On the use of variance per genotype as a tool to identify quantitative trait interaction effects: a report from the Women's Genome Health Study

Abstract

Testing for genetic effects on mean values of a quantitative trait has been a very successful strategy. However, most studies to date have not explored genetic effects on the variance of quantitative traits as a relevant consequence of genetic variation. In this report, we demonstrate that, under plausible scenarios of genetic interaction, the variance of a quantitative trait is expected to differ among the three possible genotypes of a biallelic SNP. Leveraging this observation with Levene's test of equality of variance, we propose a novel method to prioritize SNPs for subsequent gene-gene and gene-environment testing. This method has the advantageous characteristic that the interacting covariate need not be known or measured for a SNP to be prioritized. Using simulations, we show that this method has increased power over exhaustive search under certain conditions. We further investigate the utility of variance per genotype by examining data from the Women's Genome Health Study. Using this dataset, we identify new interactions between the LEPR SNP rs12753193 and body mass index in the prediction of C-reactive protein levels, between the ICAM1 SNP rs1799969 and smoking in the prediction of soluble ICAM-1 levels, and between the PNPLA3 SNP rs738409 and body mass index in the prediction of soluble ICAM-1 levels. These results demonstrate the utility of our approach and provide novel genetic insight into the relationship among obesity, smoking, and inflammation.

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. Quantile–quantile plots.

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.