We develop a Bayesian bivariate spatial model for multivariate regression analysis applicable to studies examining the influence of genetic variation on brain structure. Our model is motivated by an imaging genetics study of the Alzheimer's Disease Neuroimaging Initiative (ADNI), where the objective is to examine the association between images of volumetric and cortical thickness values summarizing the structure of the brain as measured by magnetic resonance imaging (MRI) and a set of 486 single nucleotide polymorphism (SNPs) from 33 Alzheimer's disease (AD) candidate genes obtained from 632 subjects. A bivariate spatial process model is developed to accommodate the correlation structures typically seen in structural brain imaging data. First, we allow for spatial correlation on a graph structure in the imaging phenotypes obtained from a neighborhood matrix for measures on the same hemisphere of the brain. Second, we allow for correlation in the same measures obtained from different hemispheres (left/right) of the brain. We develop a mean-field variational Bayes algorithm and a Gibbs sampling algorithm to fit the model. We also incorporate Bayesian false discovery rate (FDR) procedures to select SNPs. We implement the methodology in a new release of the R package bgsmtr. We show that the new spatial model demonstrates superior performance over a standard model in our application. Data used in the preparation of this article were obtained from the ADNI database (https://adni.loni.usc.edu).

中文翻译：

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成像遗传学的贝叶斯空间模型

我们开发了用于多元回归分析的贝叶斯双变量空间模型，适用于研究遗传变异对大脑结构影响的研究。我们的模型受到阿尔茨海默病神经影像学倡议 (ADNI) 的成像遗传学研究的启发，其目的是检查体积和皮质厚度值图像之间的关联，总结通过磁共振成像 (MRI) 测量的大脑结构以及来自 632 名受试者的 33 个阿尔茨海默病 (AD) 候选基因的 486 个单核苷酸多态性 (SNP)。开发了双变量空间过程模型以适应结构性脑成像数据中常见的相关结构。第一的，我们允许在从邻域矩阵获得的成像表型中的图结构上的空间相关性，以对大脑的同一半球进行测量。其次，我们允许从大脑的不同半球（左/右）获得的相同测量值中的相关性。我们开发了一个平均场变分贝叶斯算法和一个吉布斯采样算法来拟合模型。我们还结合贝叶斯错误发现率 (FDR) 程序来选择 SNP。我们在 R 包的新版本中实施该方法 我们还结合贝叶斯错误发现率 (FDR) 程序来选择 SNP。我们在 R 包的新版本中实施该方法 我们还结合贝叶斯错误发现率 (FDR) 程序来选择 SNP。我们在 R 包的新版本中实施该方法bgsmtr。我们展示了新的空间模型在我们的应用程序中表现出优于标准模型的性能。本文所用数据来自 ADNI 数据库 (https://adni.loni.usc.edu)。