Quantile regression analysis reveals widespread evidence for gene-environment or gene-gene interactions in myopia development

Abstract

A genetic contribution to refractive error has been confirmed by the discovery of more than 150 associated variants in genome-wide association studies (GWAS). Environmental factors such as education and time outdoors also demonstrate strong associations. Currently however, the extent of gene-environment or gene-gene interactions in myopia is unknown. We tested the hypothesis that refractive error-associated variants exhibit effect size heterogeneity, a hallmark feature of genetic interactions. Of 146 variants tested, evidence of non-uniform, non-linear effects were observed for 66 (45%) at Bonferroni-corrected significance (P < 1.1 × 10^-4) and 128 (88%) at nominal significance (P < 0.05). LAMA2 variant rs12193446, for example, had an effect size varying from -0.20 diopters (95% CI -0.18 to -0.23) to -0.89 diopters (95% CI -0.71 to -1.07) in different individuals. SNP effects were strongest at the phenotype extremes and weaker in emmetropes. A parsimonious explanation for these findings is that gene-environment or gene-gene interactions in myopia are pervasive.

Keywords: Genetic interaction; Refractive errors.

Fig. 1

Conditional quantile regression (CQR) and meta-regression (MR) can identify if genetic effect size varies in individuals depending on their position in the trait distribution. In conventional ordinary least squares (OLS) linear regression, SNP effect size is estimated under the assumption that it is the same for every person in the sample. Thus, the effect size is calculated as the slope of the regression line (dashed blue line in top-left graph) obtained by minimizing the sum of squared residuals between data points and the mean, for each genotype class (0, 1 or 2 copies of the minor allele). Alternatively, in CQR, the SNP effect size is estimated at a specific quantile of the outcome distribution. Analogous to OLS, the effect size is calculated as the slope of the quantile regression line (in the top-left graph, the nine red lines correspond to quantile regression fits for quantiles 0.1, 0.2, 0.3, …, 0.9 of the trait distribution). For the variant shown, rs12193446, the effect size (slope) differs for individuals in different quantiles of the trait distribution; this can be visualized more readily by plotting the effect size at each quantile (black circles with error bars in middle-right graph). OLS analysis assumes the effect size is constant across quantiles of the trait distribution (horizontal red line in middle-right graph, with dotted red lines indicating 95% CI). After using CQR to estimate the SNP effect size at a range of quantiles, the uniformity of the SNP effect sizes can be quantitatively assessed using MR (solid blue line in bottom-left graph, with dashed blue lines showing 95% CI)

Fig. 2

Changes in genetic effect size across the refractive error distribution for a representative subset of genetic variants associated with refractive error. Genetic effect size estimates from conditional quantile regression (CQR) are represented by the solid black line and their 95% confidence intervals are shown by the shaded grey region. The solid red line is the effect size estimate from conventional linear regression analysis with its 95% confidence intervals shown by the red dashed lines. Effect size estimates from meta-regression are shown with the solid blue line with corresponding 95% confidence intervals given by the dashed blue lines

Fig. 3

The effect of educational attainment on refractive error varies across quantiles of the refractive error distribution. Each line represents the polygenic risk score (PRS) effect size across quantiles for individuals with different times spent in education. Error bars show 95% confidence intervals