Scalable penalized regression boosts accuracy and computational efficiency for single- and cross-ancestry polygenic prediction

Technical Summary: Scalable Penalized Regression for Polygenic Prediction

Problem Statement
Polygenic scores (PGS) offer potential for early risk stratification of complex diseases but face two primary limitations: a trade-off between adaptive SNP shrinkage and computational efficiency, and pervasive Eurocentric bias in Genome-Wide Association Studies (GWAS).

1. Computational vs. Adaptive Trade-off: Existing Bayesian methods (e.g., LDpred2, PRS-CS) utilize flexible priors for adaptive shrinkage but rely on Markov Chain Monte Carlo (MCMC) procedures, resulting in high computational costs. Conversely, penalized regression methods (e.g., Lassosum) are computationally efficient but often apply non-adaptive shrinkage that does not vary with underlying effect size distributions.
2. Ancestry Bias and Transferability: Most GWAS are conducted in European (EUR) populations. PGS trained on EUR data often lose over 50% of their accuracy when applied to non-European populations (e.g., East Asian, African, South Asian) due to heterogeneity in genetic effect sizes, allele frequencies, and linkage disequilibrium (LD) patterns. Furthermore, cross-ancestry methods often suffer from heavy computational costs and lack rigorous validation in East Asian cohorts.

Methodology
The authors propose a scalable penalized regression framework that integrates spike-and-slab LASSO penalties within an ensemble model to achieve both adaptive shrinkage and computational efficiency. The framework consists of two methods:

1. Spike-and-Slab Lassosum (SSL): Designed for single-ancestry prediction.

   • Mechanism: It replaces the constant penalty in standard LASSO with a data-driven adaptive penalty derived from a spike-and-slab prior. This prior models SNP effects as a mixture of a "slab" (Laplace distribution with small $\lambda_1$ for large effects) and a "spike" (Laplace distribution with large $\lambda_0$ for small effects).
   • Optimization: The model maximizes a penalized likelihood using coordinate descent algorithms. It approximates the likelihood using GWAS summary statistics and a reference LD matrix.
   • Ensemble Learning: Instead of selecting a single optimal set of tuning parameters, SSL generates a set of PGSs across a grid of parameters ($\lambda_0, \lambda_1, \theta, s$) and combines them using the SuperLearner ensemble algorithm (utilizing LASSO, ridge, or linear regression) to produce the final score.

2. Prior Spike-and-Slab Lassosum (pSSL): An extension for cross-ancestry prediction.

   • Mechanism: pSSL incorporates prior information from an auxiliary population (e.g., EUR) into the target population's model via a hyperparameter $\eta \in [0,1]$. This is achieved by adding a regularization term that acts as a transfer learning component, effectively imposing a Gaussian prior centered on the auxiliary prediction vector.
   • Data Requirements: Unlike some cross-ancestry methods, pSSL requires only summary statistics from the auxiliary population and does not require individual-level data or LD matrices from the auxiliary population, only from the target population.
   • Ensemble: Similar to SSL, it generates multiple models across a grid of parameters (including $\eta$) and combines them via ensemble learning.

Key Contributions

• Algorithmic Innovation: The integration of spike-and-slab LASSO into a penalized regression framework allows for adaptive shrinkage (preserving strong signals while suppressing weak ones) without the computational burden of MCMC.
• Scalability: The methods utilize coordinate descent and LD block decomposition, significantly reducing runtime and memory usage compared to Bayesian approaches.
• Cross-Ancestry Framework: pSSL provides a practical solution for leveraging large EUR GWAS summary statistics to improve prediction in underrepresented populations without requiring complex multi-population LD modeling or auxiliary individual-level data.

Results

• Simulations (Single-Ancestry): In 11 simulation scenarios covering diverse genetic architectures (sparse, infinitesimal, and hybrid), SSL ranked first in 54.5% of scenarios and second in 18.2%. It achieved an average $R^2$ improvement of 39.7% over C+T, 10.2% over Lassosum, and 4.5% over PRS-CS.
• Simulations (Cross-Ancestry): In 72 cross-ancestry simulation settings, pSSL ranked first in 50.0% of scenarios, outperforming PRS-CSx (27.8%), CT-SLEB (18.1%), and PROSPER (2.7%). The advantage was most pronounced in African (AFR) populations, where pSSL achieved average $R^2$ gains of 14.4% over CT-SLEB.
• Real-Data Analysis (UK Biobank & Dongfeng-Tongji):
  • Single-Ancestry: Across 32 complex traits, SSL achieved optimal accuracy for 90.6% (UKB) and 84.4% (DFTJ) of traits. It improved $R^2$ by an average of 7.8% (UKB) and 10.4% (DFTJ) over PRS-CS.
  • Cross-Ancestry: In the DFTJ cohort (East Asian target), pSSL ranked first in 71.9% of traits, yielding an average $R^2$ gain of 12.3% over PRS-CSx. It notably outperformed others in lipid and red blood cell traits.
• Computational Efficiency:
  • SSL reduced runtime to approximately one-third of PRS-CS (32.5 min vs. 120.7 min) and used less than one-fifth of the memory (9.0 GB vs. 54.3 GB).
  • pSSL required ~1/6 of the runtime of PRS-CSx (56.3 min vs. 319.0 min) and less than 1/4 of the memory.

Significance and Claims
The paper claims that SSL and pSSL successfully bridge the gap between the computational scalability of penalized regression and the data-adaptive shrinkage of Bayesian methods.

• Equity: By demonstrating superior performance in East Asian and African populations, particularly through the pSSL framework, the authors argue these methods have great potential to promote equitable PGS application across diverse populations.
• Practicality: The ability to use summary statistics from auxiliary populations without requiring their individual-level data or LD matrices makes pSSL a practical tool for improving prediction in underrepresented groups where large-scale GWAS are scarce.
• Limitations: The authors note that their analysis was restricted to HapMap3 SNPs, which may underestimate performance in non-European groups. Additionally, the ensemble approach requires sufficient tuning samples (1,500–3,000), and the current pSSL framework is limited to two-population analysis, though this is framed as a pragmatic choice given current data landscapes.

The authors conclude that these methods advance the field by enabling accurate, efficient, and scalable single- and cross-ancestry PGS prediction.