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

Some genetic variants are associated with many traits, but a variant's GWAS statistics are also inflated by the effects of variants in LD with it and by confounding shared by all variants in a study. Existing measures of per-variant pleiotropy, such as counts of significant associations or multi-trait association tests, do not separate these sources. Stratified LD score regression separates them for one trait at a time and only through predefined annotations. We present LRCQ (LD score regression on χ 2 across many GWAS), which estimates for each locus its phenome-wide heritability enrichment: the variance of its causal effects across a set of traits, relative to an average locus. LRCQ regresses squared Z-scores from 30 or more GWAS jointly on squared LD, with per-trait LDSC intercepts and heritabilities fitted in earlier stages. Its pooled least-squares solution has a closed form whose cost does not grow with the number of traits. Its standard errors account for sample overlap and genetic correlation between GWAS. Squared Z-scores identify enrichment at the resolution of LD clumps, not single SNPs, so LRCQ reports clump-level estimates ("omni-loci"). These estimates can be aggregated over any functional annotation or gene set chosen after the analysis. In simulations with real UK Biobank LD and 30 to 1,000 traits, LRCQ was unbiased for its clump-level estimand. When GWAS share samples its test statistics are strongly right-skewed: normal-reference p-values were up to 10-fold anti-conservative at P < 0.001, and skewness-corrected p-values from the exact third cumulant restored type-I error and FDR control. Model-based standard errors were calibrated once the enrichment estimates plugged into them kept the polygenic background. It ranked enriched loci better than mean χ 2 , LD-normalised χ 2 , multi-trait omnibus tests and significant-association counts in 13 of 16 scenarios. Its main vulnerability was a misspecified LDSC intercept. Applied to 444 Pan-UK Biobank European-ancestry GWAS, LRCQ found strongly non-uniform phenome-wide enrichment: the SD of true clump-mean enrichment was 8.3, against a genome mean of 1. It identified 70 omni-loci (99 LD clumps) at FDR 5%, including CRP, CETP, APOB, AKTIP, SMOX, the SHBG region, CASZ1 and HNF1A. These ranked only moderately with mean χ 2 and poorly with counts of significant associations. Gene-level phenome-wide enrichment rose with loss-of-function constraint. Phenome-wide heritability was 3-5-fold enriched in coding, conserved, 5' UTR and promoter sequence, and depleted in repressed chromatin. LRCQ turns hundreds of biobank GWAS into an LD-corrected map of where phenome-wide genetic variance lies, and complements its companion method LRCP, which estimates genetic-effect correlations between loci.