Faculty, Staff and Student Publications
Publication Date
9-1-2023
Journal
Biometrics
Abstract
Brain segmentation at different levels is generally represented as hierarchical trees. Brain regional atrophy at specific levels was found to be marginally associated with Alzheimer's disease outcomes. In this study, we propose an ℓ1 -type regularization for predictors that follow a hierarchical tree structure. Considering a tree as a directed acyclic graph, we interpret the model parameters from a path analysis perspective. Under this concept, the proposed penalty regulates the total effect of each predictor on the outcome. With regularity conditions, it is shown that under the proposed regularization, the estimator of the model coefficient is consistent in ℓ2 -norm and the model selection is also consistent. When applied to a brain sMRI dataset acquired from the Alzheimer's Disease Neuroimaging Initiative (ADNI), the proposed approach identifies brain regions where atrophy in these regions demonstrates the declination in memory. With regularization on the total effects, the findings suggest that the impact of atrophy on memory deficits is localized from small brain regions, but at various levels of brain segmentation. Data used in preparation of this paper were obtained from the ADNI database.
Keywords
Humans, Alzheimer Disease, Brain, Neuroimaging, Regression Analysis, Atrophy, hierarchical predictors, path analysis, penalized linear models, structural neuroimaging, tree-based regularization
DOI
10.1111/biom.13775
PMID
36263865
PMCID
PMC10115907
PubMedCentral® Posted Date
9-15-2025
PubMedCentral® Full Text Version
Author MSS
Published Open-Access
yes
