Time-to-event data frequently arise in diverse fields including biomedical research, economics, engineering, and social sciences. As a significant extension of the classic linear models, quantile regression has growing appeal in survival analysis by offering flexibility in accommodating heterogeneous association as well as direct physical interpretation on event times. Although the foundation of quantile regression has been laid out, many important and challenging statistical issues have not yet been resolved for inferences with time-to-event data: (1) most current methods are derived only for randomly censored data; (2) existing methods for censored quantile regression either require stringent assumptions or involve nonignorable algorithmic complications. In the proposed research, the investigator aims to develop a comprehensive statistical methodology for quantile regression with survival data under various censoring and truncation mechanisms, such as random censoring, left truncation, doubly censoring, and competing risks. The proposed methodological framework will facilitate the development of inferential procedures including hypothesis testing, model diagnostics as well as robust explorations of the varying pattern of covariate effects. The new approaches are expected to preserve the ``computational-ease'' feature of the traditional quantile regression methods for complete data.
The proposed research will have significant impacts and many applications across a variety of fields. For example, applying quantile regression to medical or public health follow-up studies can better inform health professionals of the relationship between predictors, such as treatment or risk factors, and survival outcomes, such as time to morbidity or mortality. The enhanced understanding of variable effects may be effectively used in practice to advance disease treatment or prevention strategies. Applications of the proposed methods can also influence many other aspects of the society, for example, engineering quality control, and economic or social policy making. Results stemming from this project will be integrated with education through graduate level courses and special topic study groups, and will be widely disseminated through publications, conference presentations, internet postings, and free software.
