Semi-parametric joint models for longitudinal and time to event data

描述(由申请人提供)：纵向生物标记物和事件间隔时间数据的半参数联合模型本项目的目标是开发新的统计方法来联合建模纵向生物标记物轨迹和事件间隔时间数据。建议的方法是有动机的，并将应用于三个主要应用：1)通过器官共享联合网络(UNOS)获得的肝移植和肾脏移植；2)通过美国肾脏数据系统(USRDS)获得的终末期肾脏疾病(ESRD)数据；以及3)宾夕法尼亚大学收集的先前剖腹产(VBAC)数据。主要的动机来自于这样一个事实，即生物标记物通常是潜在疾病过程的替代品，在建模到事件发生的时间数据时需要被视为替代结果，并且生物标记物的轨迹通常需要允许随时间变化的灵活模式的非参数模型，例如平滑曲线、形状注册曲线和分支曲线。另一个动机是，在预测死亡等事件时，生物标志物的累积效应可能比同时发生的值更合适，因此我们建议将功能数据分析和生存分析的思想结合起来。我们将首先建立功能加速失效时间(AFT)模型及其与功能混合效应模型的连接模型。然后，我们将该框架扩展到包括非高斯纵向生物标记物。第三个具体目标将发展一系列曲线配准和分支曲线的非线性函数混合效应模型，以及它们与事件间隔时间数据的联合模型。每个具体目标包括方法开发、理论研究、经验模拟和应用。我们还将开发一个用户友好的软件包，其中包括所有拟议的功能，并将其发布到公共领域。

DESCRIPTION (provided by applicant): Semiparametric joint models for longitudinal biomarkers and time to event data The goal of this project is to develop novel statistics methods to jointly model longitudinal biomarker trajectories and time to event data. The proposed methods are motivated and will be applied to three major applications: 1) liver transplant and kidney transplant available through the United Network for Organ Sharing (UNOS), 2) the end stage renal disease (ESRD) data available through the United States Renal Data System (USRDS), and 3) the Vaginal birth after a prior cesarean (VBAC) data collected at the University of Pennsylvania. The main motivation comes from the fact that biomarkers are usually the surrogates of the underlying disease process and need to be treated as surrogate outcomes in modeling the time to event data, and the trajectories of the biomarkers usually require nonparametric models allowing flexible patterns over time, such as smooth curves, shape-registered curves, and branching curves. Another motivation is that in predicting the event such as death, the cumulative effects of the biomarkers may be more appropriate than the concurrent values, and therefore we propose to combine the ideas of functional data analysis and survival analysis. We will first develop the functional accelerated failure time (AFT) models and their join models with functional mixed effects models. We then extend this framework to include non-Gaussian longitudinal biomarkers. The third specific aims will develop a series of nonlinear functional mixed effect models for curve registration and branching curves, and their joint models with time to event data. Each specific aim includes methods development, theoretical studies, empirical simulations and applications. We will also develop a user-friendly software package that includes all the proposed features and post it to public domain.