Divided-and-combined omnibus test for genetic association analysis with high-dimensional data

Advances in biologic technology enable researchers to obtain a huge amount of genetic and genomic data, whose dimensions are often quite high on both phenotypes and variants. Testing their association with multiple phenotypes has been a hot topic in recent years. Traditional single phenotype multiple variant analysis has to be adjusted for multiple testing and thus suffers from substantial power loss due to ignorance of correlation across phenotypes. Similarity-based method, which uses the trace of product of two similarity matrices as a test statistic, has emerged as a useful tool to handle this problem. However, it loses power when the correlation strength within multiple phenotypes is middle or strong, for some signals represented by the eigenvalues of phenotypic similarity matrix are masked by others. We propose a divided-and-combined omnibus test to handle this drawback of the similarity-based method. Based on the divided-and-combined strategy, we first divide signals into two groups in a series of cut points according to eigenvalues of the phenotypic similarity matrix and combine analysis results via the Cauchy-combined method to reach a final statistic. Extensive simulations and application to a pig data demonstrate that the proposed statistic is much more powerful and robust than the original test under most of the considered scenarios, and sometimes the power increase can be more than 0.6. Divided-and-combined omnibus test facilitates genetic association analysis with high-dimensional data and achieves much higher power than the existing similarity based method. In fact, divided-and-combined omnibus test can be used whenever the association analysis between two multivariate variables needs to be conducted.