## PowerTOST and 3-way parallel group BE study [Power / Sample Size]

Dear Louis,

» Sorry, I forgot to mention that this is a parallel design. Does powerTOST allows for more than 2 arms?

Sorry. No .

But! If you act as described in the EMA bioequivalence guideline and evaluate by the strategy 2-at-a-time you can use the results of

If you aim for the all-at-once strategy, i.e. estimate the variability from an ANOVA using all data the above sample size estimate can nevertheless used. It is an conservative estimate since it uses lower degrees of freedom than necessary. Conservative means here you have more power than planned, but never a too low sample size.

But the degrees of freedom are only to very small extent different.

I have experimented a little bit. Here the results for the unofficial

# 2- group parallel design as implemented in PowerTOST

# 3-group parallel design, aka "3-way design"

Only a

Of course for lower sample sizes the difference may be more pronounced. But conservative!

» Sorry, I forgot to mention that this is a parallel design. Does powerTOST allows for more than 2 arms?

Sorry. No .

But! If you act as described in the EMA bioequivalence guideline and evaluate by the strategy 2-at-a-time you can use the results of

`sampleN.TOST()`

with argument `design="parallel"`

and an eventual alpha correction due to multiplicity.If you aim for the all-at-once strategy, i.e. estimate the variability from an ANOVA using all data the above sample size estimate can nevertheless used. It is an conservative estimate since it uses lower degrees of freedom than necessary. Conservative means here you have more power than planned, but never a too low sample size.

But the degrees of freedom are only to very small extent different.

`n-2`

in case of 2-group parallel versus `n-3`

in case of 3-way parallel group design.I have experimented a little bit. Here the results for the unofficial

`design="3-wayp"`

compared to the 2-group parallel design:# 2- group parallel design as implemented in PowerTOST

`sampleN.TOST(CV=0.2, targetpower=0.9, design="parallel", print=F)`

Design alpha CV theta0 theta1 theta2 Sample size Achieved power Target power

1 parallel 0.05 0.2 0.95 0.8 1.25 48 0.904962 0.9

# 3-group parallel design, aka "3-way design"

`sampleN.TOST(CV=0.2, targetpower=0.9, design="3-wayp", print=F)`

Design alpha CV theta0 theta1 theta2 Sample size Achieved power Target power

1 3-wayp 0.05 0.2 0.95 0.8 1.25 48 0.904788 0.9

Only a

*very*small difference in power.Of course for lower sample sizes the difference may be more pronounced. But conservative!

—

Regards,

Detlew

Regards,

Detlew

### Complete thread:

- Power in case of a 3-arm BE study Louis52 2018-11-14 22:40 [Power / Sample Size]
- Power in case of a 3-arm BE study d_labes 2018-11-15 13:58
- Power in case of a 3-arm BE study Louis52 2018-11-15 15:32
- PowerTOST and 3-way parallel group BE studyd_labes 2018-11-15 19:14
- PowerTOST and 3-way parallel group BE study Louis52 2018-11-15 20:52
- PowerTOST and 3-way parallel group BE study d_labes 2018-11-15 23:54

- PowerTOST and 3-way parallel group BE study Louis52 2018-11-15 20:52

- PowerTOST and 3-way parallel group BE studyd_labes 2018-11-15 19:14

- Power in case of a 3-arm BE study Louis52 2018-11-15 15:32

- Power in case of a 3-arm BE study d_labes 2018-11-15 13:58