LDpred2

LDpred2 assumes that a small fraction of SNPs have non-zero effects while most have zero effect. This is formalized through a point-normal mixture prior:

• A spike at zero for the majority of variants with no causal effect
• A normal distribution for the fraction of causal variants
• The p parameter estimates the proportion of causal variants directly from the data

This explicit modeling of genetic architecture avoids the rigid assumptions of infinitesimal models and captures the sparse, polygenic nature of complex traits more accurately than continuous shrinkage priors alone.

LDpred2 uses a Markov Chain Monte Carlo (MCMC) Gibbs sampling algorithm to iteratively estimate the posterior mean effect size for each genetic variant. The sampler cycles through:

• Updating each SNP's effect size conditional on all other SNPs
• Accounting for linkage disequilibrium (LD) through an LD matrix computed from a reference panel
• Inferring the genetic architecture parameters (heritability and polygenic fraction) alongside effect sizes

The Gibbs sampler converges to the posterior distribution, providing shrunken effect estimates that reduce the winner's curse bias inherent in standard clumping and thresholding approaches.

LDpred2 offers two distinct models to accommodate different trait architectures:

• LDpred2-inf: Assumes all SNPs contribute to the trait with effect sizes drawn from an infinitesimal normal distribution. Best suited for highly polygenic traits where causal variants are widely distributed.
• LDpred2: The sparse model using the point-normal mixture prior, ideal when only a fraction of SNPs are expected to be causal.

The auto version estimates the polygenic fraction parameter p from the data, while users can also specify a grid of p values to evaluate model sensitivity. This flexibility allows researchers to match the model to the known or suspected genetic architecture of their trait of interest.

A critical innovation in LDpred2 is the use of a sparse LD matrix rather than a dense one. The method:

• Applies a threshold to the LD correlation matrix, zeroing out small correlations
• Retains only LD values above a user-specified cutoff (typically r² > 0.01)
• Dramatically reduces memory requirements and computational time

This sparsity enables LDpred2 to scale to millions of SNPs on standard computing hardware, making it practical for large-scale biobank analyses. The sparse representation also acts as a form of regularization, reducing noise from spurious long-range LD patterns.

LDpred2 estimates the SNP heritability directly from GWAS summary statistics as part of the modeling process. The method:

• Uses the LD score regression intercept to correct for confounding
• Estimates the total heritability explained by all SNPs in the model
• Constrains effect size estimates to be consistent with the estimated heritability

This integrated estimation avoids the need for external heritability estimates and ensures that the PRS predictions are properly calibrated. The heritability parameter h² is sampled jointly with the effect sizes in the Gibbs sampler, propagating uncertainty throughout the inference.

LDpred2 implements a robust validation strategy to select optimal hyperparameters:

• Users provide a validation dataset with individual-level genotypes and phenotypes
• The model computes PRS for each set of hyperparameters (p, h²) on the validation set
• The combination maximizing AUC or R² in the validation data is selected for final prediction
• This out-of-sample tuning prevents overfitting to the discovery GWAS

The method also supports cross-validation when a separate validation cohort is unavailable, though independent validation remains the gold standard for unbiased performance estimation.

The standard baseline method for PRS construction that LDpred2 is designed to improve upon. C+T selects variants by pruning based on linkage disequilibrium and retaining only those below a strict p-value threshold.

• Mechanism: Iteratively removes variants in LD with the most significant SNP in a window
• Limitation: Assumes a single significance threshold captures the optimal predictive signal
• Contrast: LDpred2 models the full genetic architecture without arbitrary thresholding

A critical input for LDpred2 that captures the correlation structure between genetic variants in a population-matched cohort. The method uses this matrix to model how effect sizes are distributed across correlated SNPs.

• Format: Typically derived from 1000 Genomes Project or UK Biobank data
• Requirement: Must be ancestry-matched to the GWAS discovery sample
• Impact: Mismatched LD panels introduce systematic bias in posterior effect estimates

The Markov Chain Monte Carlo (MCMC) algorithm at the computational core of LDpred2. It iteratively samples from the posterior distribution of each variant's effect size conditional on all other parameters.

• Process: Cycles through variants, updating effect estimates based on the point-normal mixture prior
• Convergence: Requires sufficient burn-in iterations to reach the stationary distribution
• Output: Produces the posterior mean effect size for each variant, used to construct the final PRS

The comprehensive characterization of the number, frequency, and effect size distribution of causal variants underlying a complex trait. LDpred2 explicitly models this architecture to optimize prediction.

• Parameter p: The fraction of causal variants in the point-normal mixture prior
• Heritability (h²): The total additive genetic variance estimated from the data
• Inference: LDpred2-auto estimates these parameters directly from the GWAS summary statistics, removing the need for a validation dataset

A statistical adjustment for the overestimation bias that occurs when variant effect sizes are selected based on their statistical significance in the discovery GWAS. LDpred2 inherently addresses this through Bayesian shrinkage.

• Problem: Top SNPs in a GWAS have inflated effect estimates due to sampling noise
• LDpred2 Solution: The point-normal prior shrinks all effect estimates toward zero, with the degree of shrinkage proportional to the variant's standard error
• Result: More accurate out-of-sample prediction compared to unadjusted C+T methods