New Approaches for Censored Quantile Regression Models via Data Augmentation

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

With the availability of massive amounts of data in the modern Big Data era, heterogeneous behavior is a common phenomenon. It is an important challenge to develop statistical methods for extracting useful insights from datasets exhibiting heterogeneity, without making strong modeling assumptions that could restrict the applicability of these methods. One efficient way of doing this is to model the quantiles of an outcome variable conditional on covariates, a method referred to as quantile regression. The current project develops novel statistical methods and computational techniques for quantile regression models when some of the observations are only partially observed. The proposed research will enable the use of the rich class of quantile regression models for a large class of applications that were previously not amenable to these techniques. The proposed framework will include the high-dimensional setting where the number of covariates could potentially exceed the number of observations, a common occurrence in many biological, medical, and economics applications. The research will be broadly disseminated in scientific journals, at conferences and seminars, and software packages in R will be developed. As the proposed research is placed at the intersection of modern statistical methodology, computation, and theory with substantial applications, it will be suitable for training graduate students with a broad range of skills. The proposed research will develop novel and efficient statistical methods for quantile regression models when the responses are subject to arbitrary censoring, that is, multiple censoring types including single, double and interval censoring can occur within the same dataset, and the covariates can be high-dimensional. Three fundamental problems in censored quantile modeling will be considered in this project: (i) develop efficient inferential methods under arbitrary censoring and study their theoretical properties, (ii) devise computationally scalable algorithms having statistically desirable properties that can handle high-dimensional covariates, and (iii) develop models that account for subgroups having heterogeneous quantile effects. A fundamental challenge that will be tackled is how data augmentation and the Bayesian framework can be efficiently utilized when an explicit likelihood is unavailable. An important feature of the methods is their computational scalability while having desirable statistical properties. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.