Challenges of Adjusting Single-Nucleotide Polymorphism Effect Sizes for Linkage Disequilibrium

Genome-wide association studies (GWAS) were successful in identifying SNPs showing association with disease, but their individual effect sizes are small and require large sample sizes to achieve statistical significance. Methods of post-GWAS analysis, including gene-based, gene-set and polygenic risk scores, combine the SNP effect sizes in an attempt to boost the power of the analyses. To avoid giving undue weight to SNPs in linkage disequilibrium (LD), the LD needs to be taken into account in these analyses.

We review methods that attempt to adjust the effect sizes (β-coefficients) of summary statistics, instead of simple LD pruning.

We subject LD adjustment approaches to a mathematical analysis, recognising Tikhonov regularisation as a framework for comparison.

Observing the similarity of the processes involved with the more straightforward Tikhonov-regularised ordinary least squares estimate for multivariate regression coefficients, we note that current methods based on a Bayesian model for the effect sizes effectively provide an implicit choice of the regularisation parameter, which is convenient, but at the price of reduced transparency and, especially in smaller LD blocks, a risk of incomplete LD correction.

There is no simple answer to the question which method is best, but where interpretability of the LD adjustment is essential, as in research aiming at identifying the genomic aetiology of disorders, our study suggests that a more direct choice of mild regularisation in the correction of effect sizes may be preferable.