Spatial Knockoff Bayesian Variable Selection in Genome-Wide Association Studies

A primary objective in many fields is identifying the relevant predictors of a response from a large collection of variables. In genome-wide association studies, for example, variable selection methods have been adapted for identifying single nucleotide polymorphisms (SNPs) linked to phenotypic variation. The mechanisms of inheritance, evolution, recombination, and gene expression produce predictable structures in genotype, phenotype, and their associations. Guided by these mechanisms, we develop a scalable Bayesian variable selection regression model that unifies several recent advances in variable selection. Using a restricted regression approach, we demonstrate a computationally stable method for estimating SNP inclusion probabilities simultaneously with sets of basis functions that account for population structure. Motivated by the spatial arrangement of genes and their regulators, we also accommodate the non-uniform distribution among evolutionarily relevant SNPs by modeling their inclusion probabilities jointly with a Markov random field. We modify our Bayesian variable selection regression model to control the false discovery rate using hidden Markov knockoff variables that account for linkage disequilibrium and population structure in genomic data. In a simulation study, we demonstrate that our spatial Bayesian variable selection regression model controls the false discovery rate and increases power when the relevant variables are clustered. We conclude with a genome-wide association study of flowering time, a polygenic trait, measured across globally distributed accessions of Arabidopsis thaliana and find the discoveries of our method concentrate near described flowering time genes.