Joint Modelling of Survival and Longitudinal Data

描述（由申请人提供）：在实验性老化研究和其他纵向研究中，观察关注的事件时间（称为生存时间）以及在几个时间点测量的纵向协变量沿着变得越来越常见。科学界越来越感兴趣的是同时对这两个过程进行建模，以探索它们之间的关系，并从模型构建过程中的每个组件中借用力量。 由于计算环境的快速改善，这种联合建模方法已经变得可行。在过去的十年中，已经提出了相当多的创新方法，但它们通常涉及强大的模型限制。该提案旨在开发限制较少的替代模型，并针对相关的计算和理论挑战。我们将开发： 1.提供模型灵活性的纵向协变量的非参数混合效应法 2.更一般的生存模型和方法，以及生存组件的模型检查工具; 3.减轻计算负担和提供计算稳定性的筛子法 4.便于使用的软件，包括目标1-3在老化研究中的应用; 5.用于合并不可删失和各种测量误差结构的附加工具。 这项研究的动机是几项老龄化研究，这些研究涉及生殖模式和寿命之间的关系。它从一个称为函数数据分析的相关领域中提取工具，将观察到的纵向数据视为平滑底层过程的分散实现，可能存在测量误差。这些新方法不仅将揭示寿命与生殖史等纵向标志物之间的关系，而且还将广泛适用于临床和流行病学研究。它们涉及新兴的统计工具，这些工具将提供先进的方法和灵活的方法来模拟复杂的生物系统，并将促进模型检查。

DESCRIPTION (provided by applicant): In experimental aging studies and other longitudinal studies, it has become increasingly common to observe an event time of interest, called survival time, along with longitudinal covariates measured at several time points. A growing interest in the scientific community is to model both processes simultaneously to explore their relationship and to borrow strength from each component in the model building process. Such joint modeling approaches have become feasible due to the rapidly improving computing environment. Quite a few innovative approaches have been proposed in the last decade, but they typically involve strong model restrictions. This proposal aims at developing less restrictive alternative models and targets the associated computational and theoretical challenges. We will develop: 1. Nonparametric mixed-effects approach for longitudinal covariates that provide model flexibility; 2. More general survival models and approaches, and model checking tools for the survival component; 3. The method of sieves to alleviate the computational burden and to provide computational stability; 4. User-friendly software including applications of aims 1-3 to aging studies; 5. Additional tools to incorporate non-ignorable censoring and various measurement error structures. This research is motivated by several aging studies that address the relationship between patterns of reproduction and longevity. It draws tools from a related area called Functional Data Analysis, viewing the observed longitudinal data as scattered realizations of a smooth underlying process, possibly observed with measurement errors. The new approaches will not only shed light on the relationship between life-span and longitudinal markers such as reproductive histories, but will also be broadly applicable to clinical and epidemiological studies. They involve emerging statistical tools that will provide advanced methodology and flexible approaches to model complex biological systems, and will also facilitate model checking.