coefficients α, β, δ, γ, η, and were estimated such that for every gene g one can calculate:(2)where is the residual of the association score for gene g that cannot be explained by the effects of the predictor variables considered. After the regression a corrected gene z-score, can be written as follows:(3)A corrected gene p-value is calculated from assuming a normal distribution and a mean of 0 and standard deviation of 1 (reasonable approximation but not perfect, in particular for the less significant values of ; see Figure S8). Of all six gene properties tested, only the genetic distance, , was not significant (p>0.05) in most of the DGI permutations subjected to the regression analysis (Table S3), and hence was used for all analyses in this paper. Similar GSEA results were obtained for all gene sets and traits analyzed in this paper when only the first four variables listed in Table 1 (significant in almost all 1,000 DGI permutations tested; see Table S3) were used for the regression-based correction of gene scores ( and ) (data not shown).
