For complex diseases, the relationship between genotypes, environment factors, and phenotype is usually complex and nonlinear. Our understanding of the genetic architecture of diseases has considerably increased over the last years. However, both conceptually and methodologically, detecting gene-gene and gene-environment interactions remains a challenge, despite the existence of a number of efficient methods. One method that offers great promises but has not yet been widely applied to genomic data is the entropy-based approach of information theory. In this article, we first develop entropy-based test statistics to identify two-way and higher order gene-gene and gene-environment interactions. We then apply these methods to a bladder cancer data set and thereby test their power and identify strengths and weaknesses. For two-way interactions, we propose an information gain (IG) approach based on mutual information. For three-ways and higher order interactions, an interaction IG approach is used. In both cases, we develop one-dimensional test statistics to analyze sparse data. Compared to the naive chi-square test, the test statistics we develop have similar or higher power and is robust. Applying it to the bladder cancer data set allowed to investigate the complex interactions between DNA repair gene single nucleotide polymorphisms, smoking status, and bladder cancer susceptibility. Although not yet widely applied, entropy-based approaches appear as a useful tool for detecting gene-gene and gene-environment interactions. The test statistics we develop add to a growing body methodologies that will gradually shed light on the complex architecture of common diseases. © 2011 Wiley Periodicals, Inc.
