Semiparametric Regression for Multivariate Failure Time Data

杨，宋，DMS-9971701ABSTRACT在科学研究中经常遇到多变量失效时间数据。他们的分析因成分之间的相关性、审查和依赖时间的协变量而变得复杂得多。该项目在多变量失效时间数据的半参数回归分析中开创了一些新的方法。对于多变量失效时间数据的分量，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，如考克斯模型，以及一些新的模型。推论过程是从各种考虑因素提出的，从伪似然到鞅残差和估计函数。新方法适用于目前两种主要的建模方法：边际建模方法和脆弱建模方法。所提出的方法通过考虑各种半参数边际模型，提出了几类通用的推理过程，并消除了几乎总是与现有脆弱方法相关的计算负担，从而大大增强和扩展了现有的结果。新方法的一个关键因素是使用了一些加权经验函数。多变量失效时间数据分析在工业寿命测试、临床试验和遗传流行病学等领域都有应用。一个机器部件可能会反复出现故障；病人可能会经历几个器官的故障；表型特征可能会收集到由血亲及其配偶组成的人类谱系。通常，由于研究设计的时间框架或失去随访，没有完全观察到感兴趣的数据；此外，风险因素，如治疗指标，可能会随着时间的推移而变化。增加并发症的是来自同一患者或同一家系内的观察结果之间的相关性。新的方法应对了这些挑战，并提出了各种建模和分析工具来研究多变量故障时间数据。重点是制定灵活、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。

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.