Power estimation and sample size determination for replication studies of genome-wide association studies

BMC Genomics

Table 2 Empirical biases of power estimators of the replication study in the simulation experiments. The settings of the experiments can be seen in the main text

	\(\beta ^{(2)}\left (\widehat {\mu }^{(1)}\right)\)	\(\beta ^{(2)}\left (\widehat {\mu }_{\textit {CMLE}}^{(1)}\right)\)	\(\beta ^{(2)}\left (\widehat {\mu }_{BR2}^{(1)}\right)\)	\(\beta ^{(2)}\left (\widehat {\mu }_{\textit {EB}}^{(1)}\right)\)	\(\widehat {\eta }_{\textit {EB}}^{(2)}\)
Run 1	0.142	−0.113	0.038	0.058	0.032
Run 2	0.146	−0.109	0.045	0.021	0.001
Run 3	0.144	−0.068	0.045	0.047	0.021
Run 4	0.137	−0.090	0.042	0.052	0.026
Run 5	0.144	−0.126	0.026	0.038	0.016
Average	0.142	−0.101	0.039	0.043	0.019

\(\beta ^{(2)}\left (\widehat {\mu }^{(1)}\right)\), \(\beta ^{(2)}\left (\widehat {\mu }_{\textit {CMLE}}^{(1)}\right)\), \(\beta ^{(2)}\left (\widehat {\mu }_{BR2}^{(1)}\right)\) and \(\beta ^{(2)}\left (\widehat {\mu }_{\textit {EB}}^{(1)}\right)\) are the plug-in based estimators by using observed effect size, CMLE, BR2 and EB in the effect size estimation. \(\widehat {\eta }_{\textit {EB}}^{(2)}\) is proposed EB-based estimator. Bold face indicates the estimator achieving the smallest bias. In the experiments, \(\widehat {\eta }_{\textit {EB}}^{(2)}\) behaves better than others in terms of bias reduction

ISSN: 1471-2164