Bioequivalence and Bioavailability Forum • Parallel BE

drcampos
★

Brazil,
2012-04-10 18:11
(4766 d 18:38 ago)

Posting: # 8401
Views: 8,506

Parallel BE [Power / Sample Size]

Dear All,

I would like to know if it is possible to calculate the CV total considering the point estimate (PE) and the confidence limits of a parallel BE study. For this study Cmax - PE = 1.08 and CI = 0.82-1.18. Number of volunteers = 122.

Another information is the root mean square error, Cmax = 0.592

I would like to confirm if a number of volunteers of 126 would be adequate for a parallel BE study considering these information.

Thank you in advance.

best regards, Daniel

Helmut
★★★

Vienna, Austria,
2012-04-10 19:20
(4766 d 17:28 ago)

@ drcampos
Posting: # 8402
Views: 7,998

Parallel BE

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Dear Daniel

nice to read from you again!

❝ I would like to know if it is possible to calculate the CV total considering the point estimate (PE) and the confidence limits of a parallel BE study.

Yes. Package PowerTOST for R is very helpful. ;-)

❝ For this study Cmax - PE = 1.08 and CI = 0.82-1.18. Number of volunteers = 122.

Hhm, this is strange. The CI should be symmetrical around the PE in the log-domain, or in other words the geometric mean of the CI: $PE=\sqrt{CL_{lower}\times CL_{upper}}$ which is 0.98 and not 1.08…
Your CI is symmetrical around 100%. Can you please check in the report whether these are the – obsolete for decades! – Westlake’s confidence intervals?* If yes, the following is useless. Try to find the classical (shortest) CI in the report.

library(PowerTOST)

100*CVfromCI(lower=0.82, upper=1.18, n=122, design="parallel")

[1] 66.653

(CV_total 66.7%)

❝ Another information is the root mean square error, Cmax = 0.592

Are you sure that this value comes from log-transformed data? If yes, CV_total would be $100\sqrt{e^{0.592^2}-1}\sim 64.8\%$ or more comfortably:

100*se2CV(0.592)

[1] 64.78628

❝ I would like to confirm if a number of volunteers of 126 would be adequate for a parallel BE study considering these information.

Let’s see (power 80%, acceptance range 0.80–1.25, CV_total 66.7%); first sample size column with ‘fixed CV’ (n1)¹, second one taking uncertainty of the CV from the first study into account (n2)². Columns n3 and n4 are for CV 64.8%:


expected PE   n1   n2   n3   n4

    0.90     658  666  628  636

    0.95     318  324  304  308

    0.98     264  268  252  256

    1.00     256  260  244  248

    1.05     312  316  296  302

    1.08     428  434  408  414

    1.10     560  566  532  540

Seems that the first study passed by luck. No fun planning a new one.

Example code for PE 0.95:

library(PowerTOST) sampleN.TOST(targetpower=0.8, theta0=0.95, CV=0.667, design="parallel")
library(PowerTOST) expsampleN.TOST(targetpower=0.8, theta0=0.95, CV=0.667, dfCV=122-2, design="parallel")

The classical CI is T/R ± t_0.05·variability where α_lo = α_hi = 0.05 and total α = 0.10. Westlake suggested to select α_lo and α_hi in such a way that the resulting CI is symmetrical around 100%. If PE ≠ 1 that would require α_lo ≠ α_hi. By an iterative process t-values are found where α_lo + α_hi = 0.10 still holds.^a This procedure was soon criticized since no information about the location is available if only the CI is reported.^b With a little trial an error it should be possible to get the classical CI from Westlake’s if both the PE and the sample size are known.

Westlake WJ. Symetrical Confidence Intervals for Bioequivalence Trials. Biometrics. 1976;32(4):741–4. doi:10.2307/2529259.
Mantel N. Do We Want Confidence Intervals Symetrical About the Null Value? Biometrics. 1977;33(4):759–60.

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

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drcampos
★

Brazil,
2012-04-10 23:03
(4766 d 13:45 ago)

@ Helmut
Posting: # 8403
Views: 7,657

Parallel BE

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Dear Helmut,

Thank you again for your assistance. Your commentary about the results of the BE report could clarify some of my doubts about parallel design of BE studies. It was almost like a lecture to me!!!!

The results of the BE study (2002) presented in my last message are from this link: http://www.accessdata.fda.gov/drugsatfda_docs/nda/2004/076553_S000_Medroxyprogesterone_BIOPHARMR.pdf (The FDA report presented many deficiencies about this study!)

best regards from Brazil, Daniel

Helmut
★★★

Vienna, Austria,
2012-04-11 04:22
(4766 d 08:27 ago)

@ drcampos
Posting: # 8404
Views: 7,805

FDA’s review

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Dear Daniel!

❝ The results of the BE study (2002) presented in my last message are from this link: […] (The FDA report presented many deficiencies about this study!)

This is very interesting stuff sheding light both on (some) companies’ and FDA’s review practices!

100% Caucasians… (“ This guidance recommends that in vivo BE studies be conducted in individuals representative of the general population, taking into account age, sex, and race.”) Wasn’t even commented.
Two subjects dropped out due to non drug-related AEs (on days 72 and 83, respectively). They were excluded by the company (last 6 or 7 samples missing), but FDA requested statistical analysis of AUC and C_max “[…] since samples were collected long enough to properly characterize the absorption phase.”
The company replied that these subjects were dropped from the evaluation due to SAEs requiring hospitalization and more than 5 consecutive missing samples would result in an inaccurate and biased assessment. Not very clever:
“The DBE^* calculated AUC_0-1656 and AUC_0-1824 from the reference mean plasma profile which were 85% and 81% of the AUC_0-2856 from the reference mean plasma profile. […] these two subjects will provide accurate values for C_max and therefore the inclusion of these subjects is essential for the statistical analysis of the C_max value. Thus, based on our calculations, the DBE does not believe the inclusion of those subjects would result in an inaccurate and biased assessment of C_max (definitely) and AUC_(0-t), AUC_(0-inf) (possibly).”.
Page 12: “Were there statistically significant sequence or period effects? If so, did these affect the integrity of the study? The reviewer has not run SAS ANOVA pending the firm’s response to the deficiencies.”
Whilst the questions likely follow FDA’s standard template the reviewer’s answer is funny – this was a parallel design!
Original data set (n=122, n_T 62, n_R 60)
AUC_t 87–102%, PE 96% (geometric mean of CI 94%)
AUC_∞ 94–106%, PE 100%
C_max 82–118%, PE 108% (98%)
RSEM AUC (Which one? Likely AUC_t) 0.244
RSEM C_max 0.592
Complete data set (n=124, n_T 62, n_R 62)
AUC_t 87–101%, PE NA (94%)
AUC_∞ 92–105%, PE NA (98%)
C_max 80–115%, PE NA (96%)

Lessons learned:

Don’t exclude subjects following stupid SOPs. Luckily the samples were analyzed.
I still think that the original analysis of C_max sucks. Though the PE was reported with 108% the CI is symmetrical (-18%, +18%) around 100%. Smells of Westlake. Maybe the classical interval was outside 80–125% (not reported!) and Barbara didn’t notice it? Since all CIs of the complete data set are not symmetrical around 100% I would trust them more. For C_max we get:
100*CVfromCI(lower=0.80, upper=1.15, n=124, design="parallel") [1] 67.08022 (CV_total 67.1%)
CV2se(0.6708022) [1] 0.6095463 (RMSE)
Your samples size would be terrible.
I’m wondering whether the company followed the guidance’s recommendations:
“For parallel designs […] equal variances should not be assumed.”
CV_T was 85.8% and CV_R 58.7%. The conventional t-test is liberal; was really Welch’s test applied? Though the t-test is rather robust against violation of variance homogeneity (unequal group sizes are more critical), a lower CL of 80% would ring my alarm bells.

DBE: Division of Bioequivalence, Office of Generic Drugs

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

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d_labes
★★★

Berlin, Germany,
2012-04-11 11:57
(4766 d 00:51 ago)

@ Helmut
Posting: # 8406
Views: 7,616

A reviewer which doesn't review isn't a good reviewer

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Dear Helmut, dear Daniel!

Funny stuff.

The very best IMHO:
"... Statistical analysis of the PK parameters (I see Helmut breathing deep ) including these two (2) subjects are within acceptable limits (LAUC 0.87 - 1.01%, LAUCinf 0.92 - 1.05% and LCmax 0.8 - 1.15%).

The DBE comment: The reviewer has reviewed the information submitted and the firm's response is acceptable." (sic!)

Ok not being so straight nitpicking and viewing the % as due to the Druckfehlerteufel (typo gremlin) it must be stated: CI's given as ratios with 2 decimals acceptable!
And that within that regulatory body which is responsible for the rule "... to pass a CI limit of 80 to 125, the value would be at least 80.00 and not more than 125.00 ..." (clearly meant as %) now also adapted by the EMA :cool:

.

I bet a case of best Czech beer that the lower limit for Cmax was something like 0.7988 :yes:

(Helmut's alarm bell ringing).

Ein Taucher der nicht taucht taugt nichts. (german wordplay)

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2012-04-11 15:51
(4765 d 20:58 ago)

@ d_labes
Posting: # 8407
Views: 7,660

14 months for 1st review

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Dear Detlew!

❝ […] it must be stated: CI's given as ratios with 2 decimals acceptable!

❝ And that within that regulatory body which is responsible for the rule "... to pass a CI limit of 80 to 125, the value would be at least 80.00 and not more than 125.00 ..."

Well, guidelines are guidelines are guidelines. ;-)

Have you noticed the header on every single page?

Contains Nonbinding Recommendations

Rounding off of confidence interval values:

We recommend that confidence interval (CI) values not be rounded off; therefore, to pass a CI limit of 80 to125, the value would be at least 80.00 and not more than 125.00.

(my emphasis; you can try anything – if the assessor accepts it, …)

❝ I bet a case of best Czech beer that the lower limit for Cmax was something like 0.7988.

I wouldn’t bet on it. Why not even raise the claim to 0.795?

This review amazes me in many respects. After the stuff produced by M$ Word/Excel the pages again from an IBM Selectric.

I still have no clue how they derived their CIs. If I trust in the RMSE of 0.592, the PE of 108% for n_T=62, n_R=60 and a simple t-test I get a CI of 90–129%. If I play around with alphas (and round the CI to integers!) it needs an α₁ of 0.0008 and α₂ of 0.0992 to obtain a symmetrical CI (76–124%) but then the lower CL is <80%. Should stop this stupid trial-and-error business.

—
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,
2012-04-11 17:50
(4765 d 18:59 ago)

@ Helmut
Posting: # 8408
Views: 7,559

Guidelines - nonbinding, Scientific advice - nonbinding …

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Expand the subject line until it fits your needs.

Dear Helmut!

❝ Well, guidelines are guidelines are guidelines. ;-) Have you noticed the header on every single page? Contains Nonbinding Recommendations

❝ ...

❝ you can try anything – if the assessor accepts it, …)

This is the casus knacktus with guidelines.
Once we are urged to take them literally and if we do not we are punished by deficiency letters.
Once we take them literally and an assessor comes along and claims he is considering things different.
Once we are in breach with the guidelines with intent and another assessor comes along and says "I as a reviewer have reviewed (!) and and the firm's response is acceptable".

This is sometimes very annoying :angry:

but otherwise life would be boring :cool:

. But I must confess that sometimes I wish more boredom in my professional life.

❝ This review amazes me in many respects. After the stuff produced by M$ Word/Excel the pages again from an IBM Selectric.

And this in the year 2004!
But I as a dinosaur have respect for other dinosaurs having survived :-D

.
And I have most respect for the engineers who have developed such a machine working even decades after producing it :ok:

!

BTW: This reminds me on the Schreibmaschine "Erika", hightech by VEB Robotron which I've also seen yet being functional these days.

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2012-04-11 18:22
(4765 d 18:26 ago)

@ d_labes
Posting: # 8409
Views: 7,581

Grumpy ol’ men

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Dear Detlew!

❝ But I must confess that sometimes I wish more boredom in my professional life.

Me too.

❝ BTW: This reminds me on the Schreibmaschine "Erika" …

Wow, what a name. And this in a country where equal opportunities were implemented. To get the sexes balanced was there a “Papierschneider Erich” as well?

❝ … hightech by VEB Robotron

I loved the name when I was a child since my parents were subscribers of the
Volksstimme. Zentralorgan der Kommunistischen Partei Österreichs. :smoke:

—
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,
2012-04-11 19:04
(4765 d 17:45 ago)

@ Helmut
Posting: # 8410
Views: 7,574

Grumpy ol’ men - OT

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Dear Helmut!

❝ Wow, what a name. And this in a country where equal opportunities were implemented. To get the sexes balanced was there a “Papierschneider Erich” as well?

NOP. No chance. The name "Erich" was sacrosanct. At least since 1971.

The bloomy name of the "Schreibmaschine Erika" was more or less exceptional. Other equipment was named more via incredible acronyms.

For instance
- KC85 = Klein-Computer from 1985
- BS600 = Bodenstaubsauger 600 Watt
...

Acronyms were omnipresent in the former GDR. It was called "Aküfi" = Abkürzungsfimmel.
See here :smoke:

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2012-04-11 19:47
(4765 d 17:02 ago)

@ d_labes
Posting: # 8411
Views: 7,706

GDR - OT

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Dear Detlew!

❝ NOP. No chance. The name "Erich" was sacrosanct. At least since 1971.

Sure.

❝ Acronyms were omnipresent in the former GDR. It was called "Aküfi" = Abkürzungsfimmel.

❝ See here :smoke: .

What a great list!
ASPR – Automatisierte Systeme der Planberechnungen
DMH - Dringliche Medizinische Hilfe
D.w.E. - Deutsches weißes Edelschwein
E.g.H. - Einfarbig gelbes Höhenvieh
GKV - Geheime Kollegiums-Vorlage
H.Gr.S. - Helles Großsilberkaninchen
IAM - Informationsaufzeichnungsmaterialien
KFA - Komplexe Forschungsaufgabe
MOGEVUS - Molekulare Grundlagen der Entwicklungs-, Vererbungs- und Steuerungsprozesse
MuFuTi – Mulifunktionstisch
NVO – Verordnung über die Förderung der Tätigkeit der Neuerer und Rationalisatoren in der Neuererbewegung
PwP – Produktionsgenossenschaft werktätiger Pelztierzüchter
SIAT - Sozialistische Internationale Arbeitsteilung
SIV - Selektive Informations-Verarbeitung
SWO - Süßwasser-Straßenordnung
WPT - Wissenschaftlich-Produktive Tätigkeit

❝ Ein Taucher der nicht taucht taugt nichts.

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

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