The problem of using covariates to predict shapes of objects in a regression setting is important in many fields. A formal statistical approach, termed Geodesic regression model, is commonly used for modeling and analyzing relationships between Euclidean predictors and shape responses. Despite its popularity, this model faces several key challenges, including (i) misalignment of shapes due to pre-processing steps, (ii) difficulties in shape alignment due to imaging heterogeneity, and (iii) lack of spatial correlation in shape structures. This paper proposes a comprehensive geodesic factor regression model that addresses all these challenges. Instead of using shapes as extracted from pre-registered data, it takes a more fundamental approach, incorporating alignment step within the proposed regression model and learns them using both pre-shape and covariate data. Additionally, it specifies spatial correlation structures using low-dimensional representations, including latent factors on the tangent space and isotropic error terms. The proposed framework results in substantial improvements in regression performance, as demonstrated through simulation studies and a real data analysis on Corpus Callosum contour data obtained from the ADNI study.
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Confounder Adjustment in Shape-on-Scalar Regression Model: Corpus Callosum Shape Alterations in Alzheimer’s Disease
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.
more » « less- Award ID(s):
- 1953087
- PAR ID:
- 10467690
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Stats
- Volume:
- 6
- Issue:
- 4
- ISSN:
- 2571-905X
- Page Range / eLocation ID:
- 980 to 989
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/stats6040061
