A flexible Bayesian model for studying gene-environment interaction

Abstract

An important follow-up step after genetic markers are found to be associated with a disease outcome is a more detailed analysis investigating how the implicated gene or chromosomal region and an established environment risk factor interact to influence the disease risk. The standard approach to this study of gene-environment interaction considers one genetic marker at a time and therefore could misrepresent and underestimate the genetic contribution to the joint effect when one or more functional loci, some of which might not be genotyped, exist in the region and interact with the environment risk factor in a complex way. We develop a more global approach based on a Bayesian model that uses a latent genetic profile variable to capture all of the genetic variation in the entire targeted region and allows the environment effect to vary across different genetic profile categories. We also propose a resampling-based test derived from the developed Bayesian model for the detection of gene-environment interaction. Using data collected in the Environment and Genetics in Lung Cancer Etiology (EAGLE) study, we apply the Bayesian model to evaluate the joint effect of smoking intensity and genetic variants in the 15q25.1 region, which contains a cluster of nicotinic acetylcholine receptor genes and has been shown to be associated with both lung cancer and smoking behavior. We find evidence for gene-environment interaction (P-value = 0.016), with the smoking effect appearing to be stronger in subjects with a genetic profile associated with a higher lung cancer risk; the conventional test of gene-environment interaction based on the single-marker approach is far from significant.

Figure 1. The partition of the genotype space in the simulation study.

We conducted a principal component analysis on all subjects from the EAGLE study with genotypes at the 15 chosen tagging SNPs as coordinates. We plot subjects by their first and second principal components. Subjects with the same multilocus genotype were represented by a single point in the plot. The points in green, blue, and red colors are those subjects (genotypes) belonging to region I (consisting of genotypes having no more than 1 risk allele among the three considered functional SNPs), region II (consisting of genotypes having 2 risk alleles), and region III (consisting of genotypes have more than 2 risk alleles).

Figure 2. Boxplots of the posterior medians of the intercept () for subjects within each true cluster from each of 50 datasets simulated under the model .

(a). Boxplots of posterior medians of for subjects in cluster 1, with the true value given by the horizontal line in green; (b). Boxplots of posterior medians of for subjects in cluster 2, with the true value given by the horizontal line in blue. The posterior median of for each subject under a given simulated dataset was shifted by a constant value selected so that the median value of the shifted estimates for subjects in cluster 1 was zero.

Figure 3. Boxplots of the posterior medians of the log odds ratio () for subjects within each true cluster from each of 50 datasets simulated under the model .

(a). Boxplots of posterior medians of for subjects in cluster 1, with the true value given by the horizontal line in green; (b). Boxplots of posterior medians of for subjects in cluster 2, with the true value given by the horizontal line in blue.

Figure 4. Boxplots of the posterior medians of the intercept () for subjects within each true cluster from each of 50 datasets simulated under the model .

(a). Boxplots of posterior medians of for subjects in cluster 1, with the true value given by the horizontal line in green; (b). Boxplots of posterior medians of for subjects in cluster 2, with the true value given by the horizontal line in blue; (c). Boxplots of posterior medians of for subjects in cluster 3, with the true value given by the horizontal line in red. The posterior median of for each subject under a given simulated dataset was shifted by a constant value selected so that the median value of the shifted estimates for subjects in cluster 1 was zero.

Figure 5. Boxplots of the posterior medians of the log odds ratio () for subjects within each true cluster from each of 50 datasets simulated under the model .

(a). Boxplots of posterior medians of for subjects in cluster 1, with the true value given by the horizontal line in green; (b). Boxplots of posterior medians of for subjects in cluster 2, with the true value given by the horizontal line in blue; (c). Boxplots of posterior medians of for subjects in cluster 3, with the true value given by the horizontal line in red.

Figure 6. Cluster assignment for the EAGLE study.

The cluster assignment estimated under the model with the number of clusters K = 2. Every subject was represented by his or her first 2 principal components. Subjects with the same multilocus genotype were represented by one point in the plot.

Figure 7. DIC plots for the Bayesian risk model allowing for gene–environment interaction.

For any given number of clusters, 20 DIC values were obtained by applying the proposed method to the data from the EAGLE study 20 times with different random seeds.

Figure 8. Smoothed surface plots of the posterior medians of the odds ratios for the genetic and smoking effects on the space of the first two principal components.

(a). Posterior median of the OR for the genetic effect under the model with the number of clusters K = 2; (b). Posterior mean of the OR for the smoking effect under the model with the number of clusters K = 2.