Residual-based Alternative Partial Least Squares for Generalized Functional Linear Models

TL;DR

This paper introduces RAPLS, a novel residual-based partial least squares method for generalized functional linear models, effectively handling high-dimensional imaging data for clinical outcome prediction.

Contribution

It extends the APLS algorithm to incorporate scalar covariates and non-continuous outcomes, with theoretical guarantees and practical validation.

Findings

Demonstrates convergence rate of RAPLS estimator

Proves asymptotic normality and efficiency of calibrated RAPLS

Shows improved prediction accuracy in Alzheimer's disease data

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 residual-based alternative partial least squares (RAPLS) model for a broad class of generalized 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).