Quantile regression in brain imaging data analysis

这项建议的目标是双重的。从统计学角度出发，将发展新的分位数回归方法，在功能变系数模型（FVCM）和空间变系数模型（SVCM）中，允许系数效应随位置变化，以应对具有遗传异方差的预处理图像数据，如扩散张量图像（DTI）、磁共振图像（MRI）等图像。从应用的角度来看，FVCM和SVCM中提出的分位数回归方法将使神经科学家能够了解人类大脑（从扩散纤维束、灰质和白质方面）如何受到一些感兴趣的协变量（如性别、年龄和精神障碍（如自闭症）对角线状态）的影响。虽然这些方法是由脑成像数据驱动的，但它们也能够分析功能数据、二维（2D）表面和三维（3D）体积数据。本文重点关注三个不同但相关的研究课题：(1)分位数回归在FVCM中的应用及其在DTI数据分析中的应用；(2) SVCM分位数回归及其在MRI数据分析中的应用；(3)纵向响应的FVCM和SVCM分位数回归及其在神经影像学数据分析中的应用。这项研究将扩大现有工作的范围，并为解决神经科学以及其他各种学科（如流行病学、环境科学、社会学和生物学）中出现的实际问题提供新的统计工具。因此，它对统计理论和应用都有潜在的影响。

The objectives of this proposal are twofold. From the statistical perspective, new quantile regression methodologies in functional varying coefficient models (FVCM) and spatial varying coefficient models (SVCM), where coefficient effects are allowed to change with location, will be developed to cope with preprocessed imaging data with inherited heteroscedasticity, such as, diffusional tensor image (DTI), magnetic resonance image (MRI) and other images. From the application perspective, the proposed quantile regression methods in FVCM and SVCM will enable neuroscientists to understand how human brains (in terms of diffusion fiber tracts, gray matter and white matter) are affected by some covariates of interest, such as gender, age and mental disorder (e.g. autism) diagonal status. Although the methods are motivated by brain imaging data, they are also capable of analyzing functional data, 2-dimensional (2D) surface and 3-dimensional (3D) volume data. In particular, the proposal focuses on three different but related research topics: (1) quantile regression in FVCM and its applications in DTI data analysis; (2) quantile regression in SVCM and its applications in MRI data analysis; (3) quantile regression in FVCM and SVCM with longitudinal responses and its applications in neuroimaging data analysis. This research will broaden the scope of current work and provide new statistical tools for solving practical problems arising from not only neuroscience but also other various disciplines such as epidemiology, environmental science, sociology, and biology. Therefore, it has potential impact on both statistical theory and applications.