Common Errors in Interpreting G×E Results

Why Interpretation Requires More Than a Significant Result

A reported gene–environment (G×E) result can be statistically correct and still be interpreted incorrectly. A product-term test may address whether a model’s fitted genetic association varies across exposure levels; it does not, by itself, show that the exposure caused the variation. A nonsignificant test does not prove that the association is constant, and different p-values in separate strata do not establish that the stratum-specific effects differ. Even the meaning of “interaction” depends on the outcome and effect scale used.

These distinctions matter because G×E analyses often involve conditional estimates, several possible scales, and uncertainty that can be substantial in particular genotype–exposure groups. Interpretation should begin with the model, the contrast being tested, and the uncertainty around that contrast—not with a binary label of “significant” or “not significant.”

Interaction Is Not the Same as Causation

For a quantitative outcome, one familiar model with binary \(G\) and \(E\), each coded 0 or 1, is

Here, \(\beta_G\) is the fitted difference in mean outcome between \(G=1\) and \(G=0\) when \(E=0\). When \(E=1\), that fitted difference is \(\beta_G+\beta_{GE}\). Thus \(\beta_{GE}\) is the difference between those two genetic associations, in the outcome’s units. This is an interpretation of the model’s conditional means. It becomes a causal interpretation only if the design and assumptions support causal estimation, including appropriate control of confounding, valid measurement, and the required assumptions about selection and model specification.

In observational data, genotype and exposure groups can differ in ways that matter for the outcome. Population structure, exposure-related social or clinical factors, selection into the study, or other sources of bias can contribute to observed conditional associations. Adjusting for measured covariates may help, but adjustment alone does not guarantee that all relevant assumptions hold. A small p-value for \(\beta_{GE}\) is evidence against the model’s no-interaction null under the analysis assumptions; it is not evidence that changing \(E\) would change the genetic effect.

Nonsignificance Is Not Evidence of No Effect Modification

An interaction test asks whether the data are sufficiently incompatible with a specified null value, commonly \(\beta_{GE}=0\) for a product term. Its p-value depends both on the estimated interaction and on its standard error. A nonsignificant result can arise because the estimated interaction is small, because it is estimated imprecisely, or both. In G×E analyses, limited sample size or sparse genotype–exposure cells can make interaction estimates particularly uncertain.

A confidence interval helps show which interaction values remain reasonably compatible with the data. A wide interval that includes zero may also include materially positive and negative interactions; it does not establish that meaningful effect modification is absent. To support a claim that effects are sufficiently similar for a particular purpose, one would need to define what size of difference matters and use an analysis designed to assess that criterion. Merely failing to reject a zero-interaction null does not do this.

Compare Effects Directly, Not Their P-Values

A common error is to test the genetic association separately in each exposure stratum, observe a significant result in one and a nonsignificant result in the other, and conclude that the effects differ. Those tests address separate null hypotheses: whether each stratum-specific association equals zero. Effect modification instead concerns whether the associations differ from each other. The appropriate test is a direct contrast of the estimates, with uncertainty calculated for that contrast.

For estimates \(\hat{\theta}_1\) and \(\hat{\theta}_0\) from two exposure strata, let \(\hat{\delta}=\hat{\theta}_1-\hat{\theta}_0\). The variance of a difference is

If the estimates are independent, their covariance is zero, and the standard error of the difference is the square root of the sum of their variances. If they are not independent, the covariance must be included. This follows because subtracting estimates changes the variance according to \(\operatorname{Var}(A-B)=\operatorname{Var}(A)+\operatorname{Var}(B)-2\operatorname{Cov}(A,B)\). A direct contrast therefore accounts for the uncertainty in both estimates and, where relevant, their dependence.

Always Name the Scale

“Interaction” is incomplete unless the scale is specified. For a quantitative outcome, the linear-model product term describes departure from additivity of conditional means. For a binary outcome, additive interaction can refer to a departure from additivity of risks, whereas multiplicative interaction can refer to a departure from multiplicativity of risk ratios or odds, depending on the model. These are different contrasts. A finding of interaction on one scale need not imply interaction on another.

The scale also determines the interpretation of the numerical estimate. A coefficient on the mean scale is in outcome units; a log-scale coefficient is on a logarithmic scale; and a risk-scale contrast is expressed in risk differences or a related risk measure. Reports should name the outcome, the scale, the reference coding, and the contrast. Avoid describing a model coefficient simply as “the G×E effect” when that would leave its meaning ambiguous.

A Practical Interpretation Check

Before drawing a conclusion from a G×E result, work through the following sequence. It prevents the most common interpretive shortcuts while keeping attention on the scientific quantity actually estimated.

Common Mistakes

• Wrong: “The interaction p-value is small, so exposure causes the genetic effect to change.” Correction: The test concerns a model-defined statistical contrast. A causal claim requires design and assumptions that address confounding, selection, measurement, and model validity.
• Wrong: “The interaction is nonsignificant, so there is no effect modification.” Correction: Nonsignificance means the test did not reject its null at the chosen level. Inspect the estimate and interval; imprecision may leave important differences plausible.
• Wrong: “The genetic effect is significant in one stratum but not the other, so the effects differ.” Correction: Test the difference directly, using its standard error and the covariance structure of the estimates.
• Wrong: “There is a G×E interaction,” without naming the scale. Correction: State whether the result concerns, for example, additive mean differences or multiplicative risk ratios, and give the contrast’s units or interpretation.