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Figure S1. Power at 5.10–8 significance level to detect association signal when analysing 2000 individuals function of the amplitude of interaction effect. Power is presented for the test of marginal linear effect (MARG), the Dc test (DC), the Du test (DU), the Levene test of variances (LEV), and the joint test while using either the true exposure or exposures correlated with the true exposure at the 0.7, 0.5 and 0.3 level (joint_1.0, joint_0.7, joint_0.5 and joint_0.3 respectively). Power is presented when the main and interaction effects of the SNP are in the same direction (A,B and C), and when main effect and interaction effects are in opposite directions (D, E and F).

Figure S2. Power at 5.10–8 significance level to detect association signal when analysing 2000 individuals. Power is presented for the test of marginal linear effect (MARG), the Dc test (DC), the Du test (DU), the Levene test of variance (LEV), and the joint test while using either the true exposure or exposures correlated with the true exposure at the 0.7, 0.5 and 0.3 level (joint_1.0, joint_0.7, joint_0.5 and joint_0.3 respectively). Power is presented in the presence of two interaction effects in the same direction (A), and in the presence of a two interaction in opposite direction having either different amplitude (B) or the same amplitude (C).

Figure S3. QQplot of the Dc test (DC), Du test (DU), the Levene's test of variance (LEV), linear regression (MARG).

Figure S4. Power at 0.05 significance level of the Dc test (DC), Du test (DU), the Levene's test of variance (LEV), linear regression (MARG), the two-sample Kolmogorov-Smirnov test (KS), the two-sample Cramèr Von-Mises test (CRAMER), the two-sample Wilcoxon rank sum test (RANK), the two-sample Student's t test (t) and the generalized version of the two later tests (RANK.gen and t.gen) as described by O'Brien[O'Brien 1988]. Power has been computed among 10,000 simulations, when analyzing 300 individuals for the test of a biallelic genetic variant in the presence of one interaction effect only. The interaction effect and exposure frequency were set so that the marginal effect size is fixed at 0.2.

Figure S5. Power at 0.05 significance level of the Dc test (DC), Du test (DU), the Levene's test of variance (LEV), linear regression (MARG), the two-sample Kolmogorov-Smirnov test (KS), the two-sample Wilcoxon rank sum test (RANK), the two-sample Student's t test (t) and the generalized version of the two later tests (RANK.gen and t.gen) as described by O'Brien [O'Brien 1988]. Power has been computed among 10,000 simulations, when analyzing 2000 individuals for the test of a biallelic genetic variant in the presence of one interaction effect only. The interaction effect and exposure frequency were set so that the marginal effect size is fixed at 0.1. The Cramèr Von-Mises test was not applied in this simulation because the sample size was two large to be handled by the algorithm we used [Xiao et al., 2006].

Figure S6. Distribution of phenotypic values by genotypes (left panel) and density plot (right panel) for SNP rs1932016 in gene ABCA4. Density is plotted using the R function density() with the default parameters.

Figure S7. Distribution of phenotypic values by genotypes (left panel) and density plot (right panel) for SNP rs7324283 in gene ABCC4. Density is plotted using the R function density() with the default parameters.

Figure S8. Distribution of phenotypic values by genotypes (left panel) and density plot (right panel) for SNP rs12681149 in gene CSMD1. Density is plotted using the R function density() with the default parameters.

Figure S9. Distribution of phenotypic values by genotypes (left panel) and density plot (right panel) for SNP rs6493489 in gene CYP19A1. Density is plotted using the R function density() with the default parameters.

Figure S10. Distribution of phenotypic values by genotypes (left panel) and density plot (right panel) for SNP rs751141 in gene EPHX2. Density is plotted using the R function density() with the default parameters.

Figure S11. Distribution of phenotypic values by genotypes (left panel) and density plot (right panel) for SNP rs124410802 in gene MNDA. Density is plotted using the R function density() with the default parameters.

Figure S12. Distribution of phenotypic values by genotypes (left panel) and density plot (right panel) for SNP rs3812609 in gene NOTCH1. Density is plotted using the R function density() with the default parameters.

Figure S13. Distribution of phenotypic values by genotypes (left panel) and density plot (right panel) for SNP rs3789303 in gene PAPPA. Density is plotted using the R function density() with the default parameters.

Figure S14. Distribution of phenotypic values by genotypes (left panel) and density plot (right panel) for SNP rs11715516 in gene RARB. Density is plotted using the R function density() with the default parameters.

Figure S15. Distribution of phenotypic values by genotypes (left panel) and density plot (right panel) for SNP rs577217 in gene STARD10. Density is plotted using the R function density() with the default parameters.

Figure S16. Distribution of phenotypic values by genotypes (left panel) and density plot (right panel) for SNP rs1932016 in gene ABCA4. Density is plotted using the R function density() with the default parameters.

Table S1. Top genes associated with mammographic density based on Dc test, Du test, Levene's test and Marginal test and most relevant references from a PubMed search including both the name of the gene and the term “breast”.

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