graveendranath
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2010-01-06 08:36
(5195 d 10:32 ago)

Posting: # 4563
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 Scaled Average Bioequivalence [Regulatives / Guidelines]

Dear Helmut,

We want to conduct a study with partial replicated design (Reference twice) for Europe regulatory. My doubt is

1. Does the Europe Regulatory accepts the Scaled Average Bioequivalence method for highly variable drugs?
2. If we can show that the Intra cv for reference product is > 30% then can we use wider limits (75-133)?

Thank You

Rgds
Raveendranath
Helmut
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2010-01-06 18:01
(5195 d 01:08 ago)

@ graveendranath
Posting: # 4565
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 RSABE (EU)

Dear Raveendranath!

❝ We want to conduct a study with partial replicated design (Reference twice)

❝ for Europe regulatory. My doubt is


❝ 1. Does the Europe Regulatory accepts the Scaled Average Bioequivalence

❝ method for highly variable drugs?


Right now: No, though there are rumours, that RSABE will 'make it' to the final BE-Guideline (for Cmax only) - but we have to wait until publication (March 2010?).

❝ 2. If we can show that the Intra cv for reference product is > 30% then

❝ can we use wider limits (75-133)?


Yes. According to 2006's Q&A-document (Sections 2 and 8), if clinical justifiable (high variability of the reference alone is not enough).
It's important that you power your study to show BE for the case that CV<30%.
Example: expected CV 40%, expected T/R 95%, power 80%, n for a partial replicate design with 75%-133% = 36; if CV in the study = 29 (no widening; AR 80%-125% applicable), T/R 95.5%.

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d_labes
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Berlin, Germany,
2010-01-07 10:14
(5194 d 08:54 ago)

@ Helmut
Posting: # 4569
Views: 4,022
 

 RSABE (EU)

Dear Helmut,

❝ It's important that you power your study to show BE for the case that

❝ CV<30%. Example: expected CV 40%, expected T/R 95%, power 80%,

❝ n for a partial replicate design with 75%-133% = 36;

❝ if CV in the study = 29 (no widening; AR 80%-125% applicable), T/R 95.5%.

Where does the sample size for the partial replicate design come from? :ponder:

Regards,

Detlew
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2010-01-07 14:21
(5194 d 04:47 ago)

@ d_labes
Posting: # 4571
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 RSABE (EU)

Dear D. Labes!

❝ ❝ It's important that you power your study to show BE for the case that

❝ ❝ CV<30%. Example: expected CV 40%, expected T/R 95%, power 80%,

❝ ❝ n for a partial replicate design with 75%-133% = 36;

❝ ❝ if CV in the study = 29 (no widening; AR 80%-125% applicable), T/R

❝ 95.5%.

❝ Where does the sample size for the partial replicate design come from?

:ponder:


Oops! I've set power to 90% instead of 80%. Sorry.
So with CV 40%, 3-way replicate, 75%-133%: n=30; and with n=30, CV 29%, replicate, 80%-125%: T/R 94.4%.

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d_labes
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Berlin, Germany,
2010-01-07 14:56
(5194 d 04:13 ago)

@ Helmut
Posting: # 4573
Views: 5,805
 

 Sample size partial replicate design

Dear Helmut,

once again: Where does the sample size come from?
Can you please explain in a little bit more detail? df, design constant, exact or with non-central t? Or sample size for 2x2 multiplied by 0.75?

Don't call me obtrusive nitpicker :wink:. I'm interested in including this design (RRT, RTR, TRR, a 2-treatment-3-sequence-3-period design) into my "eierlegende wollmilchsau" but have not found any hint about sample size for ABE within that design up to now.
Do you have any reference for me?

Regards,

Detlew
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2010-01-07 15:23
(5194 d 03:45 ago)

@ d_labes
Posting: # 4575
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 Sample size partial replicate design

Dear D. Labes,

❝ once again: Where does the sample size come from?

❝ Can you please explain in a little bit more detail? df, design constant,

❝ exact or with non-central t? Or sample size for 2x2 multiplied by 0.75?


Oh, the latter. I just realize, that the method may not be applicable for the partial replicate.*

❝ Don't call me obtrusive nitpicker :wink:.


No, no; I like that. :ok:

❝ I'm interested in including this design (RRT, RTR, TRR, a 2-treatment-3-

❝ sequence-3-period design) into my "eierlegende wollmilchsau" but have

❝ not found any hint about sample size for ABE within that design up to now.

❝ Do you have any reference for me?


Based on Table 3, 75% of a 2×2 and ~125% of a 2×4 replicate seems to apply as well.


  • Hyslop T, Iglewicz B. Alternative Cross-over Designs for Individual Bioequivalence. Proceedings of the Annual Meeting of the American Statistical Association, August 5-9, 2001. online resource

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Berlin, Germany,
2010-01-07 17:21
(5194 d 01:47 ago)

@ Helmut
Posting: # 4576
Views: 4,149
 

 Sample size partial replicate design: df

Dear Helmut!

THX for the reference. But the power/sample size is unfortunately for IBE, although with sigmaD=0. This is ABE?
Moreover my glasses are not strong enough :cool: for the very, very small tables in the online resource.

Meanwhile I have tried to derive the degrees of freedom (df) and design constant by myself (in the same manner as in Chow, Liu "Design and Analysis of Bioavailability and Bioequivalence Studies", chapter 9.
Here the results (without carry-over) for the df:

source of variation  df
--------------------------
inter-subject       n-1
  sequence          2
  residual          n-3
--------------------------
intra-subject       2*n       
  period            2
  formulation       1
  residual          2*n-3
--------------------------
total               3*n-1
--------------------------

n is the total number of subjects (n1+n2+n3 with ni=number of subjects in sequence i).

As can be seen the intra-subject residual df are the same as for the 2x2x3 design (TRR/RTT or TRT/RTR).

For the design constant my brain is not big enough today.
But my believe is: it is also the same as for the 2x2x3 if we do not consider carry-over.
If yes than we can use the results for the sample size of the 2x2x3 design for that of a partial replicate design and you are fully 'rehabilitated' ;-).
Someone out there to prove me wrong?

Regards,

Detlew
d_labes
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Berlin, Germany,
2010-01-08 11:37
(5193 d 07:31 ago)

@ Helmut
Posting: # 4578
Views: 3,976
 

 Sample size partial replicate design: variance

Dear Helmut,

Let Yi.k the sequence-by-period means (i=sequence, k=period) of the PK parameters under consideration (log-transformed if necessary).
The expected values of these are under the usual model (without carry-over):
                period
sequence    1      2      3
1 TRR     µT+p1  µR+p2  µR+p3
2 RTR     µR+p1  µT+p2  µR+p3
3 RRT     µR+p1  µR+p2  µT+p3
where the pi are the period effects and µT and µR the formulation effects (means adjusted for period effects).

The contrast
F=1/6{2*Y1.1-Y1.2-Y1.3
      -Y2.1+2*Y2.2-Y2.3
      -Y3.1-Y3.2+2*Y3.3}

is then an estimate of the difference between Test and Reference.
This estimate can be shown to have variance (derivation omitted due to length)
var(F)=1/6{1/n1 + 1/n2 + 1/n3}*sigma2e
where the ni are the number of subjects in the sequence groups and sigma2e the error variance (intra-subject).

With the same number of subjects in each sequence this reduces to
var(F)=1/2*(1/n)*sigma2e
      =3/2*(1/N)*sigma2e

where N is now the total number of subjects.

This is the same as the variance of the appropriate contrast of sequence-by-period means for the usual 2x2x3 design (f.i. TRT/RTR) which is (see Chow, Liu "Design and Analysis of Bioavailability and Bioequivalence Studies", chapter 9.3.1)
var(F)=3/8*{1/n1 + 1/n2}*sigma2e
      =3/4*(1/n)*sigma2e
      =3/2*(1/N)*sigma2e


Thus we can use the design constant 1.5 also for the partial replicated design (sequences TRR/RTR/RRT)!
Or the rule 0.75*N for a 2x2 design, but now as a multiple of 3.

This concludes your definitive rehabilitation :-D.
Someone out there to prove me wrong?

BTW: The exact sample size for the partial replicate design assuming expected CV 40%, expected T/R 95%, target power 80% and BE margins 75%-133.333333% is N=27, achieved power=0.801380
BE margins 75%-133%: N=27, achieved power=0.799982

Regards,

Detlew
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