Functional Censored Quantile Regression for Investigating Heterogeneous Effects in Survival Data

项目摘要/摘要 在生物医学研究中，经常收集曲线、图像和物体形式的功能生物标记物 如今，由于数据采集技术的快速发展。在最近的研究中，有越来越多的 意识到功能性生物标记物和结果之间的潜在关联可能倾向于 相当大的异质性。这些不同的关联通常会让人们对科学fic的发现有更深入的了解 包含SignifiCan含义，但往往被许多现有的功能数据分析过程所忽视 狭隘地关注回应意味着。我们的建议旨在为研究人员提供其他工具来探索 功能生物标志物与生存时间之间关系的综合信息。 与假设协变量的恒定影响的统计模型不同，分位数回归(QR)具有 比较了不同的影响，并可能揭示结果对协变量的更详细的依赖结构。 遗憾的是，功能数据的QR几乎没有被研究过。这项提议的目标是使QR 适用于功能生存数据回归异质性研究的框架，以开发可靠的 和有效的fi估计方法，并对功能生物标志物的影响做出准确的推断。我们 将提出一种“局部”功能审查QR(FCQR)方法来评估功能生物标记物的影响 在单个或多个预先指定的分位数水平上的生存时间，并发展了相关的显著fi检验 测试功能生物标记物的影响(目标1)。然后我们将开发一种“全球”的FCQR方法来调查 功能生物标志物在分位数水平的区域内对生存时间的不同影响，这将提供 研究人员对协变量-反应关联有一个全面的了解。此外，还有两个推论 程序，包括估计标准误差的Bootstrap重采样法和基于鞅的 将开发模型诊断学(目标2)。此外，我们还将把“局部”FCQR方法推广到纵向-- 用于动态预测剩余寿命的功能性生物标志物的NAL测量(目标3)。此外，我们还将发展 fi使用的统计软件很好地实现了所提出的方法。 我们建议的创新至少有三个方面。首先，它将产生可靠和有效的fiFCQR工具 这有助于识别fi阳离子和评估新的有价值的功能生物标志物。第二，成功的 我的建议的完成可以标志着fi可以促进QR和半/非参数统计理论的发展，并且 进一步，拓宽它们在许多生物医学研究中的应用。第三，我们提出的方法也将有助于 作为fl可扩展平台，用于检查功能数据中的异构性。它们可以很容易地扩展到其他 公共卫生应用。

Project Summary/Abstract Functional biomarkers that are in the form of curves, images, and objects, are often collected in biomedical studies nowadays, due to the rapid advances in data acquisition technology. In recent research, there has been growing awareness that the underlying association between the functional biomarkers and outcomes may be prone to considerable heterogeneity. Those heterogeneous associations often shed insight on scientific discoveries and entail significant implications, but tend to be overlooked by many existing functional data analysis procedures with a narrow focus on the response mean. Our proposal aims at offering researchers alternative tools to explore the comprehensive information of the relationship between functional biomarkers and survival time. In contrast to statistical models that presume constant effects of covariates, quantile regression (QR) ac- commodates varying effects and may reveal more detailed dependence structure of outcomes on covariates. Regretfully, QR for functional data has barely been studied. The objective of this proposal is to make the QR framework applicable for investigating the regression heterogeneity in functional survival data, to develop reliable and efficient estimation approaches, and to obtain sharp inference on the effects of functional biomarkers. We will propose a “local” functional censored QR (FCQR) method to evaluate the impacts of functional biomarkers on the survival time at a single or multiple pre-specified quantile levels and develop a related significance test for testing the impact of functional biomarkers (Aim 1). Then we will develop a “global” FCQR method to investigate the varying effects of functional biomarkers on the survival time over a region of quantile levels, which will provide researchers with a comprehensive picture about the covariates-response association. In addition, two inference procedures, including a bootstrap resampling method for estimating the standard errors and the martingale-based model diagnostics, will be developed (Aim 2). Moreover, we will extend the “local” FCQR method to longitudi- nal measurements of functional biomarkers for dynamic prediction of residual life (Aim 3). Also, we will develop statistical software that efficiently implements the proposed methods. The innovation of our proposal is at least three-fold. Firstly, it will produce reliable and efficient FCQR tools that facilitate the identification and evaluation of new valuable functional biomarkers. Secondly, the successful completion of my proposal can significantly advance the theory of QR and semi/non-parametric statistics, and further, broaden their applications in lots of biomedical research. Thirdly, our proposed methods will also serve as a flexible platform for examining the heterogeneity in functional data. They can be readily extended to other public health applications.