High-Dimensional Data Issues in Aging Research

描述(申请人提供)：这项研究的广泛目标是在生物医学研究中普遍出现的高维数据的正则化方法的发展，特别是在基因组学、表观遗传学和脑成像研究中。这项建议的具体目的是受到老龄化人口中神经退行性疾病研究中出现的问题的推动，这些研究包括阿尔茨海默病患者的表观遗传学和PIB PET研究，帕金森氏病患者痴呆症的PET研究，以及年龄相关性黄斑变性的基因组相关性研究。主要内容包括：1.提出了高维分组结构回归模型中有效的变量选择方法。在具有高维分组协变量的多元线性回归、具有高维分组协变量的广义线性模型以及同时具有高维分组响应变量和高维分组协变量的多元线性回归中，我们将考虑具有新的凸罚的正则化。将开发快速算法，将检验诸如Oracle不等式之类的理论性质，并将通过广泛的模拟来评估有限样本的性能。2.开发和评价基于函数数据的疾病诊断正则化方法。我们考虑对成像数据进行泛函线性回归模型和泛函主成分分析，以实现稀疏的群体效应。文中将对所提出方法的理论和数值性能进行检验。3.为相依测试开发新的多种测试方法。我们建议使用非齐次或组齐次的隐马尔可夫模型来刻画多个测试之间的依赖结构，并开发具有更强的能力和正确控制的错误发现率的程序。我们将检验所提出方法的渐近最优性和数值性能。4.为拟议的统计方法系统地开发用户友好的计算程序，并将其传播给卫生科学研究人员。 公共卫生相关性：该应用程序旨在解决高维度数据分析中新出现的统计问题，这些问题通常出现在生物医学和公共卫生研究中。建议的方法将特别适用于神经退行性疾病的表观遗传学、基因组、PET成像研究，包括阿尔茨海默病、帕金森氏病和老年性黄斑变性。

DESCRIPTION (provided by applicant): The broad objectives of this research are developments of regularization methods for high-dimensional data that arise commonly in biomedical studies, particularly studies in genomics, epigenetics, and brain imaging. The specific aims in this proposal are motivated by problems arising in studies of neurodegenerative disorders in an aging population including epigenetic and PiB PET studies for patients with Alzheimer's disease, PET studies of dementia in patients with Parkinson's disease, and the genome-wise association study for the age- related macular degeneration. They include: 1. Developing effective variable selection methods in high- dimensional regression models with grouped structures. We will consider the regularization with a novel convex penalty in multiple linear regression with high-dimensional grouped covariates, generalized linear models with high-dimensional grouped covariates, and multivariate linear regression with both high- dimensional grouped response variables and high-dimensional grouped covariates. Fast algorithms will be developed, theoretical properties such as oracle inequalities will be examined, and finite sample performance will be evaluated through extensive simulations. 2. Developing and evaluating regularization methods for disease diagnosis with functional data. We consider functional linear regression models and functional principal component analysis for imaging data to achieve sparse group effects. Both theoretical and numerical performance of the proposed methods will be examined. 3. Developing new multiple testing methodologies for dependent tests. We propose to use the hidden Markov models, either non-homogeneous or group homogeneous, to characterize the dependence structure among the multiple tests, and develop procedures with enhanced power and correctly controlled false discovery rate. We will examine the asymptotic optimality and numerical performance of the proposed methods. 4. Developing user-friendly computing programs systematically for the proposed statistical methodologies and disseminating them to health sciences researchers. PUBLIC HEALTH RELEVANCE: The application is intended to solve emerging statistical issues in high-dimensional data analysis, which arise commonly in biomedical and public health studies. The proposed methods will be particularly useful in epigenetic, genomic, PET imaging studies on neurodegenerative disorders including Alzheimer's disease, Parkinson's disease, and age-related macular degeneration.