Figure 1.
Model of interaction.
Figure 2.
The variance prioritization procedure.
Figure 3.
Power to detect a SNP–covariate interaction effect as function of the proportion of variance explained by the interaction.
Each condition was simulated 1,000 times with 15,000 individuals according to the model shown in Figure 1. MAF refers to the minor allele frequency of SNP1 and β2 refers to the β coefficient of the C1-Y association. In all cases, SNP1 had no marginal effect (i.e. β1 = 0). Upper panel: Power to identify SNP1 as an “interacting” SNP using Levene's test with a P-value threshold of 0.05 (black), 0.01 (red) and 1.5×10−7 (green; to account for 340,000 tests using Bonferroni correction). Also shown is the power to detect the interaction itself with a linear regression interaction P-value cut-off of 1.5×10−7 (blue). Lower panel: The variance per genotype is illustrated as a function of the fraction of the total variance of the quantitative trait explained by the interaction. The homozygous major allele genotype is drawn in black, the heterozygous genotype in red and the homozygous minor allele genotype in green.
Figure 4.
Power of variance prioritization as function of the Levene's test P-value prioritization threshold.
Each condition was simulated 2,000 times with 15,000 individuals. For each condition, the Levene's test P-value threshold was varied from 0 to 1 and the power of variance prioritization calculated after accounting for multiple testing (assuming 340,000 SNPs were initially tested), as illustrated by black lines. SNP-covariate interactions were simulated in (A–D). In the case of SNP-covariate interactions, all prioritized SNPs were tested for interaction with the covariate. Red lines represent the power to detect the interaction with linear regression when correcting for all 340,000 tested SNPs (P<1.5×10−7). In (A,B), the minor allele frequency was set at 0.2, the covariate-Y regression coefficient (i.e. β2) at 0.3, and β3 was chosen such that the proportion of variance explained by the interaction was 0.1% and 0.15%, respectively. These conditions match those of Figure 3B. In (C,D), the minor allele frequency was set at 0.1, the covariate-Y regression coefficient (i.e. β2) at 0.7, and β3 was chosen such that the proportion of variance explained by the interaction was 0.1% and 0.15%, respectively. These conditions match those of Figure 3D. SNP–SNP interactions were simulated in (E–H). As in Figure 5, the allelic frequency of both SNPs was set to be equal, as well as the SNP-Y regression coefficient (i.e. β1 and β2). For SNP–SNP interactions, all prioritized SNPs were tested against all SNPs (not limited to prioritized ones). Red lines represent the power to detect the interaction with linear regression when correcting for all pairwise interactions between 340,000 SNPs (P<4.3×10−13). In (E,F), the minor allele frequency was set at 0.1, the SNP-Y regression coefficient at 0.4, and β3 was chosen such that the proportion of variance explained by the interaction was 0.2% and 0.25%, respectively. These conditions match those of Figure 5A. In (G,H), the minor allele frequency was set at 0.2, the SNP-Y regression coefficient at 0.1, and β3 was chosen such that the proportion of variance explained by the interaction was 0.2% and 0.25%, respectively. These conditions match those of Figure 5B.
Figure 5.
Power to detect a SNP–SNP interaction effect as function of the proportion of variance explained by the interaction.
Each condition was simulated 1,000 times with 15,000 individuals. For simplicity, both SNPs were assigned the same allelic frequency (MAF) as well as the same SNP-Y β coefficient (i.e. β1 = β2). Upper panel: Power to identify either SNP1 or SNP2 as an “interacting” SNP using Levene's test with a P-value threshold of 0.05 (black), 0.01 (red) and 1.5×10−7 (green; to account for 340,000 tests using Bonferroni correction). Also shown is the power to detect the interaction itself with a linear regression interaction P-value cut-off of 4.3×10−13 (blue; chosen to account for all possible pairwise interactions between 340,000 SNPs). Lower panel: The variance per genotype is illustrated as a function of the fraction of the total variance of the quantitative trait explained by the interaction. The homozygous major allele genotype is drawn in black, the heterozygous genotype in red and the homozygous minor allele genotype in green.
Figure 6.
Illustrated in (A) is the quantile-quantile plot of Levene's test of inequality of variance P-values applied to log-CRP for 339,596 SNPs in our set of 21,799 individuals. Illustrated in (B) is the quantile-quantile plot of Levene's test P-values applied to sICAM-1 in the same set of individuals.
Table 1.
Gene–environment interactions.