High-dimensional statistical inference for linkage disequilibrium score regression and its cross-ancestry extensions

Linkage disequilibrium score regression (LDSC) has emerged as an essential tool for genetic and genomic analyses of complex traits, utilizing high-dimensional data derived from genome-wide association studies (GWAS). LDSC computes the linkage disequilibrium (LD) scores using an external reference panel, and integrates the LD scores with only summary data from the original GWAS. In this paper, we investigate LDSC within a fixed-effect data integration framework, underscoring its ability to merge multi-source GWAS data and reference panels. In particular, we take account of the genome-wide dependence among the high-dimensional GWAS summary statistics, along with the block-diagonal dependence pattern in estimated LD scores. Our analysis uncovers several key factors of both the original GWAS and reference panel datasets that determine the performance of LDSC. We show that it is relatively feasible for LDSC-based estimators to achieve asymptotic normality when applied to genome-wide genetic variants (e.g., in genetic variance and covariance estimation), whereas it becomes considerably challenging when we focus on a much smaller subset of genetic variants (e.g., in partitioned heritability analysis). Moreover, by modeling the disparities in LD patterns across different populations, we unveil that LDSC can be expanded to conduct cross-ancestry analyses using data from distinct global populations (such as European and Asian). We validate our theoretical findings through extensive numerical evaluations using real genetic data from the UK Biobank study.