Why More Ancestry Adjustment Is Not Always Better
Ancestry adjustment is used to reduce confounding: allele frequencies and outcome risks may both vary across ancestry, creating an association that does not represent a within-population genotype effect. But adjustment is not automatically improved by adding more ancestry variables. A proxy may overlap strongly with the tested genotype, absorb variation that carries a genuine genetic signal, or leave too little genotype variation to estimate an effect precisely.
The key is to ask what each adjusted variable represents in the causal question. A well-chosen measure of a common cause can reduce bias. A variable that captures part of the genetic exposure, or is nearly redundant with it, can change the quantity being estimated or impair its estimation. These are different problems and require different interpretations.
Use the Causal Structure, Not the Covariate Count
Let \(A\) denote ancestry, \(G\) the tested genotype, and \(Y\) the phenotype. A basic confounding structure is \(A \rightarrow G\) and \(A \rightarrow Y\), alongside a possible effect \(G \rightarrow Y\). Because ancestry is a common cause of genotype and phenotype, failing to account for it can mix a within-ancestry genotype association with differences between ancestry groups. In this setting, adjustment for a suitable ancestry measure is intended to control confounding.
An ancestry proxy \(C\), such as a principal component, is a measured summary rather than ancestry itself. It can be useful if it represents the confounding structure adequately. But a proxy calculated from genetic markers may also capture variation in the tested locus or in nearby, correlated genetic variation. It may therefore overlap with the exposure whose association is being estimated.
A causal diagram helps make the distinction explicit. If \(C\) is a proxy for a common cause of \(G\) and \(Y\), adjustment can reduce confounding. If \(C\) also captures part of the genetic signal under study, adjustment can remove information or redefine the target. In a regression, these possibilities appear as changes in the conditional coefficient, the residual genotype variation, or both.
Importantly, correlation between \(G\) and an ancestry covariate does not by itself prove that adjustment biases a correctly specified estimate. With a homogeneous additive effect, adequate genotype variation within levels of the covariate, and a model that includes both \(G\) and the confounder correctly, the conditional coefficient for \(G\) can still estimate that effect. The practical risks are loss of precision, inadequate overlap, model misspecification, or adjustment for a variable that is part of the signal or pathway specified by the target question.
Worked Example: Adjustment Removes Confounding Without Removing the Genotype Effect
Suppose a hypothetical study uses centered variables and has \(Var(G)=1\), \(Var(C)=1\), and \(Cov(G,C)=0.60\), where \(C\) adequately represents an ancestry-related confounder. Assume the conditional outcome model is \(Y=1.2G+0.8C+\varepsilon\), with the error uncorrelated with \(G\) and \(C\). Compare the unadjusted and adjusted genotype coefficients.
The unadjusted slope is \(Cov(G,Y)/Var(G)\). From the model, \(Cov(G,Y)=1.2Var(G)+0.8Cov(G,C)=1.2(1)+0.8(0.60)=1.68\). Thus the unadjusted slope is \(1.68/1=1.68\) outcome units per genotype unit.
In the correctly specified regression of \(Y\) on both \(G\) and \(C\), the coefficient of \(G\) is \(1.2\). The unadjusted slope is larger because it includes the association between \(G\) and the outcome contribution \(0.8C\). Here, adjustment removes that confounding component while retaining the genotype effect specified in the model.
This example is a useful check against a common overstatement: an ancestry covariate correlated with genotype does not necessarily absorb the genotype coefficient. Whether it does depends on what the covariate represents and on the information available to distinguish their effects.
Why Overlap Determines Precision
In ordinary least squares regression of \(Y\) on \(G\) and covariates \(C\), the coefficient of \(G\) can be understood by first removing from both \(G\) and \(Y\) the parts predicted by \(C\), then regressing the residualized outcome on the residualized genotype. This is the partial-regression result. Adjustment therefore relies on genotype variation that remains after accounting for the covariates.
For a single genotype predictor and covariates, the standard error has the form \(SE(\hat{\beta}_G)=\hat{\sigma}/\sqrt{S_{GG}(1-R^2_{G\mid C})}\), where \(S_{GG}\) is the centered sum of squares for \(G\), \(R^2_{G\mid C}\) is the proportion of genotype variation explained by the covariates, and \(\hat{\sigma}\) is the residual standard deviation from the outcome model. As \(R^2_{G\mid C}\) approaches 1, the denominator shrinks. This is a loss of precision, even when the underlying coefficient has not been attenuated.
Worked Example: A Real Effect With Much Lower Precision
Consider a hypothetical linear association model with \(S_{GG}=100\), \(\hat{\sigma}=1\) outcome unit, and a true conditional genotype effect of \(0.50\) outcome units per genotype unit. Suppose a proposed ancestry adjustment explains 96% of the genotype variation, so \(R^2_{G\mid C}=0.96\). Compare the standard error with and without that adjustment, holding the residual standard deviation fixed for this illustration.
Without the covariate, the standard error is \(1/\sqrt{100}=0.10\). With adjustment, the remaining genotype sum of squares is \(100(1-0.96)=4\), so the standard error is \(1/\sqrt{4}=0.50\). The coefficient can remain \(0.50\), but its standard error is now five times as large.
The adjusted model has not shown that the biological effect disappeared. Rather, the data contain little genotype variation independent of the ancestry proxy, making the effect harder to distinguish from that proxy. If the proxy explained 100% of the genotype variation, the adjusted genotype coefficient could not be estimated separately at all.
When the Proxy Captures the Signal Itself
A different issue arises when the ancestry proxy tracks genetic variation that contributes to the observed phenotype association. For example, a tested marker may tag a broader genetic background that is represented in an ancestry-related score. Controlling for that score can remove the marker’s association with the phenotype. The resulting coefficient answers a conditional question—whether the marker predicts the phenotype beyond the score—not the same question as whether the marker carries a marginal genetic signal.
This change in association is not, by itself, proof that the tested marker has a causal effect. A marker can tag causal variants or other genetic background, and population structure can also produce noncausal associations. The right interpretation depends on the causal diagram and the estimand: a marginal marker association, an effect conditional on ancestry, and an independent effect beyond a genetic score are distinct quantities.
Worked Example: A Marker Association Disappears After Conditioning on a Genetic Proxy
Suppose hypothetical centered variables satisfy \(Var(C)=1\), \(Var(R)=0.25\), and \(Cov(C,R)=0\). Let the tested marker be \(G=C+R\), and let the outcome be \(Y=2C\). Here \(C\) represents genetic background associated with the phenotype, while \(R\) is the part of the marker that is unrelated to that background. Calculate the marginal marker slope and interpret the adjusted result.
Because \(G=C+R\), \(Var(G)=1+0.25=1.25\), and \(Cov(G,Y)=Cov(C+R,2C)=2\). The marginal slope is therefore \(2/1.25=1.60\) outcome units per marker unit. The marker shows an association because it tags the outcome-related genetic background \(C\).
After conditioning on \(C\), the remaining variation in \(G\) is \(R\). But \(Y=2C\) has no remaining variation associated with \(R\), since \(Cov(R,Y)=2Cov(R,C)=0\). The adjusted coefficient of \(G\) is therefore \(0/Var(R)=0\).
The adjustment has removed a real marker association, but these data do not show an independent causal effect of \(G\): the association arose because \(G\) tags \(C\). If the scientific target is the marker’s association, the marginal and conditional results answer different questions. If the target is a direct effect independent of the background, the adjusted result is relevant, provided the model and causal assumptions support that interpretation.
A Short Derivation of the Partial-Regression Result
Let \(\tilde{G}\) be the residual from regressing \(G\) on the covariates \(C\), and let \(\tilde{Y}\) be the residual from regressing \(Y\) on those same covariates. By construction, each residual is orthogonal to the fitted linear combinations of \(C\). In the regression of \(Y\) on \(G\) and \(C\), the coefficient on \(G\) must account for the part of \(Y\) not explained by \(C\), using only the part of \(G\) not explained by \(C\). The least-squares slope of those residuals is:
If \(\sum_i \tilde{G}_i^2=0\), the denominator is zero and the genotype coefficient cannot be separated from the covariates. If that sum is small, the estimate can be unstable. This explains why an ancestry proxy that closely tracks genotype can weaken evidence through reduced information even when it does not alter the true conditional effect.
Practical Checks Before Interpreting an Adjusted Result
The following checks help distinguish confounding control from loss of genetic signal. They do not replace a causal argument, but they make the consequences of adjustment visible.
Specify whether the aim is a marginal marker association, an effect conditional on ancestry, or an effect independent of a genetic background score. These are not interchangeable.
Identify whether each covariate is a proxy for a common cause, a measure that overlaps with the genotype, or a variable on a pathway included in the target effect.
Compare how well the covariates predict \(G\), and inspect whether genotype variation remains across ancestry levels. Very high predictability signals reduced precision or weak identification.
A similar coefficient with a larger standard error suggests reduced precision. A changed coefficient may indicate confounding control, a different conditional estimand, model misspecification, or signal overlap; the change alone does not decide which explanation is correct.
Common Mistake
Wrong reasoning: “Adding more ancestry components must make the genetic association less biased, so any loss of significance means the original association was false.” This treats every proxy as harmless and interprets a larger standard error or changed estimand as proof of no genetic effect.
Correction: An ancestry covariate is useful when it addresses confounding relevant to the target and the model retains enough independent genotype variation. If adjustment greatly increases uncertainty, the data may not distinguish genotype from ancestry-related variation. If the coefficient changes, examine the causal role of the covariate and specify which conditional or marginal association is being reported. Neither a loss of significance nor an attenuated coefficient, by itself, establishes that the original genetic signal was spurious.
Check Your Understanding
Use the causal structure and the regression consequences to answer the following questions.
- In the structure \(A \rightarrow G\), \(A \rightarrow Y\), and \(G \rightarrow Y\), why can adjustment for an adequate measure of \(A\) help estimate the genotype association?
- If a covariate explains nearly all variation in \(G\), what happens to the precision of the adjusted genotype coefficient, and what happens if it explains all of that variation?
- In the marker example, why does the adjusted coefficient equal zero even though the marginal slope is positive?
- Does correlation between a principal component and a tested genotype prove that adjustment biases the genotype coefficient? Explain.
- Name two distinct scientific questions that marginal and ancestry-adjusted marker coefficients can answer.