Bayesian hierarchical hypothesis testing in large-scale genome-wide association analysis

Variable selection and large-scale hypothesis testing are techniques commonly used to analyze high-dimensional genomic data. Despite recent advances in theory and methodology, variable selection and inference with highly collinear features remain challenging. For instance, collinearity poses a great challenge in genome-wide association studies involving millions of variants, many of which may be in high linkage disequilibrium. In such settings, collinearity can significantly reduce the power of variable selection methods to identify individual variants associated with an outcome. To address such challenges, we developed a Bayesian hierarchical hypothesis testing (BHHT)-a novel multiresolution testing procedure that offers high power with adequate error control and fine-mapping resolution. We demonstrate through simulations that the proposed methodology has a power-FDR performance that is competitive with (and in many scenarios better than) state-of-the-art methods. Finally, we demonstrate the feasibility of using BHHT with large sample size ( n similar to 300,000) and ultra dimensional genotypes (similar to 15 million single-nucleotide polymorphisms or SNPs) by applying it to eight complex traits using data from the UK-Biobank. Our results show that the proposed methodology leads to many more discoveries than those obtained using traditional SNP-centered inference procedures. The article is accompanied by open-source software that implements the methods described in this study using algorithms that scale to biobank-size ultra-high-dimensional data.