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

分位数回归是分析删失数据的考克斯模型的一个有价值的半参数替代方法。它直接模拟生存时间，因此很容易解释。更重要的是，它放宽了与COX模型相关的比例风险约束，对于异质数据尤其有效。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而不能代表目标总体时，关于删失分位数回归的文献有限；当删失数据来自涉及高维协变量的基因组研究时；或者当由于纳入潜在变量而存在随机效应时。在这些具有挑战性的问题的推动下，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动删失分位数回归的应用。PI将严格研究提出的新方法的理论性质，并研究它们在实际数据分析中的应用。被审查的数据出现在不同的领域，如经济、工程、医学、心理学和社会学。预计新的方法和理论将对目前关于生存数据统计分析的知识体系做出重要贡献。特别是，拟议的研究将为具有删失反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应用，仍是一个相对未被探索的研究领域。国际和平研究所将开发有用的软件包，并将其免费提供给研究界。研究成果将被纳入不同级别的统计课程。PI还将把她的研究活动与研究生教育结合起来。将特别鼓励来自少数群体的学生参与拟议的项目。

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.