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. 2021 Sep 1;190(9):1948-1960.
doi: 10.1093/aje/kwab124.

A Robust Test for Additive Gene-Environment Interaction Under the Trend Effect of Genotype Using an Empirical Bayes-Type Shrinkage Estimator

Nilotpal Sanyal, Valerio Napolioni, Matthieu de Rochemonteix, Michaël E Belloy, Neil E Caporaso, Maria Teresa Landi, Michael D Greicius, Nilanjan Chatterjee, Summer S Han

A Robust Test for Additive Gene-Environment Interaction Under the Trend Effect of Genotype Using an Empirical Bayes-Type Shrinkage Estimator

Nilotpal Sanyal et al. Am J Epidemiol. .

Abstract

Evaluating gene by environment (G × E) interaction under an additive risk model (i.e., additive interaction) has gained wider attention. Recently, statistical tests have been proposed for detecting additive interaction, utilizing an assumption on gene-environment (G-E) independence to boost power, that do not rely on restrictive genetic models such as dominant or recessive models. However, a major limitation of these methods is a sharp increase in type I error when this assumption is violated. Our goal was to develop a robust test for additive G × E interaction under the trend effect of genotype, applying an empirical Bayes-type shrinkage estimator of the relative excess risk due to interaction. The proposed method uses a set of constraints to impose the trend effect of genotype and builds an estimator that data-adaptively shrinks an estimator of relative excess risk due to interaction obtained under a general model for G-E dependence using a retrospective likelihood framework. Numerical study under varying levels of departures from G-E independence shows that the proposed method is robust against the violation of the independence assumption while providing an adequate balance between bias and efficiency compared with existing methods. We applied the proposed method to the genetic data of Alzheimer disease and lung cancer.

Keywords: Alzheimer disease; GWAS; additive risk model; case-control design; empirical Bayes; gene--APOE-ε4 interaction; gene-environment interaction; gene-smoking interaction.

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Figures

Figure 1
Figure 1
Type I error simulation under varying departure from gene-environment (G-E) independence (formula imagethe x-axis) across different type I error thresholds: A) α = 0.005; B) α = 0.001; C) α = 0.0005; D) α = 0.0001. The y-axis shows the log (to the base 10) of the ratio between an observed type I error rate and α (i.e., log10(observed type I error/α)). Three additive interaction tests—unconstrained maximum likelihood (UML)-trend, constrained maximum likelihood (CML)-trend, and empirical Bayes (EB)-trend tests—are applied to simulated data sets generated under the null hypothesis (i.e., relative excess risk due to interaction = 0); 50,000 replicated data sets are simulated for 10,000 cases and 10,000 controls with minor allele frequency (MAF) = 0.3, marginal odds ratio (MOR)(G) = 1.1, MOR(E) = 1.5. The parameters used for this simulation are presented in Web Table 2. The results of the simulation under different MAF (0.1,0.05), MOR(E) (2.5,3,3.5), and case-control ratio are shown in Web Figure 1 (different MAF values), Web Figure 2 (different MOR(E) values), and Web Figure 3 (different case-control ratio).
Figure 2
Figure 2
Simulation for evaluating bias (A) and mean squared error (MSE) (B) of relative excess risk due to interaction (RERI) under varying magnitude of gene-environment (G-E) dependence (formula imagethe x-axis) that includes the negative correlation and positive correlation. The simulated data sets are generated under the null hypothesis (RERI = 0), and 50,000 replicated data sets were simulated for 10,000 cases and 10,000 controls with marginal odds ratio (MOR) = 0.3, marginal odds ratio (MOR)(G) = 1.1, MOR(E) = 1.5. The parameters used for this simulation are presented in Web Table 2. The results of the simulation under different MAF (0.1,0.05) and MOR(E) (2.5,3,3.5) are shown in Web Figure 4 (different MAFs for the given MOR(E) = 1.5), Web Figure 5 (different MOR(E) and MAF values for evaluating bias), and Web Figure 6 (different MOR(E) and MAF values for evaluating MSE). EB, empirical Bayes; CML, constrained maximum likelihood; UML, unconstrained maximum likelihood.
Figure 3
Figure 3
Power comparison of the 3 tests—unconstrained maximum likelihood (UML)-trend, constrained maximum likelihood (CML)-trend, and empirical Bayes (EB)-trend tests (based on the α threshold of formula image)—under varying magnitudes of additive interaction (relative excess risk due to interaction, RERI) and varying marginal odds ratio (MOR)(E). A) MOR(E) = 1.5; B) MOR(E) = 2.5; C) MOR(E) = 3; D) MOR(E) = 3.5; 1,000 replicated data sets are simulated for 5,000 cases and 5,000 controls with marginal odds ratio (MOR) = 0.3, MOR(G) = 1.1. The parameters used for this simulation are presented in Web Table 3. The results of the simulation under different MAF (0.1,0.05) values are shown in Web Figure 7.
Figure 4
Figure 4
Manhattan plots for single nucleotide polymorphism (SNP) × apolipoprotein E (APOE)-ε4 interaction analysis for chromosome 19, which harbors the apolipoprotein E gene, using data from 8,861 cases and 7,613 controls of northwestern European ancestry, collected from 18 different studies. The y-axis shows formula image values from testing SNP × APOE-ε4 interaction using: A) the additive constrained maximum likelihood (CML)-trend test; B) the additive empirical Bayes (EB)-trend test (the proposed test). The result using the additive unconstrained maximum likelihood (UML)-trend test is shown in Web Figure 8. The y-axis is truncated at 15. The dashed line corresponds to genome-wide significance level of formula image.
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