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，在设计中起着至关重要的作用 以及各种医学研究的分析，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区分开来的是审查，这使得故障时间数据的分析具有唯一性和 这很困难，可能会以不同的形式出现。这项提案将调查医学领域的两个基本问题 关于几种类型的故障时间的研究、治疗比较和相对风险估计 涉及区间截尾或区间截尾故障时间数据的数据。对这些数据的分析已经被 引起了包括政府官员在内的医学调查人员和统计学家越来越多的关注 机构和制药公司。具体地说，拟议的研究包括三个目标，它们是 为1)治疗比较和抽样制定适当和/或有效的统计程序 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 回归分析二.众所周知，处理比较可能是最基本和最普遍的 在医学研究和这种研究的设计中所要求的任务，一个关键因素是确定 所需样本大小。在区间截尾数据的情况下，提出了一些比较步骤。 然而，它们中的大多数在应用上都是有限的，更重要的是，它们都不能用于样本大小 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。估计相对风险或更普遍的协变量效应是医学上的另一项常见任务 无进展生存肿瘤学研究等研究。拟议的研究将制定适当的或 当面对包括聚集数据在内的各种类型的区间删失数据时，它的有效方法。目标2 将集中在以下情况下的审查可以被视为独立于故障时间变量 学习，而目标3将处理独立性不真实的情况。统计程序或 将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，并 帮助人们对它们进行正确和/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.