LDpred

LDpred computes the posterior mean effect size for every genetic marker rather than selecting only genome-wide significant hits. It starts with GWAS summary statistics and a reference LD panel, then applies a Gibbs sampler to integrate over the posterior distribution. This yields a continuous effect size estimate for all SNPs, including those that fall below strict significance thresholds. The key insight is that many true causal variants have small effects and are missed by p-value thresholding; by modeling the full posterior, LDpred recovers signal from these sub-threshold markers and produces more predictive polygenic scores.

Unlike simple clumping and thresholding, LDpred explicitly accounts for the local correlation structure between genetic variants. It uses an external reference panel such as the 1000 Genomes Project to estimate the LD matrix for each genomic region. During inference, the model re-weights effect sizes to distinguish between a causal variant and a non-causal variant that is merely in high LD with a causal one. This prevents the double-counting of genetic effects and avoids inflating risk scores in regions of high LD. The result is a more accurate partitioning of genetic signal across correlated markers.

LDpred models the genetic architecture using a point-normal mixture prior. A parameter p represents the fraction of all genetic markers that are causal, while the remaining markers have zero effect. The variance of the causal effects is determined by the heritability of the trait. This prior can be tuned: setting p to a small value assumes a sparse architecture with few large-effect variants, while a larger p corresponds to a polygenic architecture where many variants contribute small effects. The LDpred2 extension further refines this by using a grid of p values or a continuous shrinkage prior, removing the need to specify a single fixed proportion of causal variants.

LDpred offers two operational modes that reflect different assumptions about trait architecture. In infinitesimal mode, all markers are assumed to have a non-zero effect drawn from a Gaussian distribution, which is equivalent to setting p=1. This mode is computationally simpler and performs well for highly polygenic traits like height. In non-infinitesimal mode, only a fraction p of markers are causal, and the model performs variable selection via the Gibbs sampler. The optimal mode depends on the trait: psychiatric disorders often benefit from the non-infinitesimal model, while anthropometric traits may be well-served by the infinitesimal assumption.

LDpred2 is a complete reimplementation that addresses the computational bottlenecks of the original method. Key improvements include: sparse LD matrices that ignore small correlations below a threshold to reduce memory usage, a warm-start Gibbs sampler that initializes from a computationally cheap analytic solution, and support for summary statistics with varying sample sizes across SNPs. LDpred2 also introduces a model that uses a continuous shrinkage prior instead of the discrete point-normal mixture, allowing the data to determine the appropriate amount of regularization for each marker without pre-specifying p. These enhancements make LDpred2 scalable to biobank-scale datasets with millions of individuals and tens of millions of variants.

LDpred scores are typically validated in an independent holdout cohort not used for GWAS discovery or LD estimation. The predictive performance is measured by the incremental R² over covariates such as age, sex, and principal components, or by the area under the receiver operating characteristic curve for binary traits. Empirical studies across traits including coronary artery disease, type 2 diabetes, and breast cancer have demonstrated that LDpred consistently outperforms simple clumping and thresholding. The method's ability to incorporate sub-threshold association signal is the primary driver of this improvement, particularly for traits where GWAS loci explain only a fraction of the estimated heritability.

The standard baseline method for polygenic risk score calculation. It first applies a p-value threshold to select significant SNPs from a GWAS summary statistic and then performs LD clumping to retain only independent variants. The final score is a simple sum of the allele counts weighted by their marginal effect sizes. While computationally fast, it ignores the complex correlation structure that LDpred models explicitly.

A Bayesian method that applies a sparse mixture prior on SNP effect sizes, assuming they come from a mixture of normal distributions including a point mass at zero. Unlike LDpred's infinitesimal or point-normal prior, SBayesR models a more flexible genetic architecture by allowing for multiple non-zero effect size distributions. It operates on summary statistics and a shrunk LD matrix for computational tractability.

A Bayesian polygenic prediction method that places a continuous shrinkage prior on SNP effect sizes. Unlike the discrete mixture priors in LDpred, PRS-CS uses a global-local scale mixture of normals, allowing for a smooth and adaptive shrinkage profile. The method infers the posterior effect sizes using a Gibbs sampler with an efficient block update, modeling the LD structure directly from an external reference panel.

A computationally efficient approach that constructs polygenic scores by modeling effect sizes as a mixture of a sparse causal component and an infinitesimal polygenic background. It directly estimates the parameters of this mixture model from summary statistics and an LD reference, avoiding the need for iterative MCMC sampling. This allows it to scale to biobank-scale datasets with millions of markers.

A method that reframes polygenic score construction as a LASSO regression problem using summary statistics and a reference LD panel. It applies an L1 penalty to shrink most coefficients to exactly zero, performing automatic feature selection. The tuning parameter is optimized via a pseudovalidation approach that does not require a separate validation dataset, making it a robust alternative to LDpred's Bayesian shrinkage.