Functional Beta Regression Model in Alzheimer’s Disease Studies

Abstract

Scalar-on-function linear regression models are usually considered to bridge the connection between scalar clinical outcome responses and functional predictors. However, existing methods are suffering from two primary challenges, i.e., additional constraints (e.g., boundedness) on responses and feasibility in discovering meaningful imaging biomarkers. In this paper, we propose a functional beta regression model to investigate the relationship between bounded responses and both clinical and functional covariates, which can successfully address the challenge of boundness of the data mentioned above. Specifically, we develop a regularized wavelet basis method, where the coefficient function is represented through wavelet bases and an adaptive Lasso penalty is incorporated to detect the regions with significant effects. Furthermore, to solve the issues in choosing the adaptive weights, we propose a new strategy based on the functional principal component beta regression (FPCBR). The asymptotic property of the estimation procedure is investigated. The finite-sample performance of our proposed method is assessed by using Monte Carlo simulations and a real data example from the Alzheimer’s disease study.

Keywords

Functional beta regression / Bounded response / Wavelet adaptive Lasso / Alzheimer’s disease / 62J07 / 62H25 / 62J05

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School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature

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