Topics in Multivariate Survival Analysis and Counting Processes

多元生存分析是一个发展迅速的领域，在医学、遗传流行病学、计量经济学、天文学等领域有着广泛的应用。这个项目的目的是发展在多变量生存数据分析中出现的一些半参数模型的估计方法。在这个方案中讨论两个项目。第一种是关于部分变换模型的估计，特别是在部分Cox回归和部分加速失效时间模型中的估计。这些模型在涉及在两个或更多时间尺度上记录的时间测量的多变量模型的拟合优度测试和分析中很有用。为了估计的目的，我们将使用局部多项式拟合。第二个项目涉及多变量脆弱性模型。分析这些模型的一种常用方法是非参数极大似然估计，估计的形式来自脆弱模型的计数过程定义。后者往往不适用于多变量数据，因为它们可能涉及在几个时间尺度上记录的时间测量，或者是不可预测的审查和协变量过程。在这个项目中，我们考虑了一种特别的估计方法，用于分析具有年龄尺度上记录的多变量失效时间过程的聚类族数据，该估计方法允许合并左截断和适应在分析家族性数据时产生的日历时间效应。第一个项目的结果可以应用于任何涉及删失观测的数据集。第二个项目的结果将用于分析瑞典UMEA的澳大利亚双胞胎登记处和人口数据库提供的数据集。

Multivariate survival analysis is a rapidly growing area with a wide range of applications in medicine, genetic epidemiology, econometrics, astronomy and other fields. The purpose of this project is to develop estimation methods in some semiparametric models arising in analyses of multivariate survival data.Two projects are discussed in this proposal. The first one deals with estimation in partial transformation models, specifically in partial Cox regression and partial accelerated failure time model. These models are useful in goodness-of-fit testing and analyses of multivariate models involving time measurements recorded on two or more time scales. For estimation purposes we shall use local polynomial fitting.The second project deals with multivariate frailty models. A common approach towards analysis of these models rests on nonparametric maximum likelihood estimation with the form of the estimates derived from the counting process definition of the frailty models. The latter often fails to apply to multivariate data since they can involve time measurements recorded on several time scales, or nonpredictable censoring and covariate processes. In this project we consider an ad hoc estimation method designed for analysis of clustered familial data with multivariate failure time processes recorded on age scale, The estimation method allows to incorporate left truncation and accommodate calendar time effects arising in analyses of familial data.The results of the first project can be applied to any dataset involving censored observations. Results of the second project will be applied towards analysis of datasets provided by the Australian Twin Registry and Demographic Data Base, Umea, Sweden.