Identifying brain hierarchical structures associated with Alzheimer's disease using a regularized regression method with tree predictors

TL;DR

This paper introduces a regularized regression method tailored for hierarchical brain data to identify regions associated with Alzheimer's, demonstrating consistency and revealing localized effects on memory decline.

Contribution

It proposes a novel L1-type regularization for tree-structured predictors, enabling effective identification of brain regions linked to Alzheimer's disease outcomes.

Findings

Identifies brain regions where atrophy correlates with memory decline.

Shows the proposed method's consistency in model estimation and selection.

Reveals localized effects of brain atrophy at various segmentation levels.

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. By applying to a brain structural magnetic resonance imaging dataset acquired from the Alzheimer's Disease Neuroimaging Initiative, 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.