High Dimensional Single-Index Bayesian Modeling of Brain Atrophy

Abstract

We propose a model of brain atrophy as a function of high-dimensional genetic information and low-dimensional covariates such as gender, age, APOE gene, and disease status. A nonparametric single-index Bayesian model of high-dimension is proposed to model the relationship using B-spline series prior on the unknown functions and Dirichlet process scale mixture of centered normal prior to the distributions of the random effects. The posterior rate of contraction without the random effect is established for a fixed number of regions and time points with increasing sample size. We implement an efficient computation algorithm through a Hamiltonian Monte Carlo (HMC) algorithm. The performance of the proposed Bayesian method is compared with the corresponding least square estimator in the linear model with horseshoe prior, Least Absolute Shrinkage and Selection Operator (LASSO) and Smoothly Clipped Absolute Deviation (SCAD) penalization on the high-dimensional covariates. The proposed Bayesian method is applied to a dataset on volumes of brain regions recorded over multiple visits of 748 individuals using 620,901 SNPs and 6other covariates for each individual, to identify factors associated with brain atrophy.