Fig. 3

The histograms of the error in power estimation for all associated SNPs identified from primary study. a The replication study’s power is estimated by plugging the observed effect size in power calculation formula, i.e. \(\beta ^{(2)}\left (\widehat {\mu }^{(1)}\right)\). b The power is estimated by plugging the CMLE based corrected effect size \(\widehat {\mu }^{(1)}_{\textit {CMLE}}\) in power calculation formula, i.e. \(\beta ^{(2)}\left (\widehat {\mu }^{(1)}_{\textit {CMLE}}\right)\). c The power is estimated by plugging in the BR2 estimator, i.e. \(\beta ^{(2)}\left (\hat {\mu }^{(1)}_{BR2}\right)\). d The power is estimated by plugging the EB based corrected effect size \(\widehat {\mu }^{(1)}_{\textit {EB}}\) in power calculation, i.e. \(\beta ^{(2)}\left (\widehat {\mu }^{(1)}_{\textit {EB}}\right)\). e The power is estimated by EB based method, i.e. \(\widehat {\eta }^{(2)}_{\textit {EB}}\). The mean value of the estimation error is drawn with vertical dashed line. From the figure, it can be seen that \(\widehat {\eta }^{(2)}_{\textit {EB}}\) has the smallest bias in power estimation. The biases for these 5 estimators are 0.144, -0.068, 0.045, 0.047 and 0.021, respectively