Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with complex human traits, but only a fraction of variants identified in discovery studies achieve significance in replication studies. Replication in GWAS studies has been well-studied in the context of winner's curse, which is the inflation of effect size estimates for significant variants in a study. Multiple methods have been proposed to correct for the effects of winner's curse. However, winner's curse is often not sufficient to explain lack of replication. Another reason why studies fail to replicate is that there are fundamental differences between the discovery and replication studies. A confounding factor can create the appearance of a significant finding while actually being an artifact that will not replicate in future studies. We propose a statistical framework that utilizes GWAS replication studies to model winner's curse and study-specific heterogeneity due to confounders and correct for these effects. We show through simulations and application to 100 human GWAS data sets that modeling both winner's curse and study-specific heterogeneity explains observed patterns of replication in GWAS studies better than modeling winner's curse alone.

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