libaiyi
★

China,
2018-06-26 10:00
(974 d 19:32 ago)

(edited by Ohlbe on 2018-06-26 10:24)
Posting: # 18964
Views: 10,600

## Decision of confidence interval of three period BE study [General Sta­tis­tics]

Hi,all

I am curious of the confidence interval decision of three treatment, three sequences, cross over BE study as below, if the goal is to prove the equivalence of any two of them (T1 and R or T2 and R). Will the CI still determined as 95% or 90%?

Sequence/Period  1  2  3        1          R  T1 T2       2          T1 T2 R        3          T2 R  T1

I also want to know how to select the suitable design between latin squares and William design when there exists three treatment, R T1 T2.

Edit: two posts merged. You can edit your message up to 24 hours after posting it [Ohlbe]
Helmut
★★★

Vienna, Austria,
2018-06-26 11:13
(974 d 18:19 ago)

@ libaiyi
Posting: # 18967
Views: 9,325

## Two tests and one reference

Hi libaiyi,

» […] the goal is to prove the equivalence of any two of them (T1 and R or T2 and R). Will the CI still determined as 95% or 90%?

If this is a pivotal study (say you want to demonstrate BE of a capsule (T1) and a tablet (T2) to R which is either a tablet or a capsule) IMHO, you should employ Bonferroni’s 95% which preserves the familywise error rate at 1-(1-0.05/2)2=4.9375%. Reason: When both products are approved, based on ABE a patient my switch from R to T1 or from R to T2.
Slightly off topic: Another story would be one test and two references of different regions. If we ignore tourists, we have two different populations of patients. Then we don’t have to adjust α and go with the 90% CI.

» I also want to know how to select the suitable design between latin squares and William design when there exists three treatment, R T1 T2.

That’s a matter of taste. Williams’ designs are variance-balanced even for carryover (which is not part of the model). Hence, some people (see there) prefer them over Latin Squares. BTW, the EMA’s GL states the six-sequence Williams’ design for the story mentioned above.
More important than the design is the evaluation (see this post).

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
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Brus
☆

Spain,
2020-08-31 07:58
(177 d 21:34 ago)

@ Helmut
Posting: # 21895
Views: 3,073

## Two tests and one reference

Dear Helmut and all,

If one test and two references of different regions are tested in a bioequivalence study, is it necessary a α adjustment?

In my case, we want to demonstrate if the test product is bioequivalent to R1 (European product reference) or if test product is bioequivalent to R2 (Reference product in the United Kingdom).

If I have not misunderstood, in this case, alpha should be penalized, even if they are from different regions and to market in different regions because of the word "OR"?

Is there a way to not penalize alpha? If the "O" is changed to "AND"? Executing two different clinical trials (one for Europe and one for the UK)?

Best regards,
ElMaestro
★★★

Denmark,
2020-08-31 08:23
(177 d 21:09 ago)

@ Brus
Posting: # 21896
Views: 3,043

## Two tests and one reference

Hi Brus,

» If one test and two references of different regions are tested in a bioequivalence study, is it necessary a α adjustment?
»
» In my case, we want to demonstrate if the test product is bioequivalent to R1 (European product reference) or if test product is bioequivalent to R2 (Reference product in the United Kingdom).
»
» If I have not misunderstood, in this case, alpha should be penalized, even if they are from different regions and to market in different regions because of the word "OR"?
»
» Is there a way to not penalize alpha? If the "O" is changed to "AND"? Executing two different clinical trials (one for Europe and one for the UK)?

Here's a different way to look at it:
Can the same patient(s) be affected by your two tests? If yes, it is safer to use correction. If no, no correction should be necessary.

Pass or fail!
ElMaestro
Helmut
★★★

Vienna, Austria,
2020-08-31 08:26
(177 d 21:06 ago)

@ Brus
Posting: # 21897
Views: 3,038

## Two regions: No α adjustment

Hi Brus,

» If one test and two references of different regions are tested in a bioequivalence study, is it necessary a α adjustment?

No.

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
Brus
☆

Spain,
2020-08-31 09:09
(177 d 20:23 ago)

@ Helmut
Posting: # 21899
Views: 3,030

## Two regions: No α adjustment

Dear Helmut and ElMaestro,

But, if α is not adjusted, since there are two reference products, even though they are from different regions, would there be no multiplicity issues?
Helmut
★★★

Vienna, Austria,
2020-08-31 09:26
(177 d 20:07 ago)

@ Brus
Posting: # 21900
Views: 3,030

## Two regions: different populations

Hi Brus,

» But, if α is not adjusted, since there are two reference products, even though they are from different regions, would there be no multiplicity issues?

Consider ElMaestro’s post.
The current regulatory thinking is that an α adjustment is not required since the populations of patients are different (as are the local reference products). If you are concerned about tourists, go ahead and adjust.* If you employ a lower α, any agency will accept that. However, depending on the variability expect roughly 25% larger sample sizes.
BTW, what if tourists switch from one regions’ reference to the other one’s? There is no guarantee that they are BE (see this post). Given, generally we don’t have to worry (see the references in this post).

• Thinking about the US and EU: How large is the subpopulation crossing the pond (not to speak of Europeans visiting Trumpistan). How long will tourists stay on the average? How many will run out of the medication brought with them? If you are able to estimate that, possibly you discover that you have to adjust α to 0.049999999.

library(PowerTOST) # defaults: theta0 = 0.95, targetpower = 0.8 CV  <- seq(0.15, 0.4, 0.05) res <- data.frame(CV = CV,                   alpha1 = 0.050, n1 = NA, # unadjusted                   alpha2 = 0.025, n2 = NA) # Bonferroni for (j in 1:nrow(res)) {   res$n1[j] <- sampleN.TOST(alpha = 0.050, CV = CV[j], details = FALSE, print = FALSE)[["Sample size"]] res$n2[j] <- sampleN.TOST(alpha = 0.025, CV = CV[j], details = FALSE,                             print = FALSE)[["Sample size"]] } res$penalty <- sprintf("%+.2f%%", 100 * (res$n2 - res$n1) / res$n1) names(res)[2:5] <- rep(c("alpha", "n"), 2) print(res, row.names = FALSE)    CV alpha  n alpha  n penalty  0.15  0.05 12 0.025 16 +33.33%  0.20  0.05 20 0.025 24 +20.00%  0.25  0.05 28 0.025 36 +28.57%  0.30  0.05 40 0.025 50 +25.00%  0.35  0.05 52 0.025 66 +26.92%  0.40  0.05 66 0.025 82 +24.24%

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
ElMaestro
★★★

Denmark,
2018-06-26 20:20
(974 d 09:13 ago)

@ libaiyi
Posting: # 18969
Views: 9,269

## Decision of confidence interval of three period BE study

Hi libaiyi,

» I am curious of the confidence interval decision of three treatment, three sequences, cross over BE study as below, if the goal is to prove the equivalence of any two of them (T1 and R or T2 and R). Will the CI still determined as 95% or 90%?

Due to the little word highlighted in red above I am fairly sure I would not apply any other alpha than 5%, meaning I would go with the usual 90% CIs.

Pass or fail!
ElMaestro
Helmut
★★★

Vienna, Austria,
2018-06-26 22:33
(974 d 07:00 ago)

@ ElMaestro
Posting: # 18970
Views: 9,258

## Any of two tests and one reference

Hi ElMaestro,

» » […] if the goal is to prove the equivalence of any two of them (T1 and R or T2 and R).
»
» Due to the little word highlighted in red above I am fairly sure I would not apply any other alpha than 5%, meaning I would go with the usual 90% CIs.

Good point – I missed that! In the past I did not adjust because only one will be marketed (i.e., the entire patient’s risk lies with this product). However, some regulatory statisticians (you know, coffee break chats) seem to be more strict because one gets two chances of passing. Too lazy to crawl the supplementary material of your paper about pilot studies: Is such a case covered?

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
libaiyi
★

China,
2018-06-27 06:25
(973 d 23:07 ago)

@ Helmut
Posting: # 18971
Views: 9,201

## Any of two tests and one reference

Hi Helmut

Sorry I am still a little confused, do you mean that if I try to test any of two tests and one reference (T1=R or T2=R), the CI should still be set as 90%, and if I want to test T1=T2=R, CI should be set as 95%?

Thank you so much.
ElMaestro
★★★

Denmark,
2018-06-27 06:29
(973 d 23:03 ago)

@ Helmut
Posting: # 18972
Views: 9,235

## Hey wait a moment....

Good morning Hötzi,

» Good point – I missed that! In the past I did not adjust because only one will be marketed (i.e., the entire patient’s risk lies with this product). However, some regulatory statisticians (you know, coffee break chats) seem to be more strict because one gets two chances of passing. Too lazy to crawl the supplementary material of your paper about pilot studies: Is such a case covered?

Whose paper? Some crackpot had one published paper and it covered the case of one product being tested in a pilot, then in a pivotal trial, depending on the figures. Rumours have it he is working on another manuscript dealing with scenarios like the one in this thread and that reviewers are way too tough. But then again, you cannot always trust rumours. Only trust google and wikipedia.

Hi all,

ok you'll think that I am nuts, but I think I will need to put it into reverse here:

Let us say both R1 and R2 are (truly) not BE. For simplicity think of them as products with the exact same properties even though they formally may be called something different. Since we are happy if we approve one of them, applying alpha=5% could inflate the type I error (approval of a non-BE product) if the true relative performances are around the acceptance borders.

We need that alpha correction. Sorry.

Edit: Two posts merged. [Helmut]

Pass or fail!
ElMaestro
Helmut
★★★

Vienna, Austria,
2018-06-27 09:45
(973 d 19:47 ago)

@ ElMaestro
Posting: # 18974
Views: 9,186

## Hey wait a moment....

Hi ElMaestro,

» […] I think I will need to put it into reverse here:
» Let us say both R1 and R2 are (truly) not BE…
»
» We need that alpha correction. Sorry.

You want to get both T1 and T2 approved.

T1 = R T2 = R: ⇒ 95% CI

Clearly needs an adjustment because of the simultaneous tests and both T1 and T2 will be marketed.

You want to get either T1 or T2 approved.

T1 = R T2 = R: ⇒ 95% CI

In this case I argued for no adjustment (90% CI) in the past but nowadays I’m leaning towards an adjustment because which one will be marketed is part of a decision tree.

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
Ohlbe
★★★

France,
2018-06-27 10:14
(973 d 19:19 ago)

@ Helmut
Posting: # 18975
Views: 9,224

## Pilot or pivotal ?

Dear all,

» You want to get either T1 or T2 approved.

T1 = R T2 = R: ⇒ 95% CI

In this case I argued for no adjustment (90% CI) in the past but nowadays I’m leaning towards an adjustment because which one will be marketed is part of a decision tree.

Isn't the common practice to first test T1 and T2 vs. R in a pilot study (and I will not get into a debate on whether alpha correction would be needed), select one of the two test formulations, and then test it in a pivotal study in the usual way ? How often do you see both test formulations directly tested in a pivotal study ?

OK, maybe if the product has a very low variability and the number of subjects remains very low, it could make sense and save time to directly go for the pivotal. Any experience ?

Regards
Ohlbe
ElMaestro
★★★

Denmark,
2018-06-27 11:01
(973 d 18:31 ago)

@ Ohlbe
Posting: # 18977
Views: 9,245

## Pilot or pivotal ?

Hello Ohlbe

» Isn't the common practice to first test T1 and T2 vs. R in a pilot study (and I will not get into a debate on whether alpha correction would be needed), select one of the two test formulations, and then test it in a pivotal study in the usual way ? How often do you see both test formulations directly tested in a pivotal study ?

That's right. I have never seen an evaluation of two tests in a single study in which the applicant hoped for approval of both.

» OK, maybe if the product has a very low variability and the number of subjects remains very low, it could make sense and save time to directly go for the pivotal. Any experience ?

Yes absolutely. The majority of dossiers are being accepted without pilot trials. Whether to go for a pilot before a pivotal is dictated by many factors. First to file is a very significant one, but also involved is BCS class, budgets, previous failures ("You guys need to start showing some results!"), gut feeling and much more.
However I get slightly worried when you are suddenly allowing the term sense to enter this discussion. My empirical observation is that that term has absolutely no place in the planning of BE studies.

Pass or fail!
ElMaestro
Ohlbe
★★★

France,
2018-06-27 12:13
(973 d 17:19 ago)

@ ElMaestro
Posting: # 18978
Views: 9,129

## Pilot or pivotal ?

Dear ElMaestro,

» » OK, maybe if the product has a very low variability and the number of subjects remains very low, it could make sense and save time to directly go for the pivotal. Any experience ?

» Yes absolutely. The majority of dossiers are being accepted without pilot trials.

Sure, when you only have one test formulation. But when you hesitate between two ? Would you directly go for a pivotal where both test formulations would be compared to the reference, and then file whichever one passes ?

Regards
Ohlbe
ElMaestro
★★★

Denmark,
2018-06-27 12:48
(973 d 16:45 ago)

@ Ohlbe
Posting: # 18979
Views: 9,138

## Pilot or pivotal ?

Hi Ohlbe,

» Sure, when you only have one test formulation. But when you hesitate between two ? Would you directly go for a pivotal where both test formulations would be compared to the reference, and then file whichever one passes ?

This is purely hypothetical for me. As far as I recall, I have not ever faced such a situation where two test formulations targeting the same authority were heads-on compared in a pivotal trial. I have faced it numerous times in pilot trials, but here the choice of formulation rarely is based on the CI but just on the observed GMR.

If I were in a situation, hypothetically, where I had one pivotal trial with two passing T formulations against a single, and I only needed one approval, then I am not sure what I would base my choice on. It could be cost of goods, or a risk-based assessment of the manufacturing bottlenecks for the two T formulations. Not sure, I have a feeling this would not be science-driven but Guy-in-Armani-suit-driven.

Pass or fail!
ElMaestro
Ohlbe
★★★

France,
2018-06-27 13:43
(973 d 15:49 ago)

@ ElMaestro
Posting: # 18981
Views: 9,125

## Pilot or pivotal ?

Hi ElMaestro,

» This is purely hypothetical for me. As far as I recall, I have not ever faced such a situation where two test formulations targeting the same authority were heads-on compared in a pivotal trial. I have faced it numerous times in pilot trials, but here the choice of formulation rarely is based on the CI but just on the observed GMR.

Precisely. But then, isn't this whole discussion on alpha correction purely hypothetical too ?

Sorry if I'm spoiling a nice thread...

Regards
Ohlbe
ElMaestro
★★★

Denmark,
2018-06-27 20:13
(973 d 09:20 ago)

@ Ohlbe
Posting: # 18982
Views: 9,113

## Pilot or pivotal ?

Hi Ohlbe,

» But then, isn't this whole discussion on alpha correction purely hypothetical too ?

As I see it, it is a mild case of testing into compliance if we don't correct alpha:
If T1 and T2 are both borderline bad (like GMR=0.8) then we will have increased prob >5% type I error) of approving one of them, i.e. approving an unapprovable product.

Pass or fail!
ElMaestro
jag009
★★★

NJ,
2018-06-29 18:53
(971 d 10:39 ago)

@ Ohlbe
Posting: # 19000
Views: 9,046

## Pilot or pivotal ?

Hi Olhbe

» Isn't the common practice to first test T1 and T2 vs. R in a pilot study (and I will not get into a debate on whether alpha correction would be needed), select one of the two test formulations, and then test it in a pivotal study in the usual way ? How often do you see both test formulations directly tested in a pivotal study ?
»
» OK, maybe if the product has a very low variability and the number of subjects remains very low, it could make sense and save time to directly go for the pivotal. Any experience ?

Damn. We did pivotals 4-way crossover 3T vs R before! R&D said no time and material was cheap! I said "Ooooookay..."
John
ElMaestro
★★★

Denmark,
2018-06-29 20:11
(971 d 09:22 ago)

@ jag009
Posting: # 19002
Views: 8,969

## Pilot or pivotal ?

Hello John,

» Damn. We did pivotals 4-way crossover 3T vs R before! R&D said no time and material was cheap! I said "Ooooookay..."

How many of the T's turned out BE? I hope the CRO awarded you the title of "best client ever" afterwards.

By the way and quite OT, I will be in Parsippany in July. That's still your whereabouts? Are you in office week of July 16 and does your coffee machine work ?

Pass or fail!
ElMaestro
jag009
★★★

NJ,
2018-07-03 15:38
(967 d 13:54 ago)

@ ElMaestro
Posting: # 19014
Views: 8,941

## Pilot or pivotal ?

Hi ElMaestro,

» How many of the T's turned out BE? I hope the CRO awarded you the title of "best client ever" afterwards.

Pivotals. The 2 4way 3T vs R studies turned out great as 2 out of 3 formulations made BE. I said great so which one are we going forward with and they said "the one which gives us the least headache in manufacturing. Lol

We did this for 2 products. Haha

» By the way and quite OT, I will be in Parsippany in July. That's still your whereabouts? Are you in office week of July 16 and does your coffee machine work ?

You are about 30-45 mins drive from me since I am down south (30 mile). I will be in the office 7/18 and after. Shoot me an email and I will give you my contact. Would love to meet you in person!

Thanks
John
d_labes
★★★

Berlin, Germany,
2018-06-28 17:48
(972 d 11:44 ago)

(edited by d_labes on 2018-06-28 21:33)
@ Helmut
Posting: # 18991
Views: 9,183

## Hey, hey wait another moment....

Dear Helmut, dear other Disku-Tanten,

» You want to get both T1 and T2 approved.

T1 = R T2 = R: ⇒ 95% CI

Clearly needs an adjustment because of the simultaneous tests and both T1 and T2 will be marketed.

I'm not quite sure if you are right here.
Consider the analogy with the "simultaneous" tests of AUC and Cmax.
I haven't seen any alpha correction for that case .
The IUT (intersection union test) principle protects us.
But can be very conservative.

IMHO we don't need an alpha correction for your case above, if we combine the tests with 'and'.

If we combine with 'or', e.g. any of the test products T1 or T2 is choosen for further development or for approval, than we have to split the familywise level of alpha = 0.05 and the two individual null hypotheses have to be tested at a comparisonwise type I error which is a fraction of alpha, e.g. according to the Bonferroni procedure. Means 95% CIs instead of 90% CIs in case of T1, T2 and R.

Reference (wording of my post partly copied from that Reference):
Hauschke D., Steinijans V.W., Pigeot I.
Bioequivalence Studies in Drug Development: Methods and Applications.
New York: Wiley; 2007.
Chapter 7 Designs with more than two formulations / 7.4 Multiplicity

Seems a case for sims if we don't trust in the Reference. Isn't it?
Eventually we can miss-use power.2TOST() if we consider for simplicity two simultaneous test of AUC_T1R and AUC_T2R as the two metrics, which are usually interpreted as two different metrics, e.g. AUC and Cmax, respectively.
Then of course the question of the correlation parameter rho arises. How to choose?

Regards,

Detlew
Helmut
★★★

Vienna, Austria,
2018-07-03 15:22
(967 d 14:10 ago)

@ d_labes
Posting: # 19013
Views: 8,893

## Hey, hey wait another moment....

Dear Detlew,

» IMHO we don't need an alpha correction for your case above, if we combine the tests with 'and'.

THX for reminding me (not for the first time)…

» Seems a case for sims if we don't trust in the Reference. Isn't it?

In God we trust;
all others must bring data.
W. Edwards Deming

» Eventually we can miss-use power.2TOST() if we consider for simplicity two simultaneous test of AUC_T1R and AUC_T2R as the two metrics, which are usually interpreted as two different metrics, e.g. AUC and Cmax, respectively.
» Then of course the question of the correlation parameter rho arises. How to choose?

Not sure. Whereas two PK metrics are always correlated somehow, IMHO, here it may be different. One formulation doesn’t care how it behaves in relation to the other. Too lazy to browse through my pilot studies. I’m pretty confident that some kind of correlation will show up but I doubt that it will be causation. PK is relatively simple but the outcome of a PK study with different formulations depends on an awful lot of manufacturing / process parameters. I think that the safe way would be subjects simulations. Normally for the TIE we use a true GMR of one of the BE-limits and add variability. How to do that in a higher order design? Say for one subject I will have R=1, T1=1.25±se, T2=1.25±se.
Now what?

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
d_labes
★★★

Berlin, Germany,
2018-07-04 11:28
(966 d 18:05 ago)

@ Helmut
Posting: # 19020
Views: 8,898

## Old belives die hard

Dear Detlew,

» » IMHO we don't need an alpha correction for your case above, if we combine the tests with 'and'.
» THX for reminding me (not for the first time)…

Correct.
But old belives die hard

» » Eventually we can miss-use power.2TOST() ...
» » Then of course the question of the correlation parameter rho arises. How to choose?
» Not sure. Whereas two PK metrics are always correlated somehow, IMHO, here it may be different. One formulation doesn’t care how it behaves in relation to the other...

Sounds for me like rho=0 .

Regards,

Detlew