Ancestry Diagnostics for Polygenic Score Performance

Why ancestry diagnostics require more than one check

A polygenic score can predict an outcome partly because it captures genetic associations relevant to that outcome. But it can also track ancestry-related structure: differences in allele frequencies, environments, recruitment, or outcome measurement that are associated with both the score and the outcome. The resulting prediction may work well in one evaluation sample while performing differently in another. A single performance statistic cannot identify which explanation is responsible.

An ancestry diagnostic therefore combines several views of the data. Correlations between a score and ancestry principal components (PCs) show whether the score varies along measured axes of genetic structure. Performance estimated within ancestry strata asks whether the score predicts within those groups, rather than only distinguishing groups. Covariate-adjusted models assess whether score–outcome associations change after accounting for measured PCs. Differences that remain after adjustment may reflect genuine effect heterogeneity, residual confounding, or both; the diagnostics do not, by themselves, determine which explanation is correct.

Score–principal-component correlations

For each PC, calculate the sample correlation between the score and that PC. For example, the correlation with \(C_1\) is

A large absolute correlation indicates that the score is associated with that measured axis of genetic variation in the evaluated sample. It is a diagnostic, not proof of bias: a score can correlate with PCs even when its outcome association is useful within groups. Conversely, small correlations with the PCs examined do not rule out structure along unmeasured axes, nonlinear patterns, or other sources of confounding. Report which PCs were examined, how they were calculated, and the evaluation sample used.

Correlation is also not a performance measure. It describes the relationship between \(S\) and a PC, not between \(S\) and the outcome \(Y\). The outcome association and predictive performance must be examined separately. Analyses are most informative when scores and performance are evaluated in data that are independent of the data used to develop or select the score, with the evaluation design and outcome definition held clear.

Stratified performance and adjusted associations

For a quantitative outcome, a useful starting point is the score slope in each ancestry stratum. In stratum \(g\), the simple linear model is

Here \(a_g\) is the stratum-specific intercept, \(\beta_g\) is the change in the mean outcome associated with a one-unit increase in score within that stratum, and \(\varepsilon_i\) is the residual. This model summarizes a linear association; interpreting it as a calibrated prediction also requires an appropriate evaluation design and assessment of prediction errors. The outcome and score scales should be stated so that the slope has meaningful units.

Compare slopes as well as predictive performance. For example, the within-stratum \(R^2\) is the proportion of the outcome’s sample variation in that stratum explained by the fitted linear model. It depends on the outcome variation and score variation in that stratum, as well as the strength of their association. Thus, \(R^2\) values can differ even when slopes are similar. For applied prediction, also report an outcome-appropriate measure of prediction error or discrimination; do not treat unlike metrics as interchangeable.

A covariate-adjusted model for a quantitative outcome can be written as

The coefficient \(\beta\) describes the score–outcome association conditional on the included PCs under this model. Adjustment addresses measured linear associations with those PCs, given the model form and data. It does not automatically remove confounding from omitted or poorly measured structure, nonlinear relationships, environmental differences, or selection into the evaluation sample.

To assess whether the score slope differs by stratum, include score-by-stratum interactions. With two strata, let \(G_i=1\) indicate stratum 2 and \(G_i=0\) indicate stratum 1:

The adjusted slope in stratum 1 is \(\beta\), and in stratum 2 it is \(\beta+\theta\). The interaction coefficient \(\theta\) estimates the difference in adjusted slopes. Evidence that this difference is nonzero supports effect heterogeneity on the modeled outcome scale, provided the model and its assumptions are reasonable. A nonsignificant interaction is not proof that slopes are identical: its uncertainty may be large, especially with limited sample size or little score variation within a stratum.

Why adjustment can change an association

The omitted-variable relationship makes clear why a score–outcome association can change after adjustment. Consider one measured covariate \(C\) and suppose the outcome follows

If \(Y\) is instead regressed on \(S\) alone with an intercept, its population slope is \(\operatorname{Cov}(S,Y)/\operatorname{Var}(S)\). Substituting the stated outcome model gives

The last equality uses the assumption \(\operatorname{Cov}(S,\varepsilon)=0\). If both \(\gamma\) and \(\operatorname{Cov}(S,C)\) are nonzero, omitting \(C\) shifts the score slope away from \(\beta\). With multiple covariates, the same principle applies jointly: omitted variables associated with both score and outcome can contribute to the unadjusted association. This algebra justifies treating attenuation after PC adjustment as a warning sign to investigate, not as proof that all structure-related bias has been removed.

Distinguishing residual confounding from heterogeneity

Ancestry diagnostics are most useful when interpreted jointly. A score–PC correlation indicates measured structure in the score. A change in the score coefficient after PC adjustment indicates that the conditional association differs from the unadjusted one. Variation in stratum-specific slopes or an interaction estimate indicates possible differences in association across strata. None of these findings alone separates residual confounding from genuine effect heterogeneity.

For example, an interaction can appear because PCs do not adequately capture structure within strata, or because the score has different associations with the outcome across strata. Conversely, a common adjusted slope can conceal meaningful differences if the analysis has low precision. Consider the estimates alongside their uncertainty, the amount of score variation in each stratum, and whether the strata have comparable outcome definitions and evaluation procedures. Interpretation also depends on adequate overlap: if score values barely overlap between strata, comparisons may rely heavily on extrapolation from the fitted model.

Common mistake and practical interpretation

Wrong reasoning: “The score–PC correlation is small, and the adjusted score coefficient is similar to the unadjusted one, so population structure cannot be affecting performance.” Correction: Those results only address the measured PCs and the specified linear adjustment in this evaluation sample. They cannot rule out unmeasured or nonlinear structure, differences in environments or measurement, or other sources of bias. Similarly, a difference between stratum-specific slopes is not automatically biological effect heterogeneity; omitted structure and imprecision can produce or obscure differences.

The practical value of these diagnostics is therefore not a single pass-or-fail rule. They help locate where prediction may be unstable and clarify what additional evidence would be useful. Report estimates in context, state the score and outcome scales, and separate measured association from causal interpretation. In particular, a score that predicts across ancestry groups does not by itself show that its component genetic effects are transportable or causal.