High-Dimensional Data Issues in Aging Research

描述（由申请人提供）：本研究的广泛目标是发展高维数据的正则化方法，这些方法通常出现在生物医学研究中，特别是基因组学、表观遗传学和脑成像研究中。本提案的具体目标是由老龄化人群中神经退行性疾病研究中出现的问题所驱动的，包括阿尔茨海默病患者的表观遗传学和PiB PET研究，帕金森病患者痴呆的PET研究，以及年龄相关性黄斑变性的基因组关联研究。它们包括：1；在具有分组结构的高维回归模型中开发有效的变量选择方法。我们将考虑具有高维组协变量的多元线性回归、具有高维组协变量的广义线性模型以及具有高维组响应变量和高维组协变量的多元线性回归中的一种新型凸惩罚的正则化。快速算法将被开发，理论性质如oracle不等式将被检查，有限样本性能将通过广泛的模拟评估。2. 开发和评估功能数据疾病诊断的正则化方法。我们考虑功能线性回归模型和功能主成分分析成像数据来实现稀疏组效应。所提出的方法的理论和数值性能将被检查。3. 为相关测试开发新的多重测试方法。我们建议使用隐马尔可夫模型（非齐次或群齐次）来表征多个测试之间的依赖结构，并开发具有增强功能和正确控制错误发现率的程序。我们将检验所提出的方法的渐近最优性和数值性能。4. 系统地为提出的统计方法开发用户友好的计算程序，并将其传播给健康科学研究人员。

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.