A Bayesian Spatial Model for Imaging Genetics
share
In recent work Greenlaw et al. (Bioinformatics, 2017) have developed a Bayesian group sparse multi-task regression model for analysis in studies examining the influence of genetic variation on brain structure. Their model is developed as a generalization of the group sparse multi-task regression estimator proposed by Wang et al. (Bioinformatics, 2012) to allow for uncertainty quantification. In this paper, we further develop this methodology by extending the model to accommodate more realistic correlation structures typically seen in structural brain imaging data. First, we allow for spatial correlation in the imaging phenotypes obtained from neighbouring regions in the same hemisphere of the brain. Second, we allow for correlation in the same phenotypes obtained from different hemispheres (left/right) of the brain. We employ a bivariate conditional autoregressive spatial model for the regression errors to allow for the desired correlation structures. In addition to spatial correlation, we encourage sparsity in the regression coefficients relating each SNP to the brain imaging phenotypes by assigning a group lasso prior and using the corresponding scale-mixture representation to facilitate computation. Two approaches are developed for Bayesian computation: (i) a mean field variational Bayes algorithm and (ii) a Gibbs sampling algorithm. In addition to developing the spatial model we also incorporate Bayesian false discovery rate (FDR) procedures to select SNPs. We implement the new model, the new algorithms, and Bayesian FDR for this model in a new a release of the R package bgsmtr for imaging genetics. We apply the model to the same neuroimaging and genetic data collected as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI) considered in Greenlaw et al. (2017) and demonstrate superior performance obtained from the new spatial model.
READ FULL TEXT