  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.
