Identification of SNP interactions using logic regression

Interactions of single nucleotide polymorphisms (SNPs) are assumed to be responsible for complex diseases such as sporadic breast cancer. Important goals of studies concerned with such genetic data are thus to identify combinations of SNPs that lead to a higher risk of developing a disease and to measure the importance of these interactions. There are many approaches based on classification methods such as CART and Random Forests that allow measuring the importance of single variables. But with none of these methods the importance of combinations of variables can be quantified directly. In this paper, we show how logic regression can be employed to identify SNP interactions explanatory for the disease status in a case- control study and propose two measures for quantifying the importance of these interactions for classification. These approaches are then applied, on the one hand, to simulated data sets, and on the other hand, to the SNP data of the GENICA study, a study dedicated to the identification of genetic and gene-environment interactions associated with sporadic breast cancer