Detecting Association of Rare and Common Variants by Testing an Optimally Weighted Combination of Variants


Correspondence to: Shuanglin Zhang, Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931. E-mail:


Next-generation sequencing technology will soon allow sequencing the whole genome of large groups of individuals, and thus will make directly testing rare variants possible. Currently, most of existing methods for rare variant association studies are essentially testing the effect of a weighted combination of variants with different weighting schemes. Performance of these methods depends on the weights being used and no optimal weights are available. By putting large weights on rare variants and small weights on common variants, these methods target at rare variants only, although increasing evidence shows that complex diseases are caused by both common and rare variants. In this paper, we analytically derive optimal weights under a certain criterion. Based on the optimal weights, we propose a Variable Weight Test for testing the effect of an Optimally Weighted combination of variants (VW-TOW). VW-TOW aims to test the effects of both rare and common variants. VW-TOW is applicable to both quantitative and qualitative traits, allows covariates, can control for population stratification, and is robust to directions of effects of causal variants. Extensive simulation studies and application to the Genetic Analysis Workshop 17 (GAW17) data show that VW-TOW is more powerful than existing ones either for testing effects of both rare and common variants or for testing effects of rare variants only.