Stable and predictive functional domain selection with application to brain images

TL;DR

This paper introduces FuDoS, a novel method for selecting brain subregions linked to clinical outcomes using 3D functional data, improving interpretability and predictive accuracy in neuroimaging analysis.

Contribution

FuDoS is a new two-stage functional domain selection method that segments brain images and evaluates subsets for association with outcomes, incorporating stability selection.

Findings

Successfully identifies relevant brain regions related to cognitive ability.

Demonstrates high predictive accuracy in simulations and real PET data.

Provides interpretable results aligned with known brain functions.

Abstract

Motivated by increasing trends of relating brain images to a clinical outcome of interest, we propose a functional domain selection (FuDoS) method that effectively selects subregions of the brain associated with the outcome. View each individual's brain as a 3D functional object, the statistical aim is to distinguish the region where a regression coefficient $\beta(t)=0$ from $\beta(t)\neq0$, where $t$ denotes spatial location. FuDoS is composed of two stages of estimation. We first segment the brain into several small parts based on the correlation structure. Then, potential subsets are built using the obtained segments and their predictive performance are evaluated to select the best subset, augmented by a stability selection criterion. We conduct extensive simulations both for 1D and 3D functional data, and evaluate its effectiveness in selecting the true subregion. We also investigate predictive ability of the selected stable regions. To find the brain regions related to cognitive ability, FuDoS is applied to the ADNI's PET data. Due to the induced sparseness, the results naturally provide more interpretable information about the relations between the regions and the outcome. Moreover, the selected regions from our analysis show high associations with the expected anatomical brain areas known to have memory-related functions.