Treatment Comparison and Estimation of Relative Risks with Failure Time Data

摘要 故障时间数据的统计分析一直是设计的基石，起着至关重要的作用 和分析各种医学研究，如随机临床试验。故障时间数据的一个关键特征是， 将它们与所有其他类型的数据分开是删失，这使得故障时间数据的分析是唯一的， 困难，并可能以不同的形式出现。这一建议将探讨两个基本问题，在医疗 研究、治疗比较和相对风险估计，关于几种类型的失效时间 涉及区间删失或区间删失失效时间数据的数据。对这些数据的分析， 越来越受到医学研究者和统计学家的重视，包括政府部门的统计学家 机构和制药公司。具体而言，拟议的研究包括三个目标，他们是 开发适当和/或有效的统计程序，用于1）治疗比较和采样 规模计算，2）相对风险估计和回归分析I，3）相对风险估计和 回归分析2.众所周知，治疗比较可能是最基本和最常见的 在医学研究中所需的任务和设计这样的研究，一个关键因素是确定 所需样本量。在区间删失数据的情况下，已经提出了一些比较程序。 然而，它们大多数在应用中受到限制，更重要的是，它们都不能用于样本量 计算.目标1将开发新的比较程序，允许并因此给出样本量的公式 计算.估计相对风险或更一般的协变量效应是医学领域的另一项常见任务。 研究，如无进展生存肿瘤学研究。该研究将开发适当的或 有效的方法，当一个人面对各种类型的区间删失数据，包括聚类数据。目的2 将集中在删失可以被认为是独立的故障时间变量的情况下， 目标3将处理独立性不成立的情况。统计程序或 在这项拟议研究中开发的工具将使有关研究的设计成为可能， 帮助人们进行正确和/或有效的分析。

ABSTRACT The statistical analysis of failure time data has been the cornerstone and plays an essential role in the design and analysis of various medical studies such as randomized clinical trials. A key feature of failure time data that separates them from all other types of data is censoring, which makes the analysis of failure time data unique and difficult and can occur in different forms. This proposal will investigate two fundamental problems in medical studies, treatment comparison and estimation of relative risks, with respect to several types of failure time data that involve interval-censoring or interval-censored failure time data. The analysis of such data has been attracting more and more attention among medical investigators and statistician including these in government agencies and pharmaceutical companies. Specifically, the proposed research consists of three aims and they are the development of appropriate and/or efficient statistical procedures for 1) treatment comparison and sample size calculation, 2) estimation of relative risks and regression analysis I, and 3) estimation of relative risks and regression analysis II. It is well-known that treatment comparison is perhaps the most basic and commonly required task in medical studies and for the design of such studies, a key element is the determination of the required sample size. In the case of interval-censored data, some comparison procedures have been proposed. However, most of them are limited in applications and more importantly, none of them can be used for sample size calculation. Aim 1 will develop new comparison procedures that allow and thus give formulas for the sample size calculation. Estimation of relative risks or more generally covariate effects is another common task in medical studies such as progression-free survival oncology studies. The proposed research will develop appropriate or efficient approaches to it when one faces various types of interval-censored data including clustered data. Aim 2 will focus on situations where the censoring can be regarded to be independent of the failure time variable under study, while aim 3 will deal with situations where the independence is not true. The statistical procedures or tools that will be developed in this proposed research will make the design of the concerned studies possible and help one to conduct correct and/or efficient analysis of them.