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Theory and Methods

Regression Analysis of Asynchronous Longitudinal Functional and Scalar Data

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Pages 1228-1242 | Received 07 Jul 2019, Accepted 18 Oct 2020, Published online: 08 Dec 2020
 

Abstract

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. Supplementary materials for this article are available online.

Supplementary Materials

Assumptions, more explanations on the data structure, all the technical proofs, and additional figures are provided in the supplementary materials.

Funding

Zhongyi Zhu’s research was partially supported by National Science Foundation of China grants 11671096, 112071087, and 11731011. Ting Li’s work was partially supported by the Fundamental Research Funds for the Central Universities.

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