Testing gene-environment interaction in large-scale case-control association studies: possible choices and comparisons

Abstract

Several methods for screening gene-environment interaction have recently been proposed that address the issue of using gene-environment independence in a data-adaptive way. In this report, the authors present a comparative simulation study of power and type I error properties of 3 classes of procedures: 1) the standard 1-step case-control method; 2) the case-only method that requires an assumption of gene-environment independence for the underlying population; and 3) a variety of hybrid methods, including empirical-Bayes, 2-step, and model averaging, that aim at gaining power by exploiting the assumption of gene-environment independence and yet can protect against false positives when the independence assumption is violated. These studies suggest that, although the case-only method generally has maximum power, it has the potential to create substantial false positives in large-scale studies even when a small fraction of markers are associated with the exposure under study in the underlying population. All the hybrid methods perform well in protecting against such false positives and yet can retain substantial power advantages over standard case-control tests. The authors conclude that, for future genome-wide scans for gene-environment interactions, major power gain is possible by using alternatives to standard case-control analysis. Whether a case-only type scan or one of the hybrid methods should be used depends on the strength and direction of gene-environment interaction and association, the level of tolerance for false positives, and the nature of replication strategies.

Figure 1.

Empirical power curves for the 8 approaches: case-control (CC), case-only (CO), empirical Bayes (EB) and empirical Bayes, version 2 (EB2), 2 step (TS) with different first step α₁, Akaike Information Criterion (AIC) model averaging, and Bayes model averaging (BMA with weights W = 1). Genotype information is generated on M = 100,000 markers. The interaction effect size (exp(β_GE)) at the causal locus varies from 1.0 to 2.0. The top panel corresponds to 2,000 cases and 2,000 controls, whereas the bottom panel corresponds to 2,000 cases and 4,000 controls. The left, center, and right panels correspond to different values of the G-E odds ratio at the causal locus, namely, exp(θ_GE) = 0.8, 1.0, and 1.1, respectively. The prevalence of exposure (E) is 0.5, and the allele frequency of genotype (G) at the causal locus q_A is set at 0.2. For null loci, the allele frequencies are uniformly distributed on [0.1, 0.3]. The percentage of null loci that are independent of E is fixed at p_ind = 0.995. The marginal odds ratios for E (OR₁₀) and G (OR₀₁) are fixed at 1.00 for all loci. Results are based on 5,000 simulated data sets.

Figure 2.

Empirical power curves for the 8 approaches: case-control (CC), case-only (CO), empirical Bayes (EB) and empirical Bayes, version 2 (EB2), 2 step (TS) with different first step α₁, Akaike Information Criterion (AIC) model averaging, and Bayes model averaging (BMA with weights W = 1). Genotype information is generated on M = 100,000 markers. The interaction effect size (exp(β_GE)) at the causal locus varies from 1.0 to 1.5. The left, center, and right panels correspond to different values of the G-E odds ratio at the causal locus, namely, exp(θ_GE) = 0.8, 1.0, and 1.1, respectively. The top panel corresponds to 10,000 cases and 10,000 controls, whereas the bottom panel corresponds to 10,000 cases and 15,000 controls. The prevalence of exposure (E) is 0.5, and the allele frequency of genotype (G) at the causal locus q_A is set at 0.2. For null loci, the allele frequencies are uniformly distributed on [0.1, 0.3]. The percentage of null loci that are independent of E is fixed at p_ind = 0.995. The marginal odds ratios for E (OR₁₀) and G (OR₀₁) are fixed at 1.00 for all loci. Results are based on 5,000 simulated data sets.

Figure 3.

Relative mean-squared error of the 6 approaches except for the 2-step approach corresponding to the estimation of β_GE at the causal locus. The 6 approaches are case-control (CC), case-only (CO), empirical Bayes (EB) and empirical Bayes, version 2 (EB2), Akaike Information Criterion (AIC) model averaging, and Bayes model averaging (BMA with weights W = 1). All mean-squared errors are divided by the corresponding mean-squared error of the standard case-control analysis. The interaction effect size (exp(β_GE)) at the causal locus varies from 1.0 to 2.0. The top panel corresponds to 2,000 cases and 2,000 controls, whereas the bottom panel corresponds to 2,000 cases and 4,000 controls. The left, center, and right panels correspond to different values of the G-E odds ratio at the causal locus, namely, exp(θ_GE) = 0.8, 1.0, and 1.1, respectively. The prevalence of exposure (E) is 0.5, and the allele frequency of genotype (G) at the causal locus q_A is set at 0.2. Results are based on 5,000 simulated data sets.