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Although genome-wide association studies have successfully identified thousands of risk loci for complex traits, only a handful of the biologically causal variants, responsible for association at these loci, have been successfully identified. Current statistical methods for identifying causal variants at risk loci either use the strength of association signal in an iterative conditioning framework, or estimate probabilities for variants to be causal. A main drawback of existing methods is that they rely on the simplifying assumption of a single causal variant at each risk locus which is typically invalid at many risk loci. In this work, we propose a new statistical frameworks that allows for the possibility of an arbitrary number of causal variants when estimating the posterior probability of a variant being causal. A direct benefit of our approach is that we predict a set of variants for each locus that under reasonable assumptions will …