False Appearance of Gene-Environment Interactions in Genetic Association Studies

Abstract

Under the assumption of gene-environment independence, unknown/unmeasured environmental factors, irrespective of what they may be, cannot confound the genetic effects. This may lead many people to believe that genetic heterogeneity across different levels of the studied environmental exposure should only mean gene-environment interaction--even though other environmental factors are not adjusted for. However, this is not true if the odds ratio is the effect measure used for quantifying genetic effects. This is because the odds ratio is a "noncollapsible" measure--a marginal odds ratio is not a weighted average of the conditional odds ratios, but instead has a tendency toward the null. In this study, the authors derive formulae for gene-environment interaction bias due to noncollapsibility. They use computer simulation and real data example to show that the bias can be substantial for common diseases. For genetic association study of nonrare diseases, researchers are advised to use collapsible measures, such as risk ratio or peril ratio.

FIGURE 1

Causal diagrams showing the relations between G (genetic factor), E (environmental factor), U (unknown/unmeasured factor), and D (disease).

FIGURE 2

Percent discrepancy under various scenarios [A:(OR_ED, OR_UD,) = (1,1); B:(OR_ED, OR_UD,) = (5,1); C:(OR_ED, OR_UD,) = (10,1); D:(OR_ED, OR_UD,) = (1,5); E:(OR_ED, OR_UD,) = (5.5); F:(OR_ED, OR_UD,) = (10,5); G:(OR_ED, OR_UD,) = (1,10); H:(OR_ED, OR_UD,) = (5,10); I:(OR_ED, OR_UD,) = (10,10); dotted lines: E is independent of U; dashed lines: E is associated with U]. OR = odds ratio.

FIGURE 3

Type I error rate for the gene–environment interaction in case-control studies with small sample size (n = 500) [A:(OR_ED, OR_UD,) = (1,1); B:(OR_ED, OR_UD,) = (5,1); C:(OR_ED, OR_UD,) = (10,1); D:(OR_ED, OR_UD,) = (1,5); E:(OR_ED, OR_UD,) = (5,5); F:(OR_ED, OR_UD,) = (10,5); G:(OR_ED, OR_UD,) = (1,10); H:(OR_ED, OR_UD,) = (5,10); I:(OR_ED, OR_UD,) = (10,10); dotted lines: E is independent of U; dashed lines: E is associated with U]. OR = odds ratio.

FIGURE 4

Type I error rate for the gene–environment interaction in case-control studies with moderate sample size (n = 1000) [A:(OR_ED, OR_UD,) = (1,1); B:(OR_ED, OR_UD,) = (5,1); C:(OR_ED, OR_UD,) = (10,1); D:(OR_ED, OR_UD,) = (1,5); E:(OR_ED, OR_UD,) = (5,5); F:(OR_ED, OR_UD,) = (10,5); G:(OR_ED, OR_UD,) = (1,10); H:(OR_ED, OR_UD,) = (5,10); I:(OR_ED, OR_UD,) = (10,10); dotted lines: E is independent of U; dashed lines: E is associated with U]. OR = odds ratio.

FIGURE 5

Type I error rate for the gene–environment interaction in case-control studies with large sample size (n = 5000) [A:(OR_ED, OR_UD,) = (1,1); B:(OR_ED, OR_UD,) = (5,1); C:(OR_ED, OR_UD,) = (10,1); D:(OR_ED, OR_UD,) = (1,5); E:(OR_ED, OR_UD,) = (5,5); F:(OR_ED, OR_UD,) = (10,5); G:(OR_ED, OR_UD,) = (1,10); H:(OR_ED, OR_UD,) = (5,10); I:(OR_ED, OR_UD,) = (10,10); dotted lines: E is independent of U; dashed lines: E is associated with U]. OR = odds ratio.