Quantifying and correcting for the winner's curse in quantitative-trait association studies

Quantitative traits (QT) are an important focus of human genetic studies both because of interest in the traits themselves and because of their role as risk factors for many human diseases. For large-scale QT association studies including genome-wide association studies, investigators usually focus on genetic loci showing significant evidence for SNP-QT association, and genetic effect size tends to be overestimated as a consequence of the winner's curse. In this paper, we study the impact of the winner's curse on QT association studies in which the genetic effect size is parameterized as the slope in a linear regression model. We demonstrate by analytical calculation that the overestimation in the regression slope estimate decreases as power increases. To reduce the ascertainment bias, we propose a three-parameter maximum likelihood method and then simplify this to a one-parameter method by excluding nuisance parameters. We show that both methods reduce the bias when power to detect association is low or moderate, and that the one-parameter model generally results in smaller variance in the estimate.