Lucas
★    

Brazil,
2014-02-07 12:41
(3703 d 03:49 ago)

Posting: # 12362
Views: 17,070
 

 Sample size calculation for R-SABE [RSABE / ABEL]

Hi everybody.

ANVISA (Brazil's regulatory agency) is now studying the possibility of accepting EMA's method for scaling the BE acceptance interval based on the variability of the reference medication. So we are struggling a little bit in the sample size calculation, since it is very new to us. We have always used PASS for sample size calculation, for the standard BE studies, and did not manage to reproduce the results of PowerTOST calculations for RSABE. Is a whole different calculus? For example, when I try to calculate a sample size for a full replicate crossover design (TRTR, RTRT) considering a true ratio of 0.95, a target power of 80% and a reference ISCV of 63%, in PASS I got 28 subjects (considering the equivalence limits of 69.84%–143.19%) and in PowerTOST I got 22 subjects.
Can you guys help me with that? Should I throw away my PASS? :confused:


Edit: Category changed. [Helmut]
Helmut
★★★
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Homepage
Vienna, Austria,
2014-02-07 15:21
(3703 d 01:09 ago)

@ Lucas
Posting: # 12365
Views: 15,738
 

 EMA’s ABEL

Hi Lucas,

welcome to the forum. ;-)

❝ ANVISA […] is now studying the possibility of accepting EMA's method for scaling the BE acceptance interval based on the variability of the reference medication.


Interesting.

❝ So we […] did not manage to reproduce the results of PowerTOST calculations for RSABE. Is a whole different calculus?


Yes, since the method is aggregate (scaling for CVWR >30% with a 50% cap, ratio with 80–125%) you cannot estimate the sample size directly, but have to use simulations – for some background see the paper* by the two Lászlós. Therefore, PASS (or NQuery Advisor as well) cannot do the job.

❝ […] when I try to calculate a sample size for a full replicate crossover design (TRTR, RTRT) considering a true ratio of 0.95, a target power of 80% and a reference ISCV of 63%, in PASS I got 28 subjects (considering the equivalence limits of 69.84%–143.19%) and in PowerTOST I got 22 subjects.


In PowerTOST (EMA’s method) you have to use the function sampleN.scABEL(), not sampleN.TOST() with the scaled acceptance range.

require(PowerTOST)
sampleN.scABEL(theta0=0.95, CV=0.63, targetpower=0.8, design="2x2x4")
+++++++++++ scaled (widened) ABEL +++++++++++
            Sample size estimation
---------------------------------------------
Study design:  2x2x4 (full replicate)
log-transformed data (multiplicative model)
1e+05 studies simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 0.63; CVw(R) = 0.63
Null (true) ratio = 0.95
ABE limits / PE constraints = 0.8 ... 1.25
Regulatory settings: EMA
- CVswitch =  0.3, cap on ABEL if CVw(R) > 0.5
- Regulatory constant = 0.76

Sample size search
 n    power
22   0.7312
24   0.7773
26   0.8167

László’s Table A2 gives for CVWR 65% a sample size of 28.
HVDs/HVDPs are also nasty when it comes to the ratio. I would not suggest to assume a ratio of 95% (it jumps around between studies like crazy). I generally use 90%, which in your case would mean 34 sub­jects.

❝ Should I throw away my PASS?


When it comes to reference-scaling, yes.

PS: Where does your 63% come from? If you have done a fully replicated pilot study (RTRT|TRTR or just three periods RTR|TRT) calculate CVWT as well. Sometimes the reference is an awful product and the test is substantially better. You’ll get a reward for that (the CI will be narrower). In PowerTOST you can give both CVs as a vector (test’s first). Let’s say CVWT 45% and CVWR 63%.

sampleN.scABEL(theta0=0.95, CV=c(0.45, 0.63), targetpower=0.8, design="2x2x4")
+++++++++++ scaled (widened) ABEL +++++++++++
            Sample size estimation
---------------------------------------------
Study design:  2x2x4 (full replicate)
log-transformed data (multiplicative model)
1e+05 studies simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 0.45; CVw(R) = 0.63
Null (true) ratio = 0.95
ABE limits / PE constraints = 0.8 ... 1.25
Regulatory settings: EMA
- CVswitch =  0.3, cap on ABEL if CVw(R) > 0.5
- Regulatory constant = 0.76

Sample size search
 n    power
16   0.6787
18   0.7496
20   0.8038



  • Tóthfalusi L, Endrényi L. Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs J Pharm Pharmaceut Sci. 2011; 15(1): 73–84. online

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Lucas
★    

Brazil,
2014-02-07 17:49
(3702 d 22:40 ago)

@ Helmut
Posting: # 12369
Views: 15,599
 

 EMA’s ABEL

Hi Helmut!

❝ In PowerTOST (EMA’s method) you have to use the function sampleN.scABEL(), not sampleN.TOST() with the scaled acceptance range.


I was using sampleN.RSABE. Thanks for the advice! ;-)

❝ PS: Where does your 63% come from? If you have done a fully replicated pilot study (RTRT|TRTR or just three periods RTR|TRT) calculate CVWT as well. Sometimes the reference is an awful product and the test is substantially better.


It was provided by the sponsor, but it was not obtained from a replicate design. So they do not have the actual WR nor the WT, but expect it to be equal or less than that.

I read the paper that you provided, it is going to help us study more this scaling thing.

Hey Detlew.

❝ Unfortunately I can't reproduce your numbers. Could you please post the code (function calls) you have use with PowerTOST?


sampleN.RSABE(CV=.63,design="2x2x4",regulator="EMA", targetpower=.8)

++++++++ Reference scaled ABE crit. +++++++++
           Sample size estimation
---------------------------------------------
Study design:  2x2x4 (full replicate)
log-transformed data (multiplicative model)
1e+05 studies simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 0.63; CVw(R) = 0.63
Null (true) ratio = 0.95
ABE limits / PE constraints = 0.8 ... 1.25
Regulatory settings: EMA
- CVswitch =  0.3
- Regulatory constant = 0.76

Sample size search
 n     power
16   0.62480
18   0.69921
20   0.75837
22   0.80487


But as pointed out by Helmut, I used the wrong code.

❝ For the 2x2x4 design the PASS calculations are moreover based on a model including carry-over. In today's time no one will use such an model.


I'm sorry, but we may be a little outdated down here then. We do include carry-over in our replicate studies. Where can I find more info about that to update our knowledge?

Thank you guys for the help!
Helmut
★★★
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Homepage
Vienna, Austria,
2014-02-07 18:12
(3702 d 22:18 ago)

@ Lucas
Posting: # 12370
Views: 15,836
 

 Carry-over

Hi Lucas!

❝ ❝ For the 2x2x4 design the PASS calculations are moreover based on a model including carry-over. In today's time no one will use such an model.


❝ I'm sorry, but we may be a little outdated down here then. We do include carry-over in our replicate studies.


May I ask which code you are using?

❝ Where can I find more info about that to update our knowledge?


Well, this goody…

S Senn
Cross-over Trials in Clinical Research
John Wiley & Sons, Chichester (2nd ed 2002)
ISBN: 978-0-471-49653-3

…is essentially an essay against carry-over. If there is a true sequence effect (or more precisely unequal carry-over) you can’t do anything in the analysis. The treatment estimates will be biased. Since there is no method to deal with carry-over, the only option we have is to avoid it by design, i.e., sufficiently long wash-out periods.
You will find some stuff (and linked references) in the forum.

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Lucas
★    

Brazil,
2014-02-07 18:42
(3702 d 21:47 ago)

@ Helmut
Posting: # 12371
Views: 15,476
 

 Carry-over

Helmut

❝ May I ask which code you are using?


We use Pharsight's Phoenix, and not R or SAS.

❝ If there is a true sequence effect (or more precisely unequal carry-over) you can’t do anything in the analysis. The treatment estimate will be biased.


Yes, I understand that, but did not get why it should be withdrawn from the model, because then how am I supposed to know when a carry-over effect took place... Well that's a discussion for another topic and probably has already been done here. There is no need for answering that again here, I'll just search the forum.
Thanks again guys, see ya.
Shuanghe
★★  

Spain,
2014-02-10 18:11
(3699 d 22:19 ago)

@ Lucas
Posting: # 12383
Views: 15,421
 

 Carry-over

Hi Lucas,

❝ ...then how am I supposed to know when a carry-over effect took place...


check predose concentration on period 2 or later periods if you have > 2 periods. In general carryover shouldn't be any problem if your washout is long enough.

All the best,
Shuanghe
d_labes
★★★

Berlin, Germany,
2014-02-07 15:37
(3703 d 00:53 ago)

@ Lucas
Posting: # 12366
Views: 15,664
 

 PowerTOST and Sample size estimation for R-SABE

Hi Lucas!

❝ ANVISA (Brazil's regulatory agency) is now studying the possibility of accepting EMA's method for scaling the BE acceptance interval based on the variability of the reference medication.


Fine for you. That minimizes the burden for you in case of HVD/HVDP.

❝ So we are struggling a little bit in the sample size calculation, since it is very new to us. We have always used PASS for sample size calculation, for the standard BE studies, and did not manage to reproduce the results of PowerTOST calculations for RSABE. Is a whole different calculus? For example, when I try to calculate a sample size for a full replicate crossover design (TRTR, RTRT) considering a true ratio of 0.95, a target power of 80% and a reference ISCV of 63%, in PASS I got 28 subjects (considering the equivalence limits of 69.84%-143.19%) and in PowerTOST I got 22 subjects.


Unfortunately I can't reproduce your numbers. Could you please post the code (function calls) you have use with PowerTOST?

You are right in guessing that PowerTOST and PASS uses different calculus.
In case of 'usual' power for replicate studies the difference is that PowerTOST uses by default exact calculation of the power via Owen's Q-function. PASS uses here an approximation via shifted central t-distribution. For the 2x2x4 design the PASS calculations are moreover based on a model including carry-over. In today's time no one will use such an model.

For reference scaled ABE PASS don't has a module AFAIK. At least the versions I have seen so far.

The use of the usual power calculation with simply plugging in the widened BE acceptance ranges from the EMA guidance is only a very rough approximation to the problem.

The respective functions in PowerTOST dealing with scaled ABE (sampleN.scABEL() for the EMA approach, sampleN.RSABE() for the FDA) tackle the problem by an other way: power calculation via simulations. See the PDF "Implementation details of the power calculations via simulations for scaled ABE" in the doc sub-directory of the R-package for more details.

Moreover I highly recommend you the search function of the forum. We had some discussions here concerning that problem.

❝ Should I throw away my PASS?


When it comes to reference-scaling, yes.
When it comes to replicate designs, also yes if you are interested in an exact solution.


Ups. Helmut was faster than me, as always :-D.

Regards,

Detlew
kumarnaidu
★    

Mumbai, India,
2014-04-18 15:38
(3633 d 01:52 ago)

@ d_labes
Posting: # 12858
Views: 15,043
 

 PowerTOST and Sample size estimation for R-SABE

Hi all,
I have estimated one sample size for partial reference replicated study below.
By considering 12 dropout total sample size will be 54+12=66. I have used CV from our earlier in-house study (calculated from Swr).

+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
-----------------------------------------------
Study design:  partial replicate (2x3x3)
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.95,  CV = 0.42

Sample size (total)
 n     power
54   0.807190

Now CRO has given me the same sample size but with different justification. They kept power 90%, CV=0.34 (from literature). Sample size=49+17=66.
In our earlier study we had 9 dropouts out of 66. According to them they cannot use my justification because we will be in trouble if number of dropouts will get exceeds from 12 and in that case we will have subjects <54 (calculated by me). Then what is correct here ? I am confused.

Kumar Naidu
Dr_Dan
★★  

Germany,
2014-04-18 21:29
(3632 d 20:01 ago)

@ kumarnaidu
Posting: # 12859
Views: 14,942
 

 PowerTOST and Sample size estimation for R-SABE

Dear Kumar Naidu
To get things clear: You are the sponsor of the study and the CRO is the service provider. If you have a reasonable sample size estimation and if you want to pay for 66 subjects then the CRO should perform the study as you suggest unless they have reasonable objections. In case you anticipate a formulation difference of <5% and a power of 80% then the sample size solely depends on the intra-subject variability. This variability is not carved in stone. It is up to you to assume if the true value is rather 42% or 34%.
At the end it is the responsibility of the sponsor.
I hope this helps.
Kind regards
Dr_Dan

Kind regards and have a nice day
Dr_Dan
kumarnaidu
★    

Mumbai, India,
2014-04-19 08:04
(3632 d 09:25 ago)

@ Dr_Dan
Posting: # 12860
Views: 14,956
 

 PowerTOST and Sample size estimation for R-SABE

Thanks Dr_Dan for your valuable comments.
My concern is just the number of dropouts they have kept. And according to me we should give priority to our in-house data for sample size estimation not published literature. Because the power of the study will ultimately suffer if the observed CV > assumed CV and this is same as getting more dropouts than assumed.

Kumar Naidu
Astea
★★  

Russia,
2015-06-25 03:14
(3200 d 14:16 ago)

@ d_labes
Posting: # 14982
Views: 13,256
 

 PowerTOST and Sample size estimation for R-SABE

Dear All!
I like the giraffe finally understood the power of scaled approach and I am shocked by the required sample size...
Does it mean that we DO NOT need more than 40 subjects for ANY HVD with CV 30-60% bearing in mind just GMR about 90-110% in four period replicate study?

In order to compare sampleN.TOST unscaled results with sampleN.scABEL I calculated several points for CV in the range 0.3-0.6, assuming thetha0=0.9, design="2x2x4".
The results of sampleN.scABEL naturally coincides with those of Tóthfalusi et Endrényi (in brackets):
CV 0.3  34 (35)
CV 0.35 30 (34)
CV 0.4  30 (31)
CV 0.45 28 (29)
CV 0.5  28 (28)
CV 0.55 30 (30)
CV 0.6  32 (32)


As far as I know sampleN.scABEL simulates studies to get the target power so it would be erroneously just to calculate sample size using sampleN.TOST and scale theta1 and theta2, wouldn't it?
The graph for sampleN.scABEL results has a natural minimum at CV=50% (as far as I understand it is because of the EMA limit on scale).
The difference between unscaled and scaled results is drastic. It doesn't fit in my head because there exist replicate studies completed with more than 50 subjects... It turns that it was redundantly?

[image]
d_labes
★★★

Berlin, Germany,
2015-06-25 11:19
(3200 d 06:11 ago)

@ Astea
Posting: # 14984
Views: 13,293
 

 Sample size for scABEL/RSABE vs. conventional ABE

Dear Astea!

I can't retrace why you are shocked that the sample size for scABEL is much lower than that of conventional average bioequivalence (ABE).

Quote from the paper of the two László's *:
"Both EMA and FDA developed the approaches for highly variable drugs in order to reduce the regulatory burden, i.e. to lower the required number of subjects in BE studies. The sample size tables in the Appendix demonstrate that both authorities achieve this goal."

Your computations verify that statement :cool:.

BTW: Your statement that no more than 40 subjects are needed is only valid in your investigated CV range. CV=0.8 (80%) gives for your settings n=50.
For the FDA recommended method (RSABE) and regulatory settings the sample sizes are even lower.


  • László Tóthfalusi and László Endrényi
    Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs
    J Pharm Pharmaceut Sci 15(1) 73 - 84, 2011

Regards,

Detlew
mittyri
★★  

Russia,
2015-06-25 12:43
(3200 d 04:47 ago)

@ Astea
Posting: # 14986
Views: 13,003
 

 PowerTOST and Sample size estimation for R-SABE

Dear Astea,

I completely agree with the Detlew's post above.
Let me explain some additional issues.

❝ As far as I know SampleN.scABEL simulates studies to get the target power so it would be erroneously just to calculate sample size using SampleN.TOST and scale thetha1 and theta2, wouldn't it?


Absolutely!
Please compare the results:
sampleN.scABEL(theta0=0.90, CV=0.5, targetpower=0.8, design="2x2x4")
and
sampleN.TOST(alpha=0.05, targetpower=0.8, theta0=0.9, theta1=0.6984, theta2=1.4319, CV=0.50, design="2x2x4")

❝ It doesn't fit in my head because there exist replicate studies completed with more than 50 subjects... It turns that it was redundantly?


That's not so easy...
When you performed first study with replicate design in Russia, the Sponsor wasn't sure - is it possible to wide the limits or not. Even after "the carving in red book"...
AFAIK now we can use all advantages of replicate designs in our studies, experts already approved some protocols with scABEL.

From then onward no full replicate studies with 60 subjects for sartans :-D
The most illustrative graph you can find in the Helmut's lecture (slide 98)

Kind regards,
Mittyri
Astea
★★  

Russia,
2015-06-25 15:54
(3200 d 01:35 ago)

@ mittyri
Posting: # 14991
Views: 12,977
 

 PowerTOST and Sample size estimation for R-SABE

Thanks a lot for your explanations! It seems to blame the lack of education...

"Being in minority, even a minority of one, did not make you mad"
d_labes
★★★

Berlin, Germany,
2015-06-25 16:04
(3200 d 01:25 ago)

@ Astea
Posting: # 14992
Views: 13,035
 

 Scaled ABE

Dear Astea!

❝ Thanks a lot for your explanations!


You are welcome.

❝ It seems to blame the lack of education...


Don't worry to much. All this stuff is still more or less new for many of us.
Also for regulatory bodies I strongly suppose. Remember that story concerning type I error of the scaled ABE approach.

Regards,

Detlew
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