Abstract

Many biomedical studies collect high-dimensional medical imaging data

to identify biomarkers for the detection, diagnosis, and treatment of human diseases. Consequently, it is crucial to develop accurate models that can predict a

wide range of clinical outcomes (both discrete and continuous) based on imaging

data. By treating imaging predictors as functional data, we propose a residualbased alternative partial least squares (RAPLS) model for a broad class of gen-

eralized functional linear models that incorporate both functional and scalar

covariates.

Our RAPLS method extends the alternative partial least squares

(APLS) algorithm iteratively to accommodate additional scalar covariates and

non-continuous outcomes. We establish the convergence rate of the RAPLS estimator for the unknown slope function and, with an additional calibration step,

we prove the asymptotic normality and efficiency of the calibrated RAPLS estimator for the scalar parameters. The effectiveness of the RAPLS algorithm is

demonstrated through multiple simulation studies and an application predicting

Alzheimer’s disease progression using neuroimaging data from the Alzheimer’s

Disease Neuroimaging Initiative (ADNI).

Information

Preprint No.SS-2023-0418
Manuscript IDSS-2023-0418
Complete AuthorsYue Wang, Xiao Wang, Joseph G. Ibrahim, Hongtu Zhu
Corresponding AuthorsYue Wang
Emailsyue.2.wang@cuanschutz.edu

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Acknowledgments

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

Disease Neuroimaging Initiative (ADNI) database. As such, the investigators within the ADNI contributed to the design and implementation of

ADNI and/or provided data but did not participate in the analysis or

writing of this report. A complete listing of ADNI investigators can be

found at http://adni.loni.usc.edu/wpcontent/uploads/howtoapply/

ADNIAcknowledgementList.pdf. Dr. Zhu was partially supported by the

National Institutes of Health (NIH) grants 1R01AR082684, 1OT2OD038045-

01, and the National Institute on Aging (NIA) of the National Institutes of

Health (NIH) grants U01AG079847, 1R01AG085581, RF1AG082938, and

Supplementary Materials

Online supplementary material includes additional simulations and theoretical results, proofs of the main theorems, and supporting information for

the real data application.

Supplementary materials are available for download.