A Robust Method Uncovers Significant Context-Specific Heritability in Diverse Complex Traits

Abstract

Gene-environment interactions (GxE) can be fundamental in applications ranging from functional genomics to precision medicine and is a conjectured source of substantial heritability. However, unbiased methods to profile GxE genome-wide are nascent and, as we show, cannot accommodate general environment variables, modest sample sizes, heterogeneous noise, and binary traits. To address this gap, we propose a simple, unifying mixed model for gene-environment interaction (GxEMM). In simulations and theory, we show that GxEMM can dramatically improve estimates and eliminate false positives when the assumptions of existing methods fail. We apply GxEMM to a range of human and model organism datasets and find broad evidence of context-specific genetic effects, including GxSex, GxAdversity, and GxDisease interactions across thousands of clinical and molecular phenotypes. Overall, GxEMM is broadly applicable for testing and quantifying polygenic interactions, which can be useful for explaining heritability and invaluable for determining biologically relevant environments.

Keywords: G-E correlation; GxE; disease subtypes; genetic heterogeneity; heritability; heteroskedasticity; linear mixed model; psychiatric disease.

Figure 1

The Three Key GxEMM Models in the Case of Two Discrete Environments Entry shading indicates absolute value. Hom (top) fits homogeneous genetic ($h_g^2$) and noise (${\sigma }_e^2$) levels and is equivalent to GREML. IID (middle) adds a common effect for environment-specific heritability ($h_{het}^2$, orange), pictured as a block-diagonal matrix with each block corresponding to samples from one environment. Free (bottom) allows environment-specific genetic (v_k) and noise (w_k) levels.

Figure 2

GxEMM Simulations GxEMM simulations under (A and B) homogeneity, (C and D) IID heterogeneity, (E and F) Free genetic heterogeneity, or (G and H) Free noise heterogeneity. Results are shown for Hom, IID, and Free GxEMM and, in (G) and (H), the Free GxE model with Hom noise. In the top panels, the (true or false) positive rates are shown for Wald tests at nominal p < .05. In the bottom panels, mean GxEMM estimates are shown as points (±1 SD), with true generative parameters as background lines.

Figure 3

REML and PCGC GxEMM in Binary Trait Simulations, with Liabilities Drawn from Hom GxEMM with $h_g^2=35\text{\%}$ Left plots vary the per-environment disease prevalences through the mean liability in environment 1, ${\mu }_1$, while fixing ${\mu }_2=0$. Right plots vary the population disease prevalence and then ascertain a 50/50 disease cohort. The top panels test for genetic heterogeneity between environments.

Figure 4

GxEMM Estimates Aggregated across p = 115 Traits in Outbred Rats for the Hom, IID, and Free Models p values marginally test whether variance components are 0. (A, left) Heritability estimates from each model, with labels for which violins correspond to which GxEMM model. (A, right) Homogeneous and heterogeneous heritability components in the IID model. (B) Genetic variance component estimates for the Free model, as well as noise heterogeneity estimates ($w_F-w_M$). Middle table: for each component of the violin plots, we provide the average across traits as well as the number of traits where the component is significantly different from zero. (C and D) Heritability and variance component estimates from GxEMM for two specific traits, bone density and glucose tolerance. Error bars represent 1 SE; *p < .05, **p < .01, and **p < .001.

Figure 5

GxEMM Stress-Specific Heritability Estimates for Major Depression p values marginally test whether variance components are 0. Estimates are shown aggregated over 14 different choices for the binary stress measurement that is used as the environment in GxEMM. All stress measures are correlated and have less than 50% prevalence in the dataset. (A, left) Heritabilities from the Hom, IID, and Free models. (A, right) IID heritability components. (B) Free variance components.

Figure 6

Psychiatric Disease-Specific Heritability in Prefrontal Cortex Gene Expression (A) IID and Free genetic heterogeneity tests based on permutations across 63 known SCZ-associated genes. Large points have FDR < 25%, and the horizontal line is Bonferroni-adjusted p < .05. The maximum BPD and CTRL points overlap at p = 1/(1+10,000), the minimum possible value after 10,000 permutations. (B and C) GxEMM results for 2/9 candidate SCZ genes with significant genetic heterogeneity, SNX19 (B) and FURIN (C).

Figure 7

Bias from HE Regression when Fitting Free GxEMM with Hom Noise Estimates are based on the simulations used in Figures 2G and 2H, which assume Hom genetics and Free noise. Lines provide the bias approximation derived above. The true simulation model has v₁ = v₂ = 0; the true values are shown as dotted lines in the background.