Bayesian Generalized Low Rank Regression Models for Neuroimaging Phenotypes and Genetic Markers

We propose a Bayesian generalized low-rank regression model (GLRR) for the analysis of both high-dimensional responses and covariates. This development is motivated by performing searches for associations between genetic variants and brain imaging phenotypes. GLRR integrates a low rank matrix to approximate the high-dimensional regression coefficient matrix of GLRR and a dynamic factor model to model the high-dimensional covariance matrix of brain imaging phenotypes. Local hypothesis testing is developed to identify significant covariates on high-dimensional responses. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. A simulation study is performed to evaluate the finite sample performance of GLRR and its comparison with several competing approaches. We apply GLRR to investigate the impact of 1071 SNPs on top 40 genes reported by AlzGene database on the volumes of 93 regions of interest (ROI) obtained from Alzheimer’s Disease Neuroimaging Initiative (ADNI). Supplementary materials for this article are available online.

本文提出一种贝叶斯广义低秩回归模型（Bayesian generalized low-rank regression model, GLRR），用于同时分析高维响应变量与协变量。该模型的研发旨在探索遗传变异与脑影像表型之间的关联。GLRR通过低秩矩阵近似高维回归系数矩阵，并结合动态因子模型对脑影像表型的高维协方差矩阵进行建模。本文提出局部假设检验方法，以识别对高维响应变量具有显著影响的协变量。后验推断通过高效的马尔可夫链蒙特卡洛（Markov chain Monte Carlo, MCMC）算法完成。为评估GLRR的有限样本性能并将其与多种竞争性方法进行对比，本文开展了模拟实验。我们将GLRR应用于分析1071个单核苷酸多态性（Single Nucleotide Polymorphisms, SNPs）对阿尔茨海默病神经影像倡议（Alzheimer’s Disease Neuroimaging Initiative, ADNI）采集的93个感兴趣区（regions of interest, ROI）体积的影响，这些位点对应AlzGene数据库报道的前40个基因。本文的补充材料可在线获取。