Building Scores With PRS-CSx

Why Build Ancestry-Specific Scores?

A polygenic risk score (PRS) sums genotype contributions across many variants. For an individual \(i\), a score based on \(m\) variants can be written \(S_i=\sum_{j=1}^{m}G_{ij}w_j\), where \(G_{ij}\) is the allele dosage at variant \(j\) and \(w_j\) is its estimated effect weight. In a multi-ancestry analysis, the same variant can have different marginal associations across populations because allele frequencies and linkage disequilibrium (LD) patterns differ, and because effect sizes may differ. A single set of weights can therefore transfer imperfectly to a target population.

PRS-CSx addresses this by estimating ancestry-specific SNP weights jointly from ancestry-specific GWAS summary statistics and population-matched LD reference information. It then produces ancestry-specific scores whose combination can be tuned using validation data in the target population. The important distinction is that the method allows information to be shared across populations while retaining separate effect estimates; it does not assume that every population has identical LD or identical SNP effects.

Summary Statistics, LD, and the Scaling of the Likelihood

The role of LD can be seen in a simplified model. Within ancestry group \(a\), suppose genotypes have been standardized to mean zero and variance one, the phenotype has been adjusted for specified covariates, and the residual phenotype has standard deviation \(\sigma_a\). Let \(\boldsymbol{\beta}_a\) denote joint effects measured in phenotype units per one standard-deviation increase in genotype, and let \(\mathbf R_a\) be the genotype correlation (LD) matrix. Under a linear approximation, the marginal association at a SNP reflects not only that SNP's joint effect but also correlated effects at other SNPs.

For sufficiently large samples and under the usual small-effect approximations, the vector of marginal \(z\)-statistics has approximate mean \(\sqrt{n_a}\mathbf R_a\boldsymbol{\beta}_a/\sigma_a\) and approximate noise covariance \(\mathbf R_a\). This is a working summary-statistic likelihood, not an exact identity for all GWAS designs. It relies on compatible phenotype and genotype scaling, suitable adjustment for covariates, and LD estimates that represent the GWAS population. In particular, omitting \(\sigma_a\) is justified only when the phenotype residual scale has been set to one or effects have been expressed in residual-standard-deviation units.

The appearance of \(\mathbf R_a\) explains why ancestry-matched LD matters. A marginal association can be large because the tested SNP tags a causal variant, even if its own joint effect is small. If the LD reference has a different correlation pattern, the model can attribute the marginal signal incorrectly among correlated variants. PRS-CSx uses LD information matched to each ancestry-specific GWAS rather than treating one reference panel as universally appropriate.

Joint Continuous Shrinkage and Ancestry-Specific Weights

PRS-CSx uses a Bayesian regression framework with continuous shrinkage. In general terms, each SNP effect has a prior that shrinks weakly supported effects toward zero, while allowing a small number of well-supported effects to remain comparatively large. The prior has global shrinkage, which controls the overall degree of shrinkage, and SNP-specific local variation, which allows different variants to be shrunk by different amounts. This differs from a rule that simply sets all effects below a hard threshold to zero.

The multi-ancestry model combines this shrinkage framework with ancestry-specific summary-statistic likelihoods and their corresponding LD matrices. Its joint structure allows information about shared genetic architecture to inform the ancestry-specific estimates. However, the resulting weights remain population-specific: different sample sizes, LD patterns, effect evidence, and allele frequencies can yield different posterior estimates. The method is not a guarantee that effects are shared, nor does it remove the need for well-matched GWAS and LD inputs.

A global shrinkage setting, commonly denoted \(\phi\), governs the overall strength of shrinkage in the PRS-CS framework. In practice, the appropriate setting depends on the trait and the available data. Hyperparameter selection must use validation data that are separate from the final test data, as established in the earlier material on validation and nested tuning. PRS-CSx outputs ancestry-specific weights for candidate settings; target-population validation can then guide which setting and which score combination to use.

From Ancestry-Specific Weights to a Target-Population Score

Let \(\widehat{\boldsymbol{\beta}}_a\) be the estimated weights for ancestry \(a\), and let \(\mathbf G_i\) be the target genotype vector with each dosage standardized using the same allele mean and standard deviation used to define the corresponding effect estimate. The ancestry-specific score is \(S_{ia}=\mathbf G_i^\mathsf{T}\widehat{\boldsymbol{\beta}}_a\); this standardization includes centering, and any intercept is handled separately in the prediction model. With several ancestry-specific scores, a candidate combined score can be written \(S_i(\mathbf c)=\sum_a c_a S_{ia}\), where \(\mathbf c\) denotes combination weights. Scores may be standardized within the target training or validation data before combination, provided the same transformation is then applied to the held-out data.

Validation chooses among candidate score combinations by a prespecified predictive metric appropriate to the outcome and analysis. It does not make the validation metric an unbiased estimate of final performance after many combinations have been tried. The final test set must remain untouched during this selection. For complex tuning, nested validation provides an outer assessment of the complete selection procedure. This tutorial focuses on the role of target-population validation in choosing among PRS-CSx score outputs; detailed strategies for interpreting and combining ancestry-specific scores are treated separately in the subsequent material.

Assumptions, Diagnostics, and Alternatives

The estimation is most defensible when each GWAS is well defined, variants are aligned to a common reference and allele convention, and the LD panel represents the population underlying that GWAS. The summary statistics should correspond to the modeled effect scale, and any sample overlap or correlated errors across GWAS should be considered when material. Target validation must represent the intended prediction population and must be kept separate from final evaluation data. These conditions do not ensure good prediction; they make the estimated weights interpretable under the working model.

PRS-CSx is not the only approach. Clumping and thresholding selects relatively independent variants and applies a significance cutoff; it is simpler, but the cutoff can discard useful weak effects and clumping does not model LD jointly in the same way. A single-ancestry Bayesian score can model LD and shrinkage, but may use less relevant evidence for a target population than a multi-ancestry analysis. A fixed meta-analysis can combine association evidence, but a single pooled effect can obscure ancestry-specific LD or effect differences. PRS-CSx is useful when suitable ancestry-specific GWAS, LD references, and validation data are available; it can be less reliable when those inputs are small, poorly matched, or incompatible.

A common mistake is to say, “The largest ancestry-specific GWAS must provide the best weights for everyone, so use its score alone.” Large sample size can improve precision, but it does not remove differences in LD, allele frequency, or effects, and it does not establish which score predicts best in a particular target population. The correction is to estimate with appropriate ancestry-specific LD, preserve the distinction among the resulting scores, and compare candidate combinations using properly separated validation data. A related mistake is to treat a favorable validation result as final-test performance; selection itself can overfit validation noise.