Advancing Ultra-high-dimensional Functional Regression: Exploring Genome-wide Association Studies

Music City Center 

Genome-Wide Association Studies (GWAS) with imaging phenotypes pose significant challenges due to the complex interplay between high-dimensional genetic data and intricate spatial structures inherent in imaging data. In this paper, we develop an ultra-high-dimensional functional regression model tailored for GWAS with imaging phenotypes, incorporating genetic and non-visual contextual information. We approximate the coefficient functions using bivariate penalized splines and propose a forward selection procedure based on a functional Bayesian Information Criterion. This procedure is designed to identify critical main effects and interactions, adapting to imaging data characteristics. It achieves consistent variable selection in moderately high-dimensional settings and exhibits the sure screening property in ultra-high-dimensional scenarios. Extensive simulation studies and an analysis of data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) demonstrate the superior performance of the proposed method.

Bayesian Information Criterion

Functional linear model

Bivariate splines

Forward selection

GWAS 

Section on Statistics in Genomics and Genetics