Regression Analysis of Asynchronous Longitudinal Functional and Scalar Data

• 成果类型: Article
• 署名作者: Li, Ting; Li, Tengfei; Zhu, Zhongyi; Zhu, Hongtu
• 署名单位: Shanghai University of Finance & Economics; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill; Fudan University; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1844211
• 发表日期: 2022
• 页码: 1228-1242
• 关键词: false discovery rate; white-matter damage; alzheimers-disease; diffusion tensor; models; bootstrap; genetics; rates

摘要

Many modern large-scale longitudinal neuroimaging studies, such as the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, have collected/are collecting asynchronous scalar and functional variables that are measured at distinct time points. The analyses of temporally asynchronous functional and scalar variables pose major technical challenges to many existing statistical approaches. We propose a class of generalized functional partial-linear varying-coefficient models to appropriately deal with these challenges through introducing both scalar and functional coefficients of interest and using kernel weighting methods. We design penalized kernel-weighted estimating equations to estimate scalar and functional coefficients, in which we represent functional coefficients by using a rich truncated tensor product penalized B-spline basis. We establish the theoretical properties of scalar and functional coefficient estimators including consistency, convergence rate, prediction accuracy, and limiting distributions. We also propose a bootstrap method to test the nullity of both parametric and functional coefficients, while establishing the bootstrap consistency. Simulation studies and the analysis of the ADNI study are used to assess the finite sample performance of our proposed approach. Our real data analysis reveals significant relationship between fractional anisotropy density curves and cognitive function with education, baseline disease status and APOE4 gene as major contributing factors. for this article are available online.