. Author manuscript; available in PMC: 2022 May 1.

Published in final edited form as: Pharm Stat. 2021 Jan 19;20(3):573–596. doi: 10.1002/pst.2095

Table 7.

the overall power comparison between frequentist and our study.

Scenario	Treatment	Four subgroups				Eight subgroups
Scenario	Treatment	Overall Effect	N Per Arm	Frequentist Power^@	Our study Power ^*	Overall Effect	N Per Arm	Frequentist Power^@	Our study Power ^*
No effect	A	0	200	0.05	0.05	0	400	0.05	0.05
No effect	B	0	200	0.05	0.05	0	400	0.05	0.05

Moderate and homogeneous effect	A	0	200	0.99	0.997	0	400	0.99	1
Moderate and homogeneous effect	B	0.17	200	0.99	0.997	0.17	400	0.99	1

Small and homogeneous effect	A	0	200	0.81	0.6043	0	400	0.98	0.8417
Small and homogeneous effect	B	0.085	200	0.81	0.6043	0.085	400	0.98	0.8417

Spread	A	0	200	0.99	0.9984	0	400	0.99	0.9997
Spread	B	0.15	200	0.99	0.9984	0.1375	400	0.99	0.9997

Opposite	A	0.085	200	0.05	0.9757	0.085	400	0.05	0.9987
Opposite	B	0.085	200	0.05	0.9757	0.085	400	0.05	0.9987

One nugget	A	0	200	0.29	0.6456	0	400	0.17	0.591
One nugget	B	0.0425	200	0.29	0.6456	0.0213	400	0.17	0.591

^@:

Power is calculated via the t-test for two independent sample to identify the treatment difference between the two arms.

^*:

All the powers for each scenario are from the design of hierarchical model without interim analysis and without longitudinal data under four or eight subgroups, and the power is defined to identify the treatment difference between the two arms within subgroups.