Robustness of quantifying mediating effects of genetically regulated expression on complex traits with mediated expression score regression

Abstract

Genetic association signals have been mostly found in noncoding regions through genome-wide association studies (GWAS), suggesting the roles of gene expression regulation in human diseases and traits. However, there has been limited success in colocalizing expression quantitative trait locus (eQTL) with disease-associated variants. Mediated expression score regression (MESC) is a recently proposed method to quantify the proportion of trait heritability mediated by genetically regulated gene expressions (GReX). Applications of MESC to GWAS results have yielded low estimation of mediated heritability for many traits. As MESC relies on stringent independence assumptions between cis-eQTL effects, gene effects, and nonmediated SNP effects, it may fail to characterize the true relationships between those effect sizes, which leads to biased results. Here, we consider the robustness of MESC to investigate whether the low fraction of mediated heritability inferred by MESC reflects biological reality for complex traits or is an underestimation caused by model misspecifications. Our results suggest that MESC may lead to biased estimates of mediated heritability with misspecification of gene annotations leading to underestimation, whereas misspecification of SNP annotations may lead to overestimation. Furthermore, errors in eQTL effect estimates may lead to underestimation of mediated heritability.

Keywords: LDSC; eQTL; genetically regulated expression; mediated heritability.

Figure 1.

Comparisons of the estimation of (a) mediated heritability, (b) nonmediated heritability, and (c) total heritability between unstratified and stratified MESC with true and estimated expression scores under the simulation setting 1. The total heritability was fixed at 0.5, and the $x$-axis represents different simulation settings where the mediated heritability was varied from 0 to 0.4. The label “$S$” means stratified and the label “$\mathrm{est}$” represents models using estimated expression scores. The dashed gray lines represent the true values and the red rhombuses represent the means of the estimates.

Figure 2.

Comparisons of the estimation of (a) mediated heritability, (b) nonmediated heritability, and (c) total heritability between unstratified MESC with true and estimated expression scores with varied eQTL sample size under the simulation setting 1. The total heritability was fixed at 0.5 and the mediated heritability was fixed at 0.2. The numbers represent models using the estimated expression scores with corresponding eQTL sample sizes and “True” represents using the true expression scores. The dashed gray lines represent the true values and the red rhombuses represent the means of the estimates.

Figure 3.

Comparisons of the estimation of (a) mediated heritability, (b) nonmediated heritability, and (c) total heritability between unstratified and stratified MESC with true expression scores under the simulation setting 2. The total heritability was fixed at 0.5, and the $x$-axis represents different simulation settings where the mediated heritability was varied from 0 to 0.4. The label “$S$” means stratified. The dashed gray lines represent the true values and the red rhombuses represent the means of the estimates.

Figure 4.

Comparisons of the estimation of (a) mediated heritability, (b) nonmediated heritability, and (c) total heritability between unstratified and stratified MESC with true expression scores under the simulation setting 3. The total heritability was fixed at 0.5, and the $x$-axis represents different simulation settings where the mediated heritability was varied from 0 to 0.4. The label “$S$” means stratified. The dashed gray lines represent the true values and the red rhombuses represent the means of the estimates.

Figure 5.

Comparisons of the estimation of (a) mediated heritability, (b) nonmediated heritability, and (c) total heritability between unstratified and stratified MESC with true and estimated expression scores under the simulation setting 4. The total heritability was fixed at 0.5, and the $x$-axis represents different simulation settings where the mediated heritability was varied from 0 to 0.4. The label “$S$” means stratified. The dashed gray lines represent the true values and the red rhombuses represent the means of the estimates.

Figure 6.

Comparisons of the estimation of (a) mediated heritability, (b) nonmediated heritability, and (c) total heritability between unstratified and stratified MESC with true expression scores under the simulation setting 5. The total heritability was fixed at 0.5, and the $x$-axis represents different simulation settings where the mediated heritability was varied from 0 to 0.4. The label “$S$” means stratified. The dashed gray lines represent the true values and the red rhombuses represent the means of the estimates.

Figure 7.

Comparisons of the estimation of (a) mediated heritability, (b) nonmediated heritability, and (c) total heritability between unstratified and stratified MESC with true expression scores under the simulation setting 6. The total heritability was fixed at 0.5, and the $x$-axis represents different simulation settings where the mediated heritability was varied from 0 to 0.4. The label “$S$” means stratified. The dashed gray lines represent the true values and the red rhombuses represent the means of the estimates.

Figure 8.

Comparison of the proportion of heritability mediated by cis-eQTL estimated by MESC using two different gene stratification methods. “Default” represents stratifying genes by their cis-heritability, while “Functional Annotation” represents additionally stratifying genes by functional annotations. Error bars represent jackknife standard errors.