Genegeneinter Vignette Statistical Analysis of the Interaction between a Pair of Genes

Let consider a sample of n individuals with nc controls and nd cases (nc+nd = n) and Y = [y1, . . . , yn] ′ the vector of the observed binary phenotypes. Each gene is a collection of respectively m1 and m2 SNPs. The observed genotypes for gene X1 can be represented by a n×m1 matrix: X1 = [xij ]i∈1...n;j∈1...m1 where xij ∈ {0; 1; 2} is the number of copies of the minor allele for SNP j carried by individual i. A similar representation is used for gene X2 where X2 is a n×m2 matrix. Let us further introduce X1 and X2 the matrices of observed genotypes among controls for gene 1 and 2 and X1 and X d 2 among cases for both genes. Thus X c 1 is a nc ×m1 matrix, X1 a nd ×m1 matrix, X2 a nc ×m2 matrix and X2 a nd ×m2 matrix. A general setup of the observed values can be presented as follows: