LRCQ: phenome-wide heritability enrichment of genomic loci from GWAS summary statistics

Genetic variants can be linked to numerous traits; however, a variant's GWAS statistics are also heightened due to the influences of nearby variants in linkage disequilibrium (LD) and shared confounding factors among all variants in a study. Current methods to gauge per-variant pleiotropy, such as tallying significant associations or multi-trait association tests, fail to distinguish between these sources.

Stratum-specific LD score regression addresses this issue for a single trait at a time, necessitating predefined annotations. We introduce LRCQ (LD score regression on chi-square across many GWAS), a technique that calculates each locus's phenome-wide heritability enrichment: the variance of its causal effects across a set of traits, in relation to an average locus.

LRCQ performs a joint regression of squared Z-scores from 30 or more GWAS on squared LD, incorporating per-trait LDSC intercepts and heritabilities determined in earlier stages. The resulting pooled least-squares solution is computationally efficient, with a closed form that does not depend on the number of traits. The standard errors generated by LRCQ account for sample overlap and genetic correlation between GWAS.

As squared Z-scores pinpoint enrichment at the resolution of LD clusters, not individual SNPs, LRCQ provides clump-level estimates (omni-loci). These estimates can be combined across any functional annotation or gene set selected subsequent to the analysis. Simulations utilizing real UK Biobank LD data and ranging from 30 to 1,000 traits demonstrate that LRCQ remains unbiased for its clump-level estimand.

However, when GWAS share samples, the test statistics exhibit strong right-skewness, rendering normal-reference p-values up to 10-fold excessively conservative.