Functionally-informed fine-mapping and polygenic localization of complex trait heritability

Fine-mapping aims to identify causal variants impacting complex traits. Several recent methods improve fine-mapping accuracy by prioritizing variants in enriched functional annotations. However, these methods can only use information at genome-wide significant loci (or a small number of functional annotations), severely limiting the benefit of functional data. We propose PolyFun, a computationally scalable framework to improve fine-mapping accuracy using genome-wide functional data for a broad set of coding, conserved, regulatory and LD-related annotations. PolyFun prioritizes variants in enriched functional annotations by specifying prior causal probabilities for fine-mapping methods such as SuSiE or FINEMAP, employing special procedures to ensure robustness to model misspecification and winner’s curse. In simulations with in-sample LD, PolyFun + SuSiE and PolyFun + FINEMAP were well-calibrated and identified >20% more variants with posterior causal probability >0.95 than their non-functionally informed counterparts (and >33% more fine-mapped variants than previous functionally-informed fine-mapping methods). In simulations with mismatched reference LD, PolyFun + SuSiE remained well-calibrated when reducing the maximum number of assumed causal SNPs per locus, which reduces absolute power but still produces large relative improvements. In analyses of 49 UK Biobank traits (average N=318K) with in-sample LD, PolyFun + SuSiE identified 3,025 fine-mapped variant-trait pairs with posterior causal probability >0.95, a >32% improvement vs. SuSiE; 223 variants were fine-mapped for multiple genetically uncorrelated traits, indicating pervasive pleiotropy. We used posterior mean per-SNP heritabilities from PolyFun + SuSiE to perform polygenic localization, constructing minimal sets of common SNPs causally explaining 50% of common SNP heritability; these sets ranged in size from 28 (hair color) to 3,400 (height) to 2 million (number of children). In conclusion, PolyFun prioritizes variants for functional follow-up and provides insights into complex trait architectures.

UNIQUENESS OF THE EPR–CHAMELEON MODEL

A classical deterministic, reversible dynamical system, reproducing the Einstein–Podolsky–Rosen (EPR) correlations in full respect of causality and locality and without the introduction of any ad hoc selection procedure, was constructed in Ref. 4. In this paper we prove that the above-mentioned model is unique (see Theorem 3.1) in the sense that any local causal probability measure which reproduces the EPR correlations must coincide, under natural and generic assumptions, with the one constructed in Ref. 4.