Gene-environment interactions in genome-wide association studies: a comparative study of tests applied to empirical studies of type 2 diabetes

Abstract

The question of which statistical approach is the most effective for investigating gene-environment (G-E) interactions in the context of genome-wide association studies (GWAS) remains unresolved. By using 2 case-control GWAS (the Nurses' Health Study, 1976-2006, and the Health Professionals Follow-up Study, 1986-2006) of type 2 diabetes, the authors compared 5 tests for interactions: standard logistic regression-based case-control; case-only; semiparametric maximum-likelihood estimation of an empirical-Bayes shrinkage estimator; and 2-stage tests. The authors also compared 2 joint tests of genetic main effects and G-E interaction. Elevated body mass index was the exposure of interest and was modeled as a binary trait to avoid an inflated type I error rate that the authors observed when the main effect of continuous body mass index was misspecified. Although both the case-only and the semiparametric maximum-likelihood estimation approaches assume that the tested markers are independent of exposure in the general population, the authors did not observe any evidence of inflated type I error for these tests in their studies with 2,199 cases and 3,044 controls. Both joint tests detected markers with known marginal effects. Loci with the most significant G-E interactions using the standard, empirical-Bayes, and 2-stage tests were strongly correlated with the exposure among controls. Study findings suggest that methods exploiting G-E independence can be efficient and valid options for investigating G-E interactions in GWAS.

Figure 1.

Quantile-quantile plots for approaches to modeling body mass index in the standard gene-environment (G-E) interaction test: 1) model 1: logit Pr(D|G,E) = β₀ + β_g G + β_e E + β_ge G × E, where E (body mass index) is a continuous variable (○); 2) model 2: logit Pr(D|G,E) = β₀ + β_g G + β_e1 E + β_e2 E² + β_e3 E³ + β_ge G × E, where E (modeled as body mass index − mean) is a continuous variable (▵); 3) model 3: model 1 with robust variance estimator (*); and 4) model 4: logit Pr(D|G,E) = β₀ + β_g G + β_e E + β_ge G × E, where E (body mass index) is a binary variable (+), in the Nurses’ Health Study, 1976–2006. The dashed line (y = x line) corresponds to instances where the observed (y) P value is equal to the expected (x) P value.

Figure 2.

Quantile-quantile plots and corresponding genomic inflation factors (lambda) for the 1 df tests for gene-environment (G-E) interaction (standard case-control (A), case-only (B), semiparametric maximum-likelihood estimation (C), empirical-Bayes shrinkage estimator (D), and 2-stage (E)) in the Nurses’ Health Study, 1976–2006. Point colors correspond to P values for tests of G-E dependence: <0.001 (black), <0.05 (gray), and ≥0.05 (white). For the 2-stage test (E), lambda was calculated by using P values from 7,231 single nucleotide polymorphisms tested in the second stage. The dashed line (y = x line) corresponds to instances where the observed (y) P value is equal to the expected (x) P value.

Figure 3.

Quantile-quantile plots and corresponding genomic inflation factors (lambda) for the marginal genetic effects test (unadjusted (A) and adjusted (B) for body mass index) and for joint tests of genetic main effects and gene-environment (G-E) interaction (joint 2 df (C) and semiparametric maximum-likelihood estimation (2 df (D)) in the Nurses’ Health Study, 1976–2006. Point colors correspond to P values for tests of G-E association: <0.001 (black), <0.05 (gray), and ≥0.05 (white). The dashed line (y = x line) corresponds to instances where the observed (y) P value is equal to the expected (x) P value.