  In genetic association studies, rare variants with extremely small allele
frequency play a crucial role in complex traits, and the set-based testing
methods that jointly assess the effects of groups of single nucleotide
polymorphisms (SNPs) were developed to improve powers for the association
tests. However, the powers of these tests are still severely limited due to the
extremely small allele frequency, and precise estimations for the effect sizes
of individual SNPs are substantially impossible. In this article, we provide an
efficient set-based inference framework that addresses the two important issues
simultaneously based on a Bayesian semiparametric multilevel mixture model. We
propose to use the multilevel hierarchical model that incorporate the
variations in set-specific effects and variant-specific effects, and to apply
the optimal discovery procedure (ODP) that achieves the largest overall power
in multiple significance testing. In addition, we provide Bayesian optimal
"set-based" estimator of the empirical distribution of effect sizes. Efficiency
of the proposed methods is demonstrated through application to a genome-wide
association study of coronary artery disease (CAD), and through simulation
studies. These results suggested there could be a lot of rare variants with
large effect sizes for CAD, and the number of significant sets detected by the
ODP was much greater than those by existing methods.
