Louis52
☆

2018-11-14 22:40
(903 d 00:02 ago)

Posting: # 19601
Views: 3,099

## Power in case of a 3-arm BE study [Power / Sample Size]

Hello,

For a 3 arm (Ref, Test1, Test2) study what is the power adjustment necessary in order to get an overall power of 90%. Let's say by using a Bonferroni method. Can it be done directly in PowerTost? This is in order to find the 'right' sample size.

Thanks!

d_labes
★★★

Berlin, Germany,
2018-11-15 13:58
(902 d 08:44 ago)

@ Louis52
Posting: # 19628
Views: 2,632

## Power in case of a 3-arm BE study

Dear Louis,

» For a 3 arm (Ref, Test1, Test2) study what is the power adjustment necessary in order to get an overall power of 90%. Let's say by using a Bonferroni method. Can it be done directly in PowerTost? This is in order to find the 'right' sample size.

Have a look at this post and links there in.
And use the search button to find more discussions about that topic.

The need of an alpha adjustment (f.i. by Bonferroni method) is discussed in this post. It depends on your overall hypothesis, as described in the mentioned discussions.

If such an alpha-adjustment is necessary it can be done quite easily in PowerTOST. Just change the alpha argument in the function sampleN.TOST() as needed.

Regards,

Detlew
Louis52
☆

2018-11-15 15:32
(902 d 07:10 ago)

@ d_labes
Posting: # 19629
Views: 2,610

## Power in case of a 3-arm BE study

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

Berlin, Germany,
2018-11-15 19:14
(902 d 03:28 ago)

@ Louis52
Posting: # 19630
Views: 2,592

## PowerTOST and 3-way parallel group BE study

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 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
Louis52
☆

2018-11-15 20:52
(902 d 01:50 ago)

@ d_labes
Posting: # 19631
Views: 2,569

## PowerTOST and 3-way parallel group BE study

Hello,

I could not find '3-wayp' as part of the known.designs(). Probably it's still not deployed yet.

Thanks!
d_labes
★★★

Berlin, Germany,
2018-11-15 23:54
(901 d 22:48 ago)

@ Louis52
Posting: # 19632
Views: 2,592

## PowerTOST and 3-way parallel group BE study

Dear Louis,

» I could not find '3-wayp' as part of the known.designs(). Probably it's still not deployed yet.

As I wrote: It's experimental and not public available, because I have implemented it only in my code of PowerTOST.
I think also I should'nt make it part of the package because it's very rare.
Or?

Regards,

Detlew