These authors contributed equally to this work.
A Geometric Framework for Evaluating Rare Variant Tests of Association
Version of Record online: 21 MAR 2013
© 2013 Wiley Periodicals, Inc.
Volume 37, Issue 4, pages 345–357, May 2013
How to Cite
Liu, K., Fast, S., Zawistowski, M. and Tintle, N. L. (2013), A Geometric Framework for Evaluating Rare Variant Tests of Association. Genet. Epidemiol., 37: 345–357. doi: 10.1002/gepi.21722
- Issue online: 15 APR 2013
- Version of Record online: 21 MAR 2013
- Manuscript Accepted: 13 FEB 2013
- Manuscript Revised: 12 FEB 2013
- Manuscript Received: 24 SEP 2012
- National Human Genome Research Institute. Grant Numbers: R15HG004543, R15HG006915
- rare variants;
- burden tests
The wave of next-generation sequencing data has arrived. However, many questions still remain about how to best analyze sequence data, particularly the contribution of rare genetic variants to human disease. Numerous statistical methods have been proposed to aggregate association signals across multiple rare variant sites in an effort to increase statistical power; however, the precise relation between the tests is often not well understood. We present a geometric representation for rare variant data in which rare allele counts in case and control samples are treated as vectors in Euclidean space. The geometric framework facilitates a rigorous classification of existing rare variant tests into two broad categories: tests for a difference in the lengths of the case and control vectors, and joint tests for a difference in either the lengths or angles of the two vectors. We demonstrate that genetic architecture of a trait, including the number and frequency of risk alleles, directly relates to the behavior of the length and joint tests. Hence, the geometric framework allows prediction of which tests will perform best under different disease models. Furthermore, the structure of the geometric framework immediately suggests additional classes and types of rare variant tests. We consider two general classes of tests which show robustness to noncausal and protective variants. The geometric framework introduces a novel and unique method to assess current rare variant methodology and provides guidelines for both applied and theoretical researchers.