Ancestry Structure in Gene–Environment Analysis

Why Ancestry Structure Matters for G×E

A pooled genotype–environment interaction estimate can reflect more than the within-ancestry relationship between genotype, exposure, and outcome. Allele frequencies may differ across ancestry groups, and exposure prevalence may differ as well. Consequently, the ancestry composition of one genotype–exposure group can differ from the composition of another. If ancestry also predicts the outcome, comparing those groups can mix within-ancestry differences with between-ancestry differences.

The key is to keep two issues separate. Compositional ancestry confounding arises when ancestry weights differ across genotype–exposure groups and those differences distort the pooled contrast relative to a specified common-composition contrast. Ancestry-specific effect heterogeneity arises when the interaction contrast itself differs across ancestry strata. Heterogeneity can occur even when all genotype–exposure groups have the same ancestry composition; it is not, by itself, compositional confounding.

This definition concerns distortion of a contrast, not whether ancestry-specific effects are equal. It also does not, on its own, establish a causal interaction. The interpretation depends on the outcome, genotype and exposure definitions, analysis scale, and assumptions supporting causal claims.

How Different Ancestry Weights Enter the Contrast

Let \(w_{ge,a}=P(A=a\mid G=g,E=e)\) be the ancestry proportion in a particular genotype–exposure group. The pooled mean in that group is a weighted average of its ancestry-specific means:

Because the weights may vary across the four groups, the pooled additive interaction is

To compare like with like, choose target weights \(q_a\), with \(q_a\geq 0\) and \(\sum_a q_a=1\), and use those same weights for all four means. The standardized contrast is

The target \(q_a\) might represent an overall study population or another population relevant to the research question. It is part of the estimand: different target weights can give different summaries when interaction effects vary by ancestry.

Worked Example: A Pooled Interaction With No Within-Ancestry Interaction

A Short Decomposition: Composition and Within-Stratum Effects

The difference between pooled and standardized contrasts can be written directly. Subtract the common-weight contrast from the pooled contrast, aligning the four signed cell means:

This identity follows by substituting the expressions for \(\Delta_{\mathrm{pooled}}\) and \(\Delta_q\) and collecting the coefficients of each \(\mu_{ge,a}\). It shows that the difference depends on deviations of each cell’s ancestry weights from the chosen common weights, multiplied by the corresponding ancestry-specific means. If the weights are identical across all four cells and equal to \(q_a\), every coefficient difference is zero, so \(\Delta_{\mathrm{pooled}}=\Delta_q\). The stratum-specific interactions may still differ; equal composition does not imply homogeneous effects.

Worked Example: Heterogeneity Without Compositional Confounding

Adjustment, Stratification, and What They Require

Ancestry adjustment aims to compare genotype–exposure groups at a common ancestry composition, or to estimate a model-based conditional contrast. Its success depends on the chosen model and on adequate data. For example, in the first worked example, the conditional mean model is

where \(I(A=B)\) equals 1 for stratum B and 0 for stratum A. This model includes an ancestry difference in the outcome level but has no \(G\times E\) term. It reproduces all eight ancestry-specific cell means in that example, so adjustment for ancestry recovers a zero additive interaction under the model. A model that omits ancestry would instead report the 6-unit pooled contrast.

In practice, ancestry may be represented by ancestry strata, ancestry proportions, or principal components that summarize genetic variation. These are not interchangeable guarantees of control. The adjustment must adequately represent the relevant ancestry-related structure, and the analysis needs enough observations across ancestry, genotype, and exposure combinations to estimate the desired contrasts. If ancestry-specific genotype or exposure slopes differ, simply adding an ancestry main effect may not capture that pattern. If interaction effects differ by ancestry, a model that forces one common \(G\times E\) effect may be an unsuitable summary for the scientific question.

Stratification makes the comparison explicit: estimate the interaction within each ancestry stratum, then report the stratum-specific contrasts or combine them using stated target weights. This requires enough data and variation within each stratum. If a genotype–exposure cell is absent or extremely rare in a stratum, its contrast may not be estimable with useful precision there. A pooled regression can sometimes be more efficient, but efficiency does not repair a misspecified model or create information where the data have little overlap.

For continuous outcomes, an ancestry-heterogeneity assessment can compare a model with a common interaction effect to one that allows the \(G\times E\) interaction to vary with ancestry. With discrete ancestry strata, this means including ancestry-by-\(G\times E\) terms and testing them jointly. A small p-value is evidence against a common interaction under the model and assumptions used; a large p-value does not prove homogeneity, particularly when stratum estimates are imprecise. Inspect the stratum estimates and their uncertainty as well as the test.

Worked Example: Choosing a Common-Composition Estimate

Common Pitfalls and Interpretation

• Calling every ancestry-specific difference confounding. Different \(\Delta_a\) values are effect heterogeneity. They can occur even with identical ancestry weights in every cell, as the second example shows.
• Assuming a pooled contrast is automatically a common effect. With different cell compositions, the pooled contrast may combine ancestry-specific means using different weights in each term. State the target contrast and the weights used.
• Assuming adjustment is sufficient because ancestry is included in a regression. Adjustment works only insofar as the covariates and model represent the relevant structure, the needed cells have support, and the estimand is clearly defined. Main effects alone do not automatically address ancestry-specific interaction heterogeneity.
• Treating a nonsignificant heterogeneity test as proof of equal effects. Such a test may have limited power. Report stratum-specific estimates and uncertainty, and interpret the test in light of the available data.
• Interpreting ancestry as a simple biological cause. Ancestry measures summarize aspects of population history and genetic similarity; they may also track social, geographic, or environmental differences. Statistical adjustment does not, by itself, identify which pathways produced an association.