For many complex traits, single nucleotide polymorphisms (SNPs) identified from genome-wide association studies (GWAS) only explain a small percentage of heritability. Next generation sequencing technology makes it possible to explore unexplained heritability by identifying rare variants (RVs). Existing tests designed for RVs look for optimal strategies to combine information across multiple variants. Many of the tests have good power when the true underlying associations are either in the same direction or in opposite directions. We propose three tests for examining the association between a phenotype and RVs, where two of them jointly consider the common association across RVs and the individual deviations from the common effect. On one hand, similar to some of the best existing methods, the individual deviations are modeled as random effects to borrow information across multiple RVs. On the other hand, unlike the existing methods which pool individual effects towards zero, we pool them towards a possibly non-zero common effect by adding a pooled variant into the model. The common effect and the individual effects are jointly tested. We show through extensive simulations that at least one of the three tests proposed here is the most powerful or very close to being the most powerful in various settings of true models. This is appealing in practice because the direction and size of the true effects of the associated RVs are unknown. Researchers can apply the developed tests to improve power under a wide range of true models.
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