A Novel Association Test for Rare Variants Based on Algebraic Statistics

Abstract With the rapid growth of next-generation sequencing technology, more and more rare variants are available in the human genome. In recent years, the point of study has already changed direction to rare variants in genome-wide association studies (GWAS). Although a variety of approaches have been proposed to test associations between rare variants and phenotypes of interest, it is far from the end of this problem, and it is worth exploring new statistical methods based on special features of rare variants. As we all know, the most direct way is to evaluate the association in a two-way contingency table if the phenotype is a discrete variable. The numbers of observations are very close or equal to 0s for most of cells in the contingency table due to the extremely low mutation rates of rare variants. In this paper, we propose a novel association test for rare variants based on a generalization of Fisher’s exact test, and the p-value of this exact test can be computed under the multivariate hypergeometric distribution in the framework of algebraic statistics. Simulation results show that our proposed method outperforms the existing methods, despite there is heterogeneity among causal variants. We also successfully apply our method into the genetic association study of coronary artery disease and hypertension from the Wellcome Trust Case Control Consortium.