Semiparametric Regression for Multivariate Failure Time Data

多变量失效时间数据是科学研究中经常遇到的问题。他们的分析由于成分之间的相关性、审查和时变协变量而变得非常复杂。本课题为多变量失效时间数据的半参数回归分析提供了一些新方法。针对多变量失效时间数据的组成部分，考虑了各种单变量半参数回归模型。它们包括一些熟悉的模型，如Cox模型，以及一些新的模型。从伪似然到鞅残差和估计函数，从不同的考虑提出了推理程序。新方法适用于目前两种主要的建模方法：边缘法和脆弱性法。所提出的方法通过考虑各种半参数边缘模型，通过提出几种一般推理过程，以及通过消除几乎总是与现有脆弱性方法相关的计算负担，大大增强和扩展了现有的结果。新方法的一个关键因素是一些加权经验函数的使用。多变量失效时间数据分析可以应用于工业寿命测试、临床试验和遗传流行病学等领域。一个机器部件可能反复发生故障；病人可能会经历几个器官的衰竭；表型性状可以在由血亲及其配偶组成的人类谱系中收集。通常，由于研究设计的时间框架或随访缺失，感兴趣的数据未被完全观察到；此外，风险因素，如治疗指标，可能随时间而变化。更复杂的是来自同一患者或同一家谱的观察结果之间的相关性。新的方法解决了这些挑战，并提出了多种建模和分析工具来研究多变量失效时间数据。重点是开发灵活、稳健、易于解释和易于实施的统计程序，同时保持良好的效率特性。

Yang, Song DMS-9971701ABSTRACTMultivariate failure time data are frequently encountered in scientific investigations. Their analysis is much complicated by correlations among components, censoring, and time-dependent covariates. This project initiates some new approaches in the semiparametric regression analysis of multivariate failure time data. Various univariate semiparametric regression models are considered for the components of multivariate failure time data. They include some familiar models, such as the Cox model, as well as some new models. Inference procedures are proposed from diverse considerations, ranging from pseudo likelihood to martingale residuals and estimating functions. The new procedures are applicable to the currently two main modeling approaches: the marginal and the frailty approaches. The proposed methods much enhance and extend the existing results by considering various semiparametric marginal models, by proposing several classes of general inference procedures, and by eliminating the computational burden that is almost always associated with the existing frailty methods. A key ingredient in the new approaches is the use of some weighted empirical functions.Applications of multivariate failure time data analysis may be found in industrial life testing, clinical trials and genetic epidemiology, among others. A machine component may break down repeatedly; a patient may experience failures of several organs; phenotypic traits may be collected on human pedigrees that consist of blood relatives and their spouses. Often, data of interest are not observed completely due to the time frame of the study design or loss of follow-up; also, risk factors, such as treatment indicators, may vary over time. Adding to the complication are the correlations among observations taken from the same patient or within the same pedigree. The new approaches deal with these challenges and propose various modeling and analysis tools to the study of multivariate failure time data. The emphasis is on developing statistical procedures that are flexible, robust, simple to interpret and easy to implement, while maintaining good efficiency properties.