CAREER: Semiparametric Regression Models for Censored Data

实证研究人员目前使用的截尾数据半参数回归方法很少超出著名的Cox比例风险回归模型。Cox模型假设协变量特定的风险函数是成比例的，这一假设在实践中往往不被满足。本文研究了加速失效时间回归和半参数线性变换模型族，其中Cox模型是其中的一员。这些模型的现有方法由于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，研究者提出了一些新的方法，包括改进的最小二乘法，m估计和基于最小化的加速失效时间模型的秩型估计，以及用于转换模型的基于一般计数过程的分数方程。新方法的一个重要特征是它们的推理过程可以很容易地用数值稳定的算法实现。拟议项目的结果将与许多科学学科相关并直接适用。他们将为许多重要领域的数据分析提供方法论工具，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，如确定与失业持续时间有关的因素、确定癌症的主要危险因素、测试防治艾滋病的新药、检查与系统组件寿命有关的因素、评估预防犯罪和药物滥用方面的潜在混淆因素。该研究涉及统计科学的许多重要领域：线性回归、生存分析、半参数、稳健统计、非参数统计和统计计算。在这方面，它将为研究生提供极好的机会，使他们接触到广泛的现代统计知识，并学习进行独立研究的重要技能。将开设一个研究课题/阅读课程和一个期刊俱乐部，以促进这些接触和提高教育经验。

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.