LRCP: identifying functionally related SNPs and genes from phenome-wide genetic-effect correlations using GWAS summary statistics
Genetic correlation describes which traits share genetic causes. The transposed question, which variants act alike across the phenome, has no comparable estimator, although it points directly to shared genes, pathways and regulators. Correlations of GWAS Z scores between variants across many traits are easy to compute, but they are confounded by linkage disequilibrium (LD) and, for any pair of variants, by sample overlap and genetic correlation among the GWAS. We show that in 452 Pan-UK Biobank GWAS the effective number of independent traits is only 58, and that naive tests reject 51-70% of null pairs of distal variants. We introduce LRCP (likelihood and regression on cross-products of Z scores), which estimates the phenome-wide genetic-effect correlation{rho} between SNPs by regressing Z-score cross-products on LD cross components, using per-SNP heritability enrichment from the companion method LRCQ and LDSC-derived plug-ins. For variants in different LD blocks the estimator has a closed form, and its standard errors account exactly for the dependence among GWAS. In simulations LRCP is unbiased (absolute bias at most 0.03), its 95% intervals cover 93-98%, and its type-I error is 5.0-5.7%, whereas naive correlations are attenuated by 41-64% and reject up to 51% of null pairs. In Pan-UK Biobank, LRCP recovers the expected signs among PCSK9, LDLR and APOB variants and estimates{rho} = 0.90 between the TP53 polyadenylation variant rs78378222 and MDM2 rs3730556, whose Z scores correlate at r = 0.67 across traits (conditional bootstrap P = 0.015), although this correlation lies along a shared body-size and red-cell trait axis. Single variant pairs are near the resolution of current biobanks, with precision limited by the number of genetically distinct traits. Genome-wide, among 7,793 enriched LD clumps (30.2 million distal pairs), a conditional test finds 17 pairs at FDR 5%, where naive correlation flags 23 million. Simulating the whole screen under the null shows that this test is conservative and that the 113 strongest links (P < 10-5) lie far beyond the null, which yields 0.025 such pairs per screen. Linked genes share Reactome pathways 4.9 times more often than random pairs of enriched loci. The top pairs form 19 modules, the largest of which match known biology: myeloid differentiation (IRF8, CEBPE, IKZF1), LDL and HDL metabolism, iron homeostasis (TMPRSS6, TFRC), the red-cell membrane (SPTA1, ANK1) and type-2 immunity (TSLP, IL13). LRCP turns phenome-wide summary statistics into a map of functionally related variants and genes.