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 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