Confounder Adjustment in Shape-on-Scalar Regression Model: Corpus Callosum Shape Alterations in Alzheimer’s Disease

Harshita Dogra, Shengxian Ding, Miyeon Yeon, Rongjie Liu and Chao Huang ()
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Harshita Dogra: Department of Statistics, Florida State University, Tallahassee, FL 32306, USA
Shengxian Ding: Department of Statistics, Florida State University, Tallahassee, FL 32306, USA
Miyeon Yeon: Department of Statistics, Florida State University, Tallahassee, FL 32306, USA
Rongjie Liu: Department of Statistics, Florida State University, Tallahassee, FL 32306, USA
Chao Huang: Department of Statistics, Florida State University, Tallahassee, FL 32306, USA

Stats, 2023, vol. 6, issue 4, 1-10

Abstract: Large-scale imaging studies often face challenges stemming from heterogeneity arising from differences in geographic location, instrumental setups, image acquisition protocols, study design, and latent variables that remain undisclosed. While numerous regression models have been developed to elucidate the interplay between imaging responses and relevant covariates, limited attention has been devoted to cases where the imaging responses pertain to the domain of shape. This adds complexity to the problem of imaging heterogeneity, primarily due to the unique properties inherent to shape representations, including nonlinearity, high-dimensionality, and the intricacies of quotient space geometry. To tackle this intricate issue, we propose a novel approach: a shape-on-scalar regression model that incorporates confounder adjustment. In particular, we leverage the square root velocity function to extract elastic shape representations which are embedded within the linear Hilbert space of square integrable functions. Subsequently, we introduce a shape regression model aimed at characterizing the intricate relationship between elastic shapes and covariates of interest, all while effectively managing the challenges posed by imaging heterogeneity. We develop comprehensive procedures for estimating and making inferences about the unknown model parameters. Through real-data analysis, our method demonstrates its superiority in terms of estimation accuracy when compared to existing approaches.

Keywords: imaging heterogeneity; Alzheimer’s disease; corpus callosum; square root velocity function; shape-on-scalar regression model (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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