Fig. 2

The winner’s curse exists in the estimation of effect size for SNPs identified from the primary study. The histograms of the estimation error \(\widehat {\mu }^{(1)}-\mu \) for positive effect SNPs (SNPs with log-odds ratio greater than 0) and negative effect SNPs (SNPs with log-odds ratio smaller than 0) are plotted separately. The mean values of the estimation error is drawn with vertical dashed lines. From the figure, it can be concluded that the magnitude of the observed effect sizes \(\hat {\mu }^{(1)}\) tend to be larger than the magnitude of their true effect. The observed effect sizes tend to be exaggerated