Proportional Hazards Model for Various Types of Censored Survival Data with Longitudinal Covariates

具有纵向协变量的各类删失生存数据的比例风险模型

• 批准号: 0905772
• 负责人: Jian-Jian Ren
• 金额: $ 18万
• 依托单位: The University of Central Florida Board of Trustees
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2012-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0905772&HistoricalAwards=false
• 关键词: Proportional; Hazards; Model; Various; Types

The interrelationships between time-to-event (survival time) variable and longitudinal covariates is often the primary research interest in medical and epidemiological studies. Due to the challenges encountered in some important clinical trials on AIDS and cancer research, recently the statisticians started modeling survival data and longitudinal data jointly via Cox's proportional hazards model. Such a joint modeling procedure or methodology has broad applications in many scientific research fields, but it is a considerably difficult problem due to censoring on the survival time and that the covariate process is only observed at some given time points. Up to now, statistical methods on this topic have not been fully or well developed, while the importance and needs for developing these methods have become more evident when the proposer and her collaborators recently encountered some more complicated problems which have not been studied in statistical literature; see examples listed below. Specifically, there have not been any modeling procedures that directly study the relationship between survival time and within-subject historic patterns of change in longitudinal covariates, nor have there been any works on joint modeling doubly censored or interval censored survival data together with (intensive or multi-phase intensive) longitudinal covariates, which is far more challenging than right censored data problem. In fact, there have been no published works on the Cox model with doubly censored data, not even for the case with time-independent covariates. In this research, asymptotic methods and simulations will be mainly used in the studies, and the issues under consideration include: (a) derivation of the empirical likelihood based MLE for the Cox model with longitudinal covariates for right censored, doubly censored and interval censored survival data, respectively; (b) computation algorithms for the MLE; (c) asymptotic properties of the MLE; (d) Wilk's theorem for the MLE; (e) goodness-of-fit tests for the Cox model; (f) comparison with alternative methods. At least two Ph.D. students of the proposer will be involved in and benefit from the proposed research. The new statistical methodology to be developed in this project has direct impact to medical research, epidemiology, social and behavioral sciences, etc. For instance, the data examples which we have encountered and motivate the research of this project include the following problems on joint modeling survival time and longitudinal covariates. In a prostate cancer study on mice, part of the research focus is joint modeling interval censored survival time and longitudinal covariates. In a smoking cessation study, the research focus is joint modeling right censored survival time and intensive longitudinal covariates. In a recent study of child development, the research focus is joint modeling doubly censored survival time and multi-phase intensive longitudinal covariates.

事件时间（生存时间）变量与纵向协变量之间的相互关系通常是医学和流行病学研究的主要研究兴趣。由于在一些有关艾滋病和癌症研究的重要临床试验中遇到的挑战，统计学家开始通过COX的比例危害模型共同对生存数据和纵向数据进行建模。这种联合建模程序或方法在许多科学研究领域都有广泛的应用，但是由于对生存时间的审查，这是一个相当困难的问题，并且仅在某些给定时间点观察到协变量过程。到目前为止，有关该主题的统计方法尚未完全或发达，而当提议者和她的合作者最近遇到了一些更复杂的问题时，开发这些方法的重要性和需求变得更加明显，这些问题尚未在统计文献中研究过;请参阅下面列出的示例。具体而言，没有任何建模程序可以直接研究纵向协变量变化的生存时间与受试者内部历史模式之间的关系，也没有任何有关联合建模的著作，与（密集或深度审查生存数据）一起进行了审查或间隔审查（密集或深度）多阶段密集型）纵向协变量，这比正确的审查数据问题更具挑战性。实际上，在Cox模型上没有具有双重审查数据的发表作品，甚至没有时间无关的协变量。在这项研究中，渐近方法和模拟将主要用于研究中，所考虑的问题包括：（a）基于经验可能性的MLE推导了具有纵向协变量的COX模型的基于经验可能性的MLE，可用于纵向审查，双重审查，双重审查，间隔审查的生存存活率数据分别； （b）MLE的计算算法； （c）MLE的渐近特性； （D）Wilk的Mle定理； （e）COX模型的合适性测试； （f）与替代方法进行比较。至少有两个博士学位提议者的学生将参与并受益于拟议的研究。该项目中要开发的新统计方法对医学研究，流行病学，社会和行为科学等有直接影响。生存时间和纵向协变量。在对小鼠的前列腺癌研究中，研究重点的一部分是关节建模间隔审查生存时间和纵向协变量。在一项戒烟研究中，研究重点是关节建模右审查生存时间和密集的纵向协变量。在最近关于儿童发育的研究中，研究重点是联合建模双重审查的生存时间和多相密集的纵向协变量。