodates varying effects of covariates in a realistic and robust fashion. The proposed developments will complement standard survival analysis techniques and have the potential to substantially influence survival analysis in practice.
