We next compared the performance of the regression-based correction to an analytical method previously proposed to correct for the difference in number of (genotyped or imputed) SNPs per gene (Sidak's correction, [26], [39]). The Sidak correction did not perform as well as the regression-based correction (correlation with permutation-corrected gene p-values: r = 0.94, p<1e-30, but most gene p-values lie below diagonal; see Figure S3 for details). This is probably due to the method's assumption of independence between all SNPs in a gene region (eq. 4 in Materials and Methods). We then tested a modification of Sidak's correction proposed by Saccone et al. [40], which assumes that about 50% of all SNPs in a given chromosomal region are in high linkage disequilibrium (eq. 5 in Materials and Methods). This correction was comparable to, or slightly better than the regression method in the DGI test case (correlation with permutation-corrected gene p-values: r = 0.97, p<1e-30; Figure S3). These results are in concordance with our findings that number or density of SNPs is a dominant confounder on the best SNP per gene score, (Table 1), and that correcting for linkage disequilibrium between SNPs is necessary.
