Population Structure As Instrument Confounding

Why Population Structure Matters for Mendelian Randomization

A genetic variant is not automatically independent of the factors that influence an outcome. In a population with ancestry-related structure, allele frequencies can differ across ancestry groups, while outcome risks can also differ because of environmental, social, geographic, or other background factors. The variant can then be associated with outcome risk through ancestry, even when the variant itself has no causal effect on the outcome.

This is a violation of the instrument independence assumption, not necessarily evidence that the variant acts through an unintended biological pathway. The distinction matters: population structure creates a noncausal association through differences between groups, whereas horizontal pleiotropy concerns a variant’s effect on the outcome through a pathway other than the exposure of interest.

For clarity, consider a binary instrument \(Z\), ancestry group \(A\), exposure \(X\), and outcome \(Y\). The same issue applies to a genetic dosage, such as the number of effect alleles, rather than a binary instrument. In a simplified causal framework, the instrument should be relevant to \(X\), independent of outcome-related potential outcomes, and have no effect on \(Y\) except through \(X\). Population structure threatens independence if \(Z\) and outcome determinants vary together across ancestry groups. It can also make the instrument–exposure association reflect ancestry differences, so relevance and interpretation should be assessed in the population and analysis being used.

How Ancestry Creates an Instrument–Outcome Association

Suppose allele frequencies differ across ancestry groups. Then \(P(A=a\mid Z=1)\) may differ from \(P(A=a\mid Z=0)\). If outcome risk also varies by ancestry, the two instrument groups have different mixtures of background outcome risk. Consequently, their marginal outcome risks can differ even if the instrument has no causal effect on the outcome. If the instrument does affect the exposure, that marginal association may combine the intended causal pathway with this ancestry-related imbalance.

A useful decomposition makes the source of the difference explicit. Let \(m_{za}=E[Y\mid Z=z,A=a]\), using a binary outcome so that this conditional mean is a risk. The marginal difference in outcome risks can be written by adding and subtracting the risk under \(Z=0\) averaged over the ancestry distribution among those with \(Z=1\):

The first term compares instrument groups within ancestry strata, with a common set of weights. The second is a composition term: it arises because ancestry distributions differ between the instrument groups, and it is nonzero when ancestry-specific baseline risks differ. This is an associational decomposition; a causal interpretation of the first term requires the relevant assumptions to hold within strata.

A Pure Confounding Example

Population structure can produce an instrument–outcome association even when there is no within-ancestry association at all. The next example isolates that possibility: outcome risk depends on ancestry but not on instrument status within either ancestry group.

What Ancestry Adjustment Does

Adjustment for ancestry aims to compare instrument groups at the same measured ancestry distribution, rather than comparing groups whose ancestry composition differs. In practice, ancestry may be represented using measured covariates such as self-reported background, genetic principal components, geographic variables, or combinations of these, depending on the study. These measures are not interchangeable, and no single adjustment automatically captures every relevant source of structure.

One way to express the idea is direct standardization. Choose common weights \(q(a)\) that sum to one across ancestry strata. Compute a standardized risk for each instrument value using those same weights, then contrast the standardized risks. For example, in the pure-confounding example, use equal weights of \(0.5\) for \(A_1\) and \(A_2\):

The standardized contrast is zero because, within each ancestry stratum, the risks are identical across instrument groups. More generally, regression adjustment or stratification can be used to condition on measured ancestry variables. The exact model and estimand depend on the outcome and analysis, but the central requirement is that comparisons are made among people with comparable measured ancestry rather than relying only on an unadjusted marginal association.

Study-Design Safeguards and Their Limits

Adjustment is not the only response. Design choices can reduce population structure before estimation, and analysis should reflect the population from which participants were selected.

• Restricting or matching on ancestry-related characteristics can make comparison groups more similar. Restriction may reduce generalizability and does not guarantee that meaningful structure within the selected group has been removed.
• Recruiting across relevant groups and recording ancestry-related covariates allows the analysis to account for measured structure. Adequate overlap matters: if a variant is nearly absent in a stratum, the data may provide little information for a within-stratum comparison.
• Using genetic principal components or related measures can capture some broad axes of genetic variation. They are proxies, not complete measurements of every social, geographic, or genetic difference relevant to the outcome.
• Within-family designs compare genetic differences among relatives, often siblings. Because relatives share much of their ancestry and family background, these designs can reduce confounding from population structure and some family-level factors. They have their own assumptions and may be less statistically precise.

Ancestry is not a simple biological category that fully determines a person’s characteristics. Genetic variation is continuous and overlapping, while social and environmental conditions can also be patterned by geography, family history, and social processes. Adjustment should therefore be justified by the study context, carefully described, and not treated as a guarantee that all confounding has disappeared.

The causal interpretation also depends on the Mendelian randomization assumptions beyond population structure. Ancestry adjustment cannot repair a failure of the exclusion restriction, and a strong instrument does not by itself establish independence. Conversely, an association between ancestry and the instrument is not proof that the MR estimate is biased: bias depends on whether the imbalance also connects the instrument to outcome determinants and on how the analysis handles that structure.

Common Mistake

A related error is to assume that adjustment for a few principal components proves that independence holds. Such adjustment can reduce measured structure, but adequacy depends on the variables measured, model specification, sample composition, and the causal structure of the study. The conclusion should be calibrated to the design and evidence rather than stated as certainty.