Basic PRS Construction
Given GWAS summary statistics $\hat{\boldsymbol{\beta}}$ and an individual’s genotype vector $\mathbf{g} \in {0,1,2}^M$, the raw PRS is:
\[\text{PRS} = \sum_{i=1}^{M} \hat{\beta}_i\, g_i = \hat{\boldsymbol{\beta}}^\top \mathbf{g}\]Because LD inflates the sum (correlated SNPs contribute redundant signal), raw summation overestimates variance explained. Two families of solutions are standard: clumping + thresholding (C+T) and Bayesian re-weighting (LDpred).
Clumping and Thresholding (C+T)
- Clump: Starting from the most-significant SNP, assign all SNPs within distance $d$ (e.g., 250 kb) with $r^2 > r^2_{\text{thresh}}$ (e.g., 0.1) to that index SNP and remove them.
- Threshold: Retain only index SNPs with $p < p_T$ (optimised by cross-validation).
C+T is simple and robust but discards information from removed SNPs.
LDpred2
LDpred2 places a spike-and-slab prior on effect sizes:
\[\beta_j \sim \pi\,\mathcal{N}(0,\,\sigma_\beta^2) + (1-\pi)\,\delta_0\]and estimates the posterior mean $\mathbb{E}[\boldsymbol{\beta} \mid \hat{\boldsymbol{\beta}}, \mathbf{R}]$ using Gibbs sampling over the LD matrix $\mathbf{R}$, the heritability $h^2$, and the polygenicity $\pi$. The LDpred2-auto variant jointly infers $h^2$ and $\pi$ from summary statistics alone.
Cross-Ancestry Portability
PRS built on European GWAS cohorts show systematically lower predictive accuracy in non-European populations:
| Ancestry | Relative PRS $R^2$ (vs. European) |
|---|---|
| East Asian | 0.75 |
| South Asian | 0.65 |
| African | 0.35 |
Causes include differences in LD patterns, allele frequencies, and causal variant sets. Multi-ancestry GWAS meta-analyses and ancestry-specific LD reference panels (e.g., SDPRX, PRS-CSx) improve portability by jointly modelling effect sizes across populations.