PRS-CS in detail: Bayesian regression with continuous shrinkage

PRS-CS, introduced by Ge and colleagues in 2019, is a Bayesian polygenic-scoring method that addresses two problems classical scoring cannot solve. First, marginal GWAS effect sizes are inflated for SNPs in linkage disequilibrium with the true causal variant. Second, even after LD pruning, classical scores treat all retained SNPs as having effects sampled from the same prior, which underfits highly polygenic traits and overfits sparse ones.

The continuous shrinkage prior

PRS-CS places a continuous shrinkage prior on each SNP's true effect size. Concretely, the prior on the effect of SNP j is N(0, σ²_j × σ²_g), where σ²_j is a SNP-specific scaling drawn from a Gamma distribution with shape parameter a (default 1) and rate parameter δ_j × phi. The hyperparameter phi controls the global degree of shrinkage: small phi shrinks all effects toward zero aggressively, large phi allows large effects to remain large.

The choice of phi is critical. PRS-CS-auto, the recommended mode, places a half-Cauchy hyperprior on phi and learns it from the data jointly with the SNP effects. PRS-CS-fixed lets the user set phi externally, useful when transferring a model to a new cohort with known polygenicity.

The Gibbs sampler

The posterior over SNP effects, σ²_g, and phi has no closed form, so PRS-CS uses a Gibbs sampler. Each iteration cycles through the parameters, drawing each one from its full conditional distribution given the others. The implementation details that matter for accuracy are the LD-block partitioning and the within-block multivariate normal updates.

• The genome is partitioned into approximately independent linkage-disequilibrium blocks.
• Within each block, effects are sampled jointly from a multivariate normal whose covariance is the inverse of (LD_matrix + diagonal shrinkage terms).
• σ²_g is sampled from an inverse-Gamma posterior whose parameters depend on the current effect sizes.
• Phi is sampled from a continuous distribution determined by the integrated prior and the current SNP-specific scalings.

Convergence diagnostics

Effective sample size is also computed per chain from the autocorrelation function. Low ESS is flagged separately because R-hat alone can be misleading when the chains are stuck in correlated regions of the posterior.

LD reference handling

PRS-CS requires an LD reference matched to the user's ancestry. Haeckel ships sparse LD panels covering all major continental ancestries, computed from publicly available reference VCFs. When a user's ancestry is admixed, the platform computes a blended reference at evaluation time with a conservative mixing parameter chosen to avoid amplifying mismatch between the panel and the user.

When PRS-CS performs best

PRS-CS dominates classical methods on highly polygenic traits where the assumption of small effects spread across thousands of SNPs is correct. Height, BMI, schizophrenia, and most psychiatric traits fall into this category. For traits with a small number of large-effect variants (a handful of MHC associations driving most autoimmune signals, for example), LDpred2 or SBayesR sometimes outperforms PRS-CS because their priors better accommodate the spike of large effects.