CAREER: Semiparametric Regression Models for Censored Data

目前经验研究人员对删失数据的半参数回归方法很少扩展到著名的Cox比例风险回归模型之外。考克斯模型假设协变量特有的风险函数是成比例的，这一假设在实践中往往得不到满足。本文研究了加速失效时间回归模型和半参数线性变换模型，Cox模型是其中的一员。这些模型的现有方法因其数值困难和严格的假设而变得复杂。为了避免这些复杂性，研究人员提出了一些新的方法，包括改进的最小二乘法，加速失效时间模型的M估计和基于最小化的秩型估计，以及转换模型的基于计数过程的通用得分方程。新方法的一个重要特点是，它们的推理过程可以很容易地用数值稳定的算法来实现。拟议项目的结果将相关并直接适用于许多科学学科。它们将提供方法论工具，用于分析许多重要领域的数据，包括经济学、工商管理、工业工程、医学、生物学和公共卫生。这些方法可以处理的科学研究问题的例子多种多样，如确定与失业时间有关的因素、确定癌症的主要危险因素、测试抗击艾滋病的新药、检查与系统部件寿命有关的因素、评估预防犯罪和药物滥用的潜在混杂因素。这项研究涉及到统计科学中的许多重要领域：线性回归、生存分析、半参数统计、稳健统计、非参数统计和统计计算。在这方面，它将为研究生提供接触广泛的现代统计学以及学习进行独立研究的重要技能的绝佳机会。将开发一个研究主题/阅读课程和一个期刊俱乐部，以促进这些曝光和增强教育体验。

Semiparametric regression methods for censored data currently used by empirical researchers rarely extend beyond the well-known Cox proportional hazards regression model. The Cox model assumes that covariate-specific hazard functions are proportional, an assumption often not satisfied in practice. The proposed research investigates the accelerated failure time regression and the family of semiparametric linear transformation models, of which the Cox model is a member. Existing methods for these models are complicated by their numerical difficulties and stringent assumptions. To circumvent these complications, the investigator proposes a number of new approaches, including modified least squares method, the M-estimation and a minimization-based rank-type estimation for the accelerated failure time model and a general counting process-based score equations for the transformation models. An important feature of the new approaches is that their inference procedures can be readily implemented with numerically stable algorithms.Results from the proposed project will be relevant and directly applicable to many scientific disciplines. They will provide methodologic tools for analysis of data across many important fields, including economics, business administration, industrial engineering, medicine, biology and public health. Examples of the scientific research problems that the methods can deal with are as diverse as identification of factors associated with the duration of unemployment, determination of major risk factors for cancer, testing of new drugs to combat AIDS, examination of factors associated with the lifespan of system components, evaluation of potential confounding factors in crime prevention and drug abuse. The research touches many important areas in statistical science: linear regression, survival analysis, semiparametrics, robust statistics, nonparametric statistics and statistical computing. In this connection, it will generate excellent opportunities for graduate students to have exposures to a broad spectrum of modern statistics as well as to learn vital skills in conducting independent researches. A research topic/reading course and a journal club will be developed to facilitate these exposures and enhance the educational experience.