Quantile Regression with Multivariate Failure Time Data

在医学研究和其他研究领域中，研究人员经常寻求用于理解和建模多个感兴趣的变量（例如，年龄、性别、诊断）相互依赖-分位数回归是这些方法之一。在这项拟议的研究中，我们计划扩展该领域的一些最新进展，以模拟多变量事件时间（例如双胞胎或密切相关的人的疾病发生时间）。文献中对多元分位数的定义各有优缺点。我们将学习分析和几何定义，重点是半空间深度、椭球和投影。我们将通过对删失观测值的随机插补来定义分位数轮廓。然后进行了多变量失效时间的双样本检验。本文主要研究多变量失效时间分位数回归模型参数的估计方法，并讨论估计量的渐近性。有效的计算方法将被调查，特别是对于两个样本的测试。本研究的成功完成将进一步完善分位数回归理论，拓宽分位数回归方法在相关领域的应用。

In medical studies and other areas of research, researchers often seek methods for understanding and modeling how multiple variables of interest (e.g., age, gender, diagnosis) depend on each other - quantile regression is one of these methods. In this proposed research, we plan to extend some most recent developments in this area to model multivariate event times (e.g. disease occurrence times of twins or closely related persons). There are different definitions of multivariate quantile in the literature, all with advantages and drawbacks. We are going to work on both analytical and geometric definitions, with an emphasis on the halfspace depth, ellipsoids and projections. We are going to define quantile contours through random imputation for the censored observations. Then we conduct two-sample test of multivariate failure times. We are going to develop estimation methods of the multivariate failure time quantile regression model parameters and investigate the asymptotics of the estimators. Efficient computation approaches will be investigated, especially for the two-sample test. Successful completion of the proposed research will advance the theory of quantile regression and widen the application of the methods in relevant areas.