Portability in Admixed Target Populations

Why Admixed Targets Need More Than One Portability Number

A polygenic score is often evaluated in a target population by reporting one measure of predictive performance. In an admixed target, that summary can combine people with different genome-wide ancestry proportions and different ancestry origins at the particular loci contributing to the score. A single number may therefore conceal where the score predicts well, where it predicts poorly, and whether a pooled association partly reflects differences between ancestry groups rather than prediction within them.

The relevant distinction is between global ancestry, the genome-wide proportion of ancestry from each reference population, and local ancestry, the ancestry assigned to a particular chromosomal segment. Neither is a complete description of an individual's genetic background, and neither should be interpreted as a biological cause of an outcome. They are information for defining and evaluating prediction in a target population.

Definition: For individual \(i\), let \(q_{ik}\) be the estimated global ancestry proportion from source \(k\), with \(\sum_k q_{ik}=1\). At locus \(j\), let \(L_{ijk}\) be the number of the individual's two chromosome copies assigned to ancestry \(k\), so \(L_{ijk}\) is 0, 1, or 2 and \(\sum_k L_{ijk}=2\). Global ancestry summarizes ancestry across the genome; local ancestry describes ancestry at a locus or segment. These estimates depend on reference panels and local-ancestry methods.

Decomposing a Score by Local Ancestry

Suppose a score uses \(J\) variants, with fixed weights \(w_j\). Let \(G_{ij}\) be the number of copies of the effect allele carried by individual \(i\) at variant \(j\), and let \(G_{ijk}\) be the number of those copies carried on chromosome segments assigned to ancestry \(k\). Then \(G_{ij}=\sum_k G_{ijk}\). Using uncentered allele dosages, the score and its ancestry-specific contributions are

S_i=\sum_{j=1}^{J} w_j G_{ij} =\sum_{k=1}^{K} S_{ik}, \qquad S_{ik}=\sum_{j=1}^{J} w_j G_{ijk}.

This identity partitions the score's weighted alleles by the local ancestry of the chromosome copies carrying them. It does not mean the score weights are ancestry-specific, nor that \(S_{ik}\) is a separate validated score. If a score is centered or standardized, its centering convention must be specified and applied consistently before interpreting these components.

One way to describe performance in an admixed validation sample is to assess a prespecified prediction metric overall and within strata of global ancestry proportion. Another is to examine ancestry-specific score contributions while adjusting for global ancestry and relevant design variables. For example, a linear association model might be

Y_i=\alpha+\sum_{k=1}^{K-1}\theta_k q_{ik} +\sum_{k=1}^{K}\gamma_k S_{ik} +\mathbf{Z}_i^\mathsf{T}\boldsymbol{\eta}+\varepsilon_i.

Here \(Y_i\) is the measured outcome, \(\mathbf{Z}_i\) contains prespecified covariates such as age, study site, or other relevant predictors, and one global ancestry proportion is omitted because the proportions sum to one. The \(\gamma_k\) describe conditional associations of score components with the outcome under this model. They are not direct causal effects of ancestry or of the score component. If score components are strongly correlated, their separate coefficients may be imprecise or poorly identified; a model specification does not remove that limitation.

The appropriate performance measure depends on the outcome and intended use. Whatever measure is chosen, compare like with like: use the same outcome definition and evaluation procedure across the full target and ancestry-defined subsets, and report uncertainty. Validation should reflect the target population's ancestry composition and sampling design. Ancestry estimates are imperfect, so sensitivity to reference panels, ancestry grouping, or uncertain local assignments may matter.

Why Pooled Performance Can Differ From Within-Stratum Performance

A pooled association contains both within-stratum covariation and differences in average score and outcome between strata. This follows from the law of total covariance. Let \(A\) denote an ancestry-defined stratum, such as a prespecified range of global ancestry proportions. Write \(E(S\mid A)\) and \(E(Y\mid A)\) for stratum-specific means. Add and subtract those conditional means inside the covariance:

\begin{aligned} \operatorname{Cov}(S,Y) &=E\left[(S-E(S\mid A))(Y-E(Y\mid A))\right]\\ &\quad+E\left[(E(S\mid A)-E(S))(E(Y\mid A)-E(Y))\right]\\ &=E\left[\operatorname{Cov}(S,Y\mid A)\right] +\operatorname{Cov}(E(S\mid A),E(Y\mid A)). \end{aligned}

The first term averages the within-stratum covariances; the second is the covariance of stratum means. The same decomposition applies to variances. Consequently, a pooled regression slope, which is \(\operatorname{Cov}(S,Y)/\operatorname{Var}(S)\) in a simple linear regression with an intercept, can differ from the slopes within strata. The pooled result may reflect between-stratum mean differences as well as within-stratum prediction.

Worked Example: A Pooled Association With a Between-Stratum Contribution

Hypothetical data: Consider two equally sized global-ancestry strata in an admixed validation sample. In stratum 1, the score \(S\) and outcome \(Y\) each have variance 1, their covariance is 0.60, and their means are 0 and 0. In stratum 2, the variances are again 1, the covariance is 0.30, and the means are 2 for \(S\) and 1 for \(Y\). Compare the within-stratum associations with the pooled association.

Within stratum 1, the correlation is \(0.60/\sqrt{1\cdot1}=0.60\), so the simple-regression \(R^2\) is \(0.60^2=0.360\). Within stratum 2, the correlation is \(0.30\), so \(R^2=0.30^2=0.0900\).

The overall means are \(\bar S=1\) and \(\bar Y=0.5\). The mean differences from these overall means are \((-1,-0.5)\) in stratum 1 and \((1,0.5)\) in stratum 2. Thus the between-stratum covariance is \(0.5[(-1)(-0.5)]+0.5[(1)(0.5)]=0.500\). The pooled covariance is \(0.5(0.60)+0.5(0.30)+0.500=0.950\).

For \(S\), the pooled variance is the average within-stratum variance, 1, plus the between-stratum variance of the means, 1, giving 2. For \(Y\), the pooled variance is \(1+0.25=1.25\). Therefore the pooled correlation is \(0.950/\sqrt{2(1.25)}=0.601\), and the pooled simple-regression \(R^2\) is approximately \(0.361\). This pooled \(R^2\) is not the average of the within-stratum values, which is \([0.360+0.0900]/2=0.225\). The difference arises in part from the between-stratum mean pattern; it does not show that the score has equally good within-stratum performance.

These numbers are hypothetical and illustrate a decomposition, not an empirical claim. In real data, stratum means can also reflect environmental or study-design differences. The pooled association alone cannot identify why those means differ.

Local Ancestry Can Change Score Composition

Even among people with similar global ancestry proportions, the ancestry of the chromosome copies at score variants can differ. That matters because a score's weights are applied to alleles, while allele frequencies, linkage disequilibrium (LD), and effect sizes may vary across ancestries. LD is the correlation structure among genetic variants. If a scored variant tags a causal variant differently across ancestry backgrounds, the same weight need not predict the same underlying genetic signal on those chromosome segments. If effects also differ, a score can be mismatched in more than one way.

The score decomposition makes this issue concrete, but does not by itself separate LD mismatch from effect-size heterogeneity. The ancestry contribution \(S_{ik}\) is built with the score's fixed weights; the outcome association of that contribution depends on the target data and on the surrounding genetic and non-genetic structure. Earlier material on LD mismatch and effect-size heterogeneity provides the relevant distinctions; here the emphasis is on how both can coexist across local ancestries within one target sample.

Worked Example: Two Local-Ancestry Contributions Can Cancel in the Total Score

Hypothetical individual: At variant 1, one effect-allele copy lies on an ancestry-A segment and none lie on ancestry-B segments. At variant 2, both effect-allele copies lie on ancestry-B segments. Let \(w_1=0.40\) and \(w_2=-0.20\).

The ancestry-A contribution is \(S_A=0.40(1)+(-0.20)(0)=0.40\). The ancestry-B contribution is \(S_B=0.40(0)+(-0.20)(2)=-0.40\). Hence the total score is \(S=S_A+S_B=0\).

Now suppose, solely to illustrate possible effect heterogeneity, that the outcome's genetic component at these copies is described by effects \(\beta_{1A}=0.50\) and \(\beta_{2B}=0.30\). That component is \(0.50(1)+0.30(2)=1.10\), not zero. The score contributions cancel because of the score weights, while the hypothetical outcome contributions do not. This single person's calculation is not an estimate of population performance, but it shows why total score values can conceal differing local-ancestry contributions and why a score's weights should not be assumed to match effects in every ancestry background.

Worked Example: A Tag Variant Can Predict Differently on Different Ancestry Segments

Hypothetical model: Suppose a standardized causal variant \(C\) has variance 1 and has the same effect \(\beta=0.50\) on both ancestry backgrounds. Let \(Y=0.50C+\varepsilon\), where \(\varepsilon\) is independent of \(C\) and has variance \(0.75\). Then \(\operatorname{Var}(Y)=0.50^2(1)+0.75=1\). A standardized tag variant \(T\) is used as the score on a local segment.

Assume the correlation between \(T\) and \(C\) is 0.80 on ancestry-A segments and 0.20 on ancestry-B segments. Since \(\operatorname{Cov}(T,Y)=0.50\operatorname{Corr}(T,C)\) and both \(T\) and \(Y\) have variance 1, the squared correlation between the tag score and outcome is \(R^2=0.50^2\operatorname{Corr}(T,C)^2\). On ancestry A this is \(0.25(0.80^2)=0.160\); on ancestry B it is \(0.25(0.20^2)=0.0100\).

The effect was held constant, so this difference comes from the tag's different relationship to the causal variant in the hypothetical model. In actual admixed targets, local-ancestry-specific effects, allele frequencies, and covariation among score components may also matter. The two \(R^2\) values cannot simply be averaged to obtain the admixed target's \(R^2\) without additional assumptions about score and outcome distributions and how local segments combine.

A Practical Evaluation Strategy

A careful portability assessment in an admixed target starts by defining the target population and the performance estimand, rather than treating one ancestry label as the analysis. The estimand might be the score's predictive performance for the whole target population, performance within specified global-ancestry strata, or associations of local-ancestry-specific score contributions conditional on global ancestry. These answer different questions.

Define the target and outcome.
Specify who the admixed target represents, the outcome and measurement scale, and the performance metric. State whether the goal is whole-population prediction or a comparison across ancestry-defined subsets.

Estimate ancestry at both scales.
Use global ancestry proportions to describe genome-wide composition and local ancestry estimates at score loci to form ancestry-specific dosage components. Document reference panels and uncertainty in these estimates.

Evaluate the score in the intended target.
Report the prespecified metric overall and, where adequately supported, within defined global-ancestry strata. Use the same outcome and evaluation rules across comparisons, and quantify uncertainty.

Investigate composition without overinterpreting it.
When relevant, compare local-ancestry-specific score contributions in models that account for global ancestry and study design. Check whether the contributions are distinguishable and whether results are sensitive to ancestry definitions or local-ancestry uncertainty.

This strategy does not turn ancestry adjustment into a universal fix. Global ancestry covariates can help distinguish within-ancestry association from broad ancestry-related structure, but they cannot ensure that all confounding is removed. Local ancestry is also estimated with error, and a component model may be unstable if its score contributions are highly correlated. Results should therefore be presented as conditional predictive associations under stated modeling and validation choices.

Common Mistake: Treating a Pooled Estimate as Universally Portable

Wrong reasoning: “The score has a useful pooled \(R^2\) in this admixed sample, so it predicts equally well for every ancestry composition and local ancestry background represented there.” A pooled measure does not establish this. As the covariance decomposition shows, the pooled association can include between-stratum differences; local LD and effects can also vary even among people with similar global proportions.

Correction: State exactly which target population and metric the pooled estimate describes. Examine appropriate within-stratum performance and, where the question requires it, local-ancestry-specific score contributions. Do not interpret differences as causal effects of ancestry, and do not claim equal performance in subgroups merely because a pooled estimate is precise.

Key takeaway: In an admixed target, global ancestry describes genome-wide composition while local ancestry identifies the ancestry background of score alleles. Pooled score performance can combine within-stratum prediction with between-stratum differences, and ancestry-specific LD or effects can make a single population-wide estimate an incomplete summary.

Check Your Understanding

Use these questions to check whether you can distinguish the different sources of information in an admixed-target analysis.

What does global ancestry summarize, and how does it differ from local ancestry at a score locus?
Why can the pooled covariance between a score and an outcome differ from the average within-stratum covariance?
If ancestry-specific score components are strongly correlated, what limitation can arise when estimating their separate coefficients?
In a model where the causal effect is constant but tag–causal correlation differs by ancestry, what feature of the prediction changes?
Why does a pooled performance estimate not establish that the score works equally well across all ancestry compositions in the target?