Bioequivalence and Bioavailability Forum • FDA Progesterone on HVD vs Endrenyi

FI
☆

Austria,
2012-03-09 14:50
(4424 d 20:24 ago)

Posting: # 8244
Views: 9,701

FDA Progesterone on HVD vs Endrenyi [RSABE / ABEL]

Dear all,

I cross-checked the L. Endrenyi/L Tothfalusi chapter in Kanfer/Shargel’s book “Generic Drug Product Development” and found a difference to the code provided by FDA for Progesterone:
The so called “x” (=PE²-SE²) in the Progesterone BE recommendation does not resemble the Em (=PE²) which would be necessary to have the identical formula for the Confidence limit calculation:

CL = Em-Es + √(Lm+Ls) acc. to your Kanfer/Shargel Chapter

I tried now to simulate data in EXCEL to find out, which one is correct and calculated a “third” way of concluding BE: simply the exponentiated CI for the difference of the means using the SE of the differences.

Instead of solving the problem, I have now 3 (slightly) differing results; This might be due to simple programming mistake but I couldn’t find them up to now;

1) Does anyone know, if there is a(nother) mistake in the FDA recommendation (the “x” as described above)?

Thanks a lot

Edit: Category changed. [Helmut]

Helmut
★★★

Vienna, Austria,
2012-03-09 17:36
(4424 d 17:38 ago)

@ FI
Posting: # 8245
Views: 8,628

FDA Progesterone on HVD vs Endrenyi

Post reply

Servus Franz,

welcome to the forum!

That’s very interesting, inasmuch the progesterone guidance specifically states:

For detailed information on this approach, please refer to the published book chapter, Davit B, Conner D. Reference-scaled average bioequivalence approach. In: Kanfer I, Shargel L, eds. Generic Drug Product Development – International Regulatory Requirements for Bioequivalence. New York, NY: Informa Healthcare, 2010: 271-272.

❝ I cross-checked the L. Endrenyi/L Tothfalusi chapter in Kanfer/Shargel’s book “Generic Drug Product Development”…

I don’t have this book; stupid question: Are you sure that you are dealing with the right chapter (see above)?

❝ … and found a difference …

❝ I tried now to simulate data in EXCEL to find out, which one is correct and calculated a “third” way of concluding BE: simply the exponentiated CI for the difference of the means using the SE of the differences.

❝ Instead of solving the problem, I have now 3 (slightly) differing results; This might be due to simple programming mistake but I couldn’t find them up to now;

With EMA’s full replicate data set I got in Phoenix/WinNonlin (6.3 beta RC3):

FDA’s code

Estimate   0.143765

StdError   0.0490802

sWR        0.446446

>0.294, scaling allowed

pointest   1.15461

x          0.0182596

boundx     0.0509076

critbound -0.0920763

≤0, RSABE demonstrated
Of course we could calculate a 90% CI of the PE (1.06386–1.25311) but this doesn’t help – there’s no widening of the acceptance range like for the EMA. FDA’s unscaled mixed effects model gives 1.0710–1.2489; EMA’s Method A 1.0711–1.2489 and Method B 1.0711–1.2497.

Now let’s see:

\(E_m=(\mu_T-\mu_R)^2\)
\(E_s={\theta_{s}}^{2}\cdot {\sigma_{w}}^{2}\) (the FDA’s switching condition \({\theta_{s}}^{2}\) is 0.893 = CV of ~25.83%!)
\(C_m=(|m_T - m_R|+t_{\alpha,N-S}\cdot SE)^2\)
\(C_s={\theta_{s}}^{2} \cdot (N-S) \cdot {\sigma_{w}}^{2}/{\chi_{\alpha,N-S}}^{2}\)
\(L_m=(C_m-E_m)^2\)
\(L_s=(C_s-E_s)^2\)
\(CL=E_m-E_s+\sqrt{(L_m+L_s)}\)

I got (quick and dirty as always):

Em 0.0206685

Es 0.148147

Cs 0.113948

Cm 0.0509076

Lm 0.000914403

Ls 0.00116952

CL 0.214465

(ℯ^0.214465 = 1.23920)
:confused:

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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

d_labes
★★★

Berlin, Germany,
2012-03-10 17:49
(4423 d 17:26 ago)

@ FI
Posting: # 8247
Views: 8,434

All the answers to questions never asked are here

Post reply

Dear FI, dear Helmut,

❝ The so called “x” (=PE²-SE²) in the Progesterone BE recommendation does not resemble the Em (=PE²) which would be necessary to have the identical formula for the Confidence limit calculation:

❝

❝ CL = Em-Es + √(Lm+Ls) ...

@FI: Chapeau! Argus eyes :cool:

.

See The unknown x here in the forum (but be warned: rather lengthy thread) and J. Detlors attempt to explain this difference.

I personally are more convinced of the formulas according to the two Laszlo's. Especially because there is no explanation in the Progesterone guidance for their "x". J. Detlors explanation is only a guess.

But the FDA's formula is better for making our sponsors happy, as Helmut's numerical example clearly shows. And sponsor's happyness is what they pay for :-D

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2012-03-17 15:46
(4416 d 19:28 ago)

@ FI
Posting: # 8293
Views: 8,296

Which book?

Post reply

Servus Franz!

❝ I cross-checked the L. Endrenyi/L Tothfalusi chapter in Kanfer/Shargel’s book “Generic Drug Product Development”

Cough. That’s not a book, but a series of books…
#201 (International Regulatory Requirements for Bioequivalence, informa 2010) referred in FDA’s guidance contains no chapter by the two Laszlos. Before buying another one of the series in the blind which one do you have?

BTW, it’s funny that the guidance states in the introduction:

For detailed information on this approach, please refer to the published book chapter […]

which actually gives much less information than the guidance itself.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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

FI
☆

Austria,
2012-03-19 21:15
(4414 d 13:59 ago)

@ Helmut
Posting: # 8302
Views: 8,233

Which book?

Post reply

Servus Helmut!

❝ ❝ I cross-checked the L. Endrenyi/L Tothfalusi chapter in Kanfer/Shargel’s book Generic Drug Product Development

Sorry for late reply. I'm preparing a full response, but daily work is overwhelming.

to be more precise: Kanfer/Shargel’s book Generic Drug Product Development, Bioequivalence issue, Volume 180 ISBN-13: 978-0-8493-7784-6, page 97;

Let me get back next week to this ;-)

ciao
FI

FI
☆

Austria,
2012-04-02 13:07
(4400 d 23:07 ago)

@ Helmut
Posting: # 8364
Views: 8,129

Which book?

Post reply

Dear Helmut and all,

SAS results correspond with your Phoenix-results:

Diff of ln(means): 0.143765

SE:                0.049080

sWR                0.044645

point estimate     1.15461

x                  0.018260

y                 -0.15879

boundx             0.050908

boundy            -0.12299

theta² (0.25)      0.79669 

theta              0.892574         

critbound         -0.092076

<=0, RSABE demonstrated

„Confidence limit”-Calculation, like Endrenyi/Tothfalusi call it in SAS:

Em (should be x…)  0.020668

Es (=-y)           0.15879

Cm (=boundx)       0.050908

Cs (=-boundy)      0.12299

Lm                 0.001065889

Ls                 0.001281992

CL                -0.091257

Small difference, but can be critical;

Now my EXCEL Sheet (I know, that EXCEl has bad reputation, but +-*/² and sqrt are exact):

Unfortunately I get a different value for the variance of the differences of the pooled formulation data:
MSE=0.165897781 in EXCEL and
0.1662119811 from SAS, if I take the „stderr“-value from „iout2“ to calculate MSE using: MSE=stderr²*69;
(accordingly: SE in EXCEL: 0.0490338, in SAS 0.49080)

But, if I look at the residual from „iout1“ (please see SAS program of FDA):
exactly the result of my EXCEL calculation appears: residual=0.1658977 :confused:

However the stderr from iout2 is used in SAS for further assessment;
results from EXCEL:

Critbound  -0.09209837 acc. to FDA

CL         -0.091279223 acc. to E/T

My knowledge in SAS is not enough, to draw the formula somewhere.
Can someone give me a hint on the reason for the 2 different variability results, and may be a comparison of the formulas?

thanks a lot
FI

d_labes
★★★

Berlin, Germany,
2012-04-03 12:56
(4399 d 23:18 ago)

@ FI
Posting: # 8375
Views: 8,076

To standard err is also human

Post reply

Dear FI,

❝ Unfortunately I get a different value for the variance of the differences of the pooled formulation data:

❝ MSE=0.165897781 in EXCEL and

❝ 0.1662119811 from SAS, if I take the „stderr“-value from „iout2“ to calculate MSE using: MSE=stderr²*69;

❝ (accordingly: SE in EXCEL: 0.0490338, in SAS 0.49080)

(emphasis by me)

"Hier liegt der Hund begraben!" (That's the crux of the matter.)
The formula you use to relate MSE and stderr of the difference T-R is only appropriate if the study is balanced with respect to the number of subjects within the sequences.

If this is not the case you have to use ⁽¹⁾
stderr² = MSE*(0.25*(1/n₁ + 1/n₂))
for the 'full replicate' design (2-sequence-4period).
Only if you set n₁=n₂=N/2 (N=total number of subjects) you get
stderr² = MSE*(1/N)
or the other way round
MSE = N*stderr²
you have used.

Since here for the EMA I dataset n₁=36 (RTRT), n₂=33 (TRTR)and MSE=0.1658977 you get stderr=0.04908023, that value you obtain from 'iout2' regardless if you use Proc GLM or Proc MIXED. :cool:

BTW: The formula for the partial replicate design (3-sequence-3-period) is
stderr² = MSE*((1/6)*(1/n₁ + 1/n₂ + 1/n₃))

❝ My knowledge in SAS is not enough, to draw the formula somewhere.

As you see: It's a question of the power to know and not of knowledge in SAS :-D

⁽¹⁾S-C Chow and J-P Liu
Design and Analysis of Bioavailability and Bioequivalence Studies
Chapman & Hall / CRC, Boca Raton, 3rd Ed. (2009)
Chapter 9.4 (but cave! model without carry over for the 2x2x4, formula 9.4.12)

Hope this helps.

—
Regards,

Detlew