New Developments on Quantile Regression Analysis of Censored Data: Theory, Methodology and Computation

分位数回归最近作为一种有价值的半参数替代流行的Cox模型来分析审查数据。它直接模拟了生存时间；这很容易解释。更重要的是，它放松了与Cox模型相关的比例风险约束，对于异构数据尤其强大。尽管最近取得了显著进展，但一些重要和具有挑战性的统计问题仍未得到解决。例如，当样本来自观察性研究且不代表目标人群时，关于截尾分位数回归的文献有限；当被审查的数据来自涉及高维协变量的基因组学研究时；或者当由于潜在变量的合并而出现随机效应时。在这些具有挑战性的问题的激励下，该项目将开发新的方法、理论和算法，这些方法、理论和算法有可能显著推进审查分位数回归的应用。PI将严格研究提出的新程序的理论性质，并调查其在实际数据分析中的应用。审查数据出现在经济学、工程学、医学、心理学和社会学等多个领域。新的方法和理论有望对目前生存数据统计分析的知识体系做出重要贡献。特别是，该研究将为具有审查响应的高维数据分析做出及时的贡献，这在现代基因组学中具有重要的应用，并且仍然是一个相对未开发的研究领域。PI将开发有用的软件包，并将其免费提供给研究界。研究结果将纳入不同层次的统计课程。该项目还将把她的研究活动与研究生教育结合起来。来自少数民族的学生将被特别鼓励参加拟议的项目。

Quantile regression has recently emerged as a valuable semiparametric alternative to the popular Cox model for analyzing censored data. It directly models survival time; thus is easy to interpret. More importantly, it relaxes the proportional hazards constraint associated with the Cox model and is particularly powerful for heterogeneous data. Despite the remarkable recent progress, several important and challenging statistical problems remain unsolved. For example, there exists limited literature on censored quantile regression when the sample arises from an observational study and is not representative of the target population; when the censored data come from genomics studies involving high-dimensional covariates; or when random effects are present due to the incorporation of latent variables. Motivated by these challenging problems, this project will develop novel methodology, theory and algorithms, which have the potential to significantly advance the applications of censored quantile regression. The PI will rigorously study the theoretical properties of the proposed new procedures and investigate their applications in practical data analysis. Censored data arise in diverse fields such as economics, engineering, medicine, psychology and sociology. The new methodology and theory are expected to make important contributions to the current body of knowledge on statistical analysis of survival data. In particular, the proposed research will make timely contributions to high-dimensional data analysis with censored responses, which has important applications in modern genomics and is still a relatively unexplored research area. The PI will develop useful software packages and make them freely available to the research community. The research results will be incorporated in different levels of statistical courses. The PI will also incorporate her research activity with graduate education. Students from minority groups will be especially encouraged to participate in the proposed projects.