Abstract

We propose a functional joint modeling (FJM) framework for correlating imaging re

sponses with genetic markers and clinical variables. Our FJM consists of a nonlinear multivariate

functional principal component analysis (NMFPCA) and a functional multiple-index varying coefficient model (FMVCM). The NMFPCA, with unknown link functions, is used to extract meaningful

functional principal component (FPC) scores of genetic markers, while the FMVCM identifies the

varying association of the extracted FPC scores and clinical variables with imaging data.

We

propose an efficient estimation procedure to estimate unknown functions in our FJM and a regularization approach to simultaneously select relevant features from infinite-dimensional functional

data and learn the model structure. The asymptotic convergence rate of estimators and model selection consistency are investigated. The proposed method is evaluated through simulation studies

and applied to an imaging genetic data set extracted from the Alzheimer’s Disease Neuroimaging

Initiative (ADNI) study.

∗These authors are jointly supervised this work: Xinyuan Song and Hongtu Zhu, Emails for Corre-

Information

Preprint No.SS-2023-0152
Manuscript IDSS-2023-0152
Complete AuthorsQingzhi Zhong, Xinyuan Song, Hongtu Zhu
Corresponding AuthorsHongtu Zhu
Emailshtzhu@email.unc.edu

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Acknowledgments

The authors would like to express their gratitude to the editor, and the anonymous referees for their careful reading and useful comments which led to an improved presentation

of the paper. Data used in preparation of this article were obtained from the Alzheimer’s

Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or

provided data but did not participate in analysis or writing of this report. A complete

listing of ADNI investigators can be found at: http://adni.loni.usc.edu/wp-content/

uploads/how_to_apply/ADNI_Acknowledgement_List.pdf. This work was partially supported by GRF grant 14302519 from the Research Grant Council of the HKSAR for Dr.

Song. Zhong’s work was supported by National Natural Science Foundation of China

(12401349) and China Postdoctoral Science Foundations (2024M751116).

Supplementary Materials

The Supplementary Material contains the theoretical proofs in Section 4, the estimation

procedure in Section 3, ADNI analysis given APOE-ϵ4 and disease status in Section 6,

and Web Tables 1–11 and Figures 1–7 in Sections 5 and 6.

Supplementary materials are available for download.