Quantifying the susceptibility of polygenic scores to ancestry stratification

Polygenic scores aim to predict phenotypes from genetic data, yet they remain vulnerable to spurious correlations arising from environmental variation that covaries with population structure. While standard methods like Principal Component Analysis (PCA) and Linear Mixed Models (LMMs) mitigate this, quantifying the residual risk for specific applications remains challenging. Here, we develop a theoretical framework that quantifies the proportion of genetic variance in a GWAS panel explained by an external ancestry gradient (H), providing a direct measure of stratification susceptibility. We show that this baseline risk is amplified by the ascertainment process itself, which creates a directional bias ({Phi}) that is particularly strong for variants with intermediate probabilities of ascertainment. Applying this framework to the UK Biobank, we find that while uncorrected susceptibility is drastically higher in diverse cohorts, PCA correction effectively flattens this disparity. We observe that the residual susceptibility (H') in corrected diverse panels is often comparable to, or marginally lower than, that found in restricted homogeneous subsets, suggesting that sample diversity need not compromise stratification control. However, for both study designs, residual structure often remains just above or indistinguishable from the theoretical limit of detection. Because even undetectable levels of structure can accumulate to produce significant bias in highly polygenic scores, we introduce a diagnostic to calculate the critical magnitude of environmental confounding required to explain an observed signal. Using this diagnostic, we find that both the well-known divergence in height scores between Sardinia and mainland Europe and novel signals of divergence in systolic blood pressure scores within the British Isles appear relatively robust to residual stratification, albeit for different reasons. While the Sardinia signal would require moderate-to-strong environmental confounding to align with a vanishingly small residual ancestry axis, the systolic blood pressure signals would require implausibly large environmental effects to be explained as artifacts.