Quantile Regression with Multivariate Failure Time Data

在医学研究和其他研究领域，研究人员经常寻求方法来理解和建模感兴趣的多个变量(例如，年龄、性别、诊断)是如何相互依赖的-分位数回归就是这些方法之一。在这项拟议的研究中，我们计划扩展这一领域的一些最新发展，以建立多变量事件时间的模型(例如，双胞胎或近亲的疾病发生时间)。文献中对多元分位数有不同的定义，各有优缺点。我们将在解析和几何定义上工作，重点是半空间深度、椭球体和投影。我们将通过随机归因于删失的观测值来定义分位数轮廓。然后对多变量失效次数进行两样本检验。我们将发展多元失效时间分位数回归模型参数的估计方法，并研究估计量的渐近性。将研究有效的计算方法，特别是对于两个样本的测试。这项研究的成功完成，将推动分位数回归理论的发展，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.