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

BMC Genomics

Table 3 Root mean square error (RMSE) 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	0.246	0.334	0.201	0.202	0.195
Run 2	0.243	0.312	0.196	0.191	0.188
Run 3	0.247	0.303	0.203	0.198	0.192
Run 4	0.236	0.307	0.186	0.192	0.186
Run 5	0.249	0.317	0.198	0.196	0.194
Average	0.244	0.315	0.197	0.196	0.191

\(\beta ^{(2)}\left (\widehat {\mu }^{(1)}\right)\), \(\beta ^{(2)}\left (\widehat {\mu }_{\textit {CMLE}}^{(1)}\right)\), \(\beta ^{(2)}\left (\hat {\mu }^{(1)}_{BR2}\right)\) 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 RMSE. In the experiments, \(\widehat {\eta }_{\textit {EB}}^{(2)}\) behaves better than others in terms of higher estimation accuracy

ISSN: 1471-2164