Restricted parameter space models for testing gene-gene interaction

There is a growing recognition that interactions (gene-gene and gene-environment) can play an important role in common disease etiology. The development of cost-effective genotyping technologies has made genome-wide association studies the preferred tool for searching for loci affecting disease risk. These studies are characterized by a large number of investigated SNPs, and efficient statistical methods are even more important than in classical association studies that are done with a small number of markers. In this article we propose a novel gene-gene interaction test that is more powerful than classical methods. The increase in power is due to the fact that the proposed method incorporates reasonable constraints in the parameter space. The test for both association and interaction is based on a likelihood ratio statistic that has a x(2) distribution asymptotically. We also discuss the definitions used for "no interaction" and argue that tests for pure interaction are useful in genome-wide studies, especially when using two-stage strategies where the analyses in the second stage are done on pairs of loci for which at least one is associated with the trait.