ElMaestro
★★★

Denmark,
2019-01-08 16:29

Posting: # 19760
Views: 1,020

## Power.TOST and "3x3" [R for BE/BA]

Dear all,
or perhaps mainly the powerTOST authors and maintainers

thanks a lot for power.TOST and related functions. They are great.

I have a question about e.g.

> power.TOST(CV=.3, theta0=.95, n=30, design="3x3") [1] 0.6973262

Is that the chance of showing BE for one of the comparisons, for two comparisons if we assume two are tests formulations and one if ref, or is it "all against all" which is also a common comparison?

Now, I am asking because theta0 seems to be a single number, not a vector.
Imagine we have formulations A, B and C; if true ratios for A/B and B/C are 0.95 then in my little simple universe the true ratio for A/C is ~0.9. Therefore, I imagine it is not for all against all (3 comparisons in my case).

So I wonder what goes on behind the curtains in R when I give the command above and how I should interpret the output here. I read the documentation and did not see an obvious answer but I am also not so well versed with power.TOST.

Many thanks for any input.
Or output, depending on your perspective.

I could be wrong, but...
Best regards,
ElMaestro
d_labes
★★★

Berlin, Germany,
2019-01-09 18:47
(edited by d_labes on 2019-01-09 19:01)

@ ElMaestro
Posting: # 19763
Views: 825

## Power.TOST and "3x3" or other 'higher order' designs

Dear ElMaestro!

» Dear All,
» or perhaps mainly the powerTOST authors and maintainers

» thanks a lot for power.TOST and related functions. They are great.
You are welcome. And welcome in approach to improve PowerTOST. With code, or with documentation. Also questions are helpful in that direction.

If your question(s) is/are targeted the maintainer, email him. I think he is kindly enough to answer .

» I have a question about e.g.
»
» > power.TOST(CV=.3, theta0=.95, n=30, design="3x3") » [1] 0.6973262
»
» Is that the chance of showing BE for one of the comparisons, for two comparisons if we assume two are tests formulations and one if ref, or is it "all against all" which is also a common comparison?

Good question, next question.
AFAIK it is the power of showing BE for one comparison (of two formulations whatever kind, Test or Reference) if the evaluation of the 90% CIs is done via an ANOVA with all date taken in consideration. Any multiplicity considerations are left out. That's because they depend on the combination of more than one test via and or or.

Hope this is enough explanation. If not, don't hesitate to torture me further .

PS: Since my wife is now also retired and at home, be patient. I have not so much spare time since before .

Regards,

Detlew
ElMaestro
★★★

Denmark,
2019-01-10 08:12

@ d_labes
Posting: # 19765
Views: 761

## Power.TOST and "3x3" or other 'higher order' designs

Dear d_labes,

thanks a lot for the response.

» Good question, next question.
» AFAIK it is the power of showing BE for one comparison (of two formulations whatever kind, Test or Reference) if the evaluation of the 90% CIs is done via an ANOVA with all date taken in consideration. Any multiplicity considerations are left out. That's because they depend on the combination of more than one test via and or or.
»
» Hope this is enough explanation. If not, don't hesitate to torture me further .

Actually, I have an odd feeling about this; if we do e.g.
power.TOST(CV=CVx, theta0=1.25, n=Nx, design="3x3")
for any combo of CVx and Nx, then power is seemingly never exceeding 0.05 i.e. nominal alpha. As I see it power converges to 0.05 with incresing Nx.

If we had two serial tests with nominal alpha =0.05 and without any concern for multiplicity then then I'd expect the result in some scenarios to exceed 0.05. So I think the result emitted from 3x3 for a given CV and sample size in its present form may in practice be the answer to this question:
1. If we have three formulations A, B and C, and the true ratio for A/C is theta0, regardless of the ratio for B/C, what is then the chance that A/C evaluates to BE (without using elimination of irrelevant treatments as per EMA)?

Accordingly I guess it is not the answer to this question:
2. If we have three formulations A, B and C, and the true ratio for A/C is theta0, and the true ratio for B/C is also theta0, what is then the chance that either A/C or B/C or both evaluate to BE (without using elimination of irrelevant treatments as per EMA)?

I wonder if a scenario exists where a sponsor would decide to run a 3-treatment test but where only the chance of showing BE for a particular pair (as in contrast to any pair) is desired or realistically considered. I am thinking the latter question may in practice be a somewhat more relevant question for companies and for regulators (the latter translating into a type I consideration). In my world it is often a matter of also assuming e.g. 0.95 for one pair and 0.90 for another pair.

But I really could be entirely wrong in these considerations? Let me know your thoughts, please.

» PS: Since my wife is now also retired and at home, be patient. I have not so much spare time since before .

Yes, I hear people tend to get really busy when they retire. My uncle went into retirement and bought a hammond organ which he had in his sleeping room. I believe there was no space in his living room due to an excess of ugly old furniture. The organ kept him occupied 24/7. He did not let himself be stopped by the fact that he had a complete lack of musical talent and that he was entirely tone deaf. Like his wife, the neighbours in the apartment complex were not entirely enthusiastic about his new hobby. But it kept him very busy and he played on and on. Tinnitus specialists in the area where he lived saw a prominent rise in their income during those years.

I could be wrong, but...
Best regards,
ElMaestro
d_labes
★★★

Berlin, Germany,
2019-01-10 20:15

@ ElMaestro
Posting: # 19766
Views: 737

## Power.TOST and "3x3" or other 'higher order' designs

Dear ElMaestro,

you are totally right in pointing at the shortcomings of PowerTOST with regard to higher order designs with more than two treatments. And here especially with more then one TOST to obtain BE.

IMHO there is no easy way to obtain power/sample size with two or more combined TOST's.
Some spare results are obtainable via using power.2TOST() / sampleN.2TOST(). But restricted to two TOST. But immediately the question arises how the correlation of the data of both TOST should be quantified. And so on.
As discussed here numerous times.

During implementing PowerTOST it was the question: "Leave higher order designs (more than two treatments) out" or not. I decided to not leave them out, with knowing the shortcomings of such an implementation. Not covering all the whistles and bells with more than one TOST. Serial or not.
In the sense "Something is better than nothing".

And in the sense that we don't adapt the power/sample size estimation with regard to having more than one PK metric to fulfill BE judgement.

So far so good for my excuse .
If you have any idea to escape from the shortcomings: Let me know.

» » PS: Since my wife is now also retired and at home, be patient. ...
»
» Yes, I hear people tend to get really busy when they retire. My uncle went into retirement and bought a hammond organ which he had in his sleeping room. ... The organ kept him occupied 24/7... Tinnitus specialists in the area where he lived saw a prominent rise in their income during those years.
Thus at least the Tinnitus specialists are happy with your uncle, growing old. Fortunately.
As I said years ago: "Getting old is not for Sissies."
Not for the person getting old and especially not for the persons around that of growing old.

Regards,

Detlew
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