Bioequivalence and Bioavailability Forum

Helmut
★★★

Vienna, Austria,
2010-01-28 01:52
(5998 d 21:07 ago)

Posting: # 4652
Views: 8,436

Canada: Draft Guidances published [Regulatives / Guidelines]

Dear all,

on January 25 Health Canada published two draft guidances:

Conduct and Analysis of Comparative Bioavailability Studies (190KB PDF)
Comparative Bioavailability Standards: Formulations Used for Systemic Effects (58KB PDF)

The purpose of these documents is to update and consolidate eleven existing Health Canada documents related to the conduct and analysis of comparative bioavailability studies and the standards to be met in those studies in order to comply with Sections C.08.002(2)(h), C.08.002.1(2)(c)(ii) and C.08.003(3) of the Food and Drug Regulations. Until such time as these guidances are finalized and published, current bioequivalence requirements remain unchanged and proposals in the draft guidances are not to be implemented.
Section 2.6: Analytical Methodology in the draft document Conduct and Analysis of Comparative Bioavailability Studies, is currently still under revision and further consultation will be undertaken, as appropriate. Health Canada invites stakeholders to provide advance recommendations on analytical methodology, particularly assay validation. These recommendations will be taken into consideration in revising this section.

The existing documents which will be superseded, once the two draft documents are finalized, are as follows:

Guidance for Industry: Conduct and Analysis of Bioavailability and Bioequivalence Studies - Part A: Oral Dosage Formulations Used for Systemic Effects (1992).
Report C (of the Expert Advisory Committee on Bioavailability and Bioequivalence): Report on Bioavailability of Oral Dosage Formulations, Not in Modified Release Form, of Drugs Used for Systemic Effects, Having Complicated or Variable Pharmacokinetics (1992).
Guidance for Industry: Conduct and Analysis of Bioavailability and Bioequivalence Studies - Part B: Oral Modified Release Formulations (1996).
Draft Policy: Bioequivalence Requirements: Drugs Exhibiting Non-Linear Pharmacokinetics (2003).
Notice to industry: Removal of Requirement for 15% Random Replicate Samples (2003).
Draft Guidance for Industry: Use of Metabolite Data in Comparative Bioavailability Studies (2004).
Notice to industry: Bioequivalence requirements for combination drug products (2004).
Guidance for Industry: Bioequivalence Requirements: Comparative Bioavailability Studies Conducted in the Fed State (2005).
Notice to Industry: Bioequivalence Requirements for Drugs for Which an Early Time of Onset or Rapid Rate of Absorption Is Important (rapid onset drugs) (2005).
Notice to Industry: Bioequivalence Requirements for Long Half-life Drugs (2005).
Guidance for Industry: Bioequivalence Requirements: Critical Dose Drugs (2006).

Comments should be provided to Health Canada within 60 days of the publication of this Notice.

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

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earlybird
☆

2010-02-09 09:35
(5986 d 13:25 ago)

@ Helmut
Posting: # 4737
Views: 7,114

Outlier

Post reply

Dear Members,

according Canada's new Draft Guideline for outlier testing a "studentised residual" test should be performed.

Which test do they think about?

What about Hotelings T², Cooks distance, Mahalanobis distance, robust regression, Lund' test? Are these "studentised residual" tests?

As I do not know all these tests exactly, I want hear other opinion?

earlybird

Edit: Linked to another thread. [Helmut]

Helmut
★★★

Vienna, Austria,
2010-02-09 15:55
(5986 d 07:04 ago)

@ earlybird
Posting: # 4738
Views: 7,180

Outlier (tests?)

Post reply

Dear earlybird!

❝ according Canada's new Draft Guideline for outlier testing a "studentised residual" test should be performed.

Almost. TPD wants a test of the studentised residuals (Section 2.3.4 Outlier consideration, page 8):

First, in order to be considered an extreme value, the observation must be outside the range of all the other observations regardless of formulation. Second it must be identified by an outlier test. It is recommended that the outlier test be a simple studentised residual tested against a conservative t-value at the .02 level of significance and degrees of freedom for the design. In other words the test should only identify observations which are very different from all others collected.

I'm not sure whether 't-value' should read 'table-value' or 'value of the t-distribution'...

❝ Which test do they think about?

Hhm, no idea. For an overview see this post. Especially Pikounis et al. (2001) is quite helpful. Everything is implemented in bear.

❝ What about Hotelings T²

Well, that's a multivariate test; what do you want to test here?

❝ Cooks distance, Mahalanobis distance,

Exploratory only, i.e., no tests.

❝ robust regression,

On what?

❝ Lund' test?

Obsolete, I would say.

❝ Are these "studentised residual" tests?

As said above we should test the studentised residuals; there's no "studentised residual test".
For identification I use to plot the studentised intra-subject residual vs. the model response and had only two additional reference lines based on the normal distribution (0.05), i.e. at ±1.960. For 0.02 that would transfer to ±2.326. I'm not sure what TPD means by 'degrees of freedom for the design'. Most likely the one of the residual error (n₁+n₂-2 in a 2×2 cross-over). Examples: n=24, t_0.02,22 2.508, n=36 t_0.02,34 2.441. But that's no test; multiplicity issues are ignored (can they?)...

—
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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earlybird
☆

2010-02-09 17:45
(5986 d 05:15 ago)

@ Helmut
Posting: # 4739
Views: 7,083

Outlier (tests?)

Post reply

Dear HS,

❝ Almost. TPD wants a test of the studentised residuals

Ok sometimes the small words inbetween are important i.e. "of"

❝ ❝ What about Hotelings T²

❝

❝ Well, that's a multivariate test; what do you want to test here?

This was a suggestion from one of your's previous posts

❝ ❝ Cooks distance, Mahalanobis distance,

❝

❝ Exploratory only, i.e., no tests.

❝

❝ ❝ robust regression,

❝

❝ On what?

ok, I have to check, that again

❝ ❝ Lund' test?

❝

❝ Obsolete, I would say.

❝

❝ ❝ Are these "studentised residual" tests?

❝

❝ As said above we should test the studentised residuals; there's no "studentised residual test".

❝ For identification I use to plot the studentised intra-subject residual vs. the model response and had only two additional reference lines based on the normal distribution (0.05), i.e. at ±1.960. For 0.02 that would transfer to ±2.326. I'm not sure what TPD means by 'degrees of freedom for the design'. Most likely the one of the residual error (n₁+n₂-2 in 2×2 cross-over).

❝ Examples: n=24, t_0.02,22 2.508, n=36 t_0.02,34 2.441. But that's no test; multiplicity issues are ignored (can they?)...

so all in all you mean

1. I should ask the Canadian what they mean exactly
2. Wait until the guideline is final?

Greetings,
earlybird

Helmut
★★★

Vienna, Austria,
2010-02-09 18:05
(5986 d 04:54 ago)

@ earlybird
Posting: # 4740
Views: 7,171

Outlier (tests?)

Post reply

Dear earlybird!

❝ ❝ ❝ What about Hotelings T²

❝ ❝

❝ ❝ Well, that's a multivariate test; what do you want to test here?

❝

❝ This was a suggestion from one of your's previous posts

Hhm, do you mean this post? Sorry, but I don't remember what I meant there. :-D

One application of Hotelling's T² in NCA-PK is the assessment of steady state. Test for differences of all pre-dose concentrations; if significant, run pairwise comparisons (that's the multivariate part) in order to find out, when steady state was reached (the first nonsignificant difference). Again sorry for the confusion; but I don't see how Hotelling's T² would be applicable as an outlier test.

❝ so all in all you mean

❝

❝ 1. I should ask the Canadian what they mean exactly

❝ 2. Wait until the guideline is final?

Good idea (best directly to Eric Ormsby)
No. That's the sheep/shepard-relationship of the pharmaceutical industry. Wait - and complain when it's too late. Come up with a suggestion and send a comment to Health Canada (contact details in the News-Section).

—
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

earlybird
☆

2010-02-09 18:18
(5986 d 04:41 ago)

@ Helmut
Posting: # 4741
Views: 7,035

Outlier (tests?)

Post reply

Dear HS,

❝ ❝ This was a suggestion from one of your's previous posts

❝

❝ Hhm, do you mean this post? Sorry, but I don't remember what I meant there. :-D

Exactly, and now as I know how to avoid full quotes (TOFU) ;-)

, next time I will learn how to insert the link of a previous post :-)

❝ ❝ so all in all you mean

❝ ❝

❝ ❝ 1. I should ask the Canadian what they mean exactly

❝ ❝ 2. Wait until the guideline is final?

❝

Good idea (best directly to Eric Ormsby)
❝
No. That's the sheep/shepard-relationship of the pharmaceutical
❝ industry. Wait - and complain when it's too late. Come up with a
❝ suggestion and send a comment to Health Canada (contact details
❝ in the News-Section).

ok, I keep you informed!

Greetings
earlybird

d_labes
★★★

Berlin, Germany,
2010-02-10 14:51
(5985 d 08:09 ago)

@ Helmut
Posting: # 4744
Views: 7,031

Outlier "im Quadrat"

Post reply

Dear Helmut!

❝ Hhm, do you mean this post? Sorry, but I don't remember what I meant there. :-D

This may be the age! Or too much work! Or both! You are not alone. :waving:

❝ Again sorry for the confusion; but I don't see how Hotelling's T² would be applicable as an outlier test.

Have a look into

J.-P. Liu, C.-S- Weng
"Detection of Outlying Data in Bioavailability/Bioequivalence Studies"
Statistics in Medicine, Vol. 10, 1375-1389 (1991)

and eventually you remember ...

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2010-02-11 18:56
(5984 d 04:03 ago)

@ d_labes
Posting: # 4752
Views: 7,413

Hotelling's T²

Post reply

Dear D Labes!

❝ ❝ [...] Sorry, but I don't remember what I meant there. :-D

❝

❝ This may be the age! Or too much work! Or both!

Yes, both for sure.

Thanks for the reminder; an overview is also given in the textbook most of us have our bookshelves:
S-C Chow and J-p Liu
Design and Analysis of Bioavailability and Bioequivalence Studies
Chapter 8 Assumptions of Outlier Detection for Average Bioequivalence,
Section 8.4.2 Hotelling T²
Chapman & Hall/CRC Press, Boca Raton, pp 240-247 (3^rd ed. 2008)

Hotelling's T² is included in bear since version 2.2.0 (02/2009).

—
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,
2010-02-10 14:36
(5985 d 08:23 ago)

@ Helmut
Posting: # 4743
Views: 7,251

Lund!

Post reply

Dear Helmut, dear earlybird!

❝ Almost. TPD wants a test of the studentised residuals (Section 2.3.4 Outlier consideration, page 8):

❝ First, in order to be considered an extreme value, the observation must be outside the range of all the other observations regardless of formulation. Second it must be identified by an outlier test. It is recommended that the outlier test be a simple studentised residual tested against a conservative t-value at the .02 level of significance and degrees of freedom for the design. In other words the test should only identify observations which are very different from all others collected.

❝ I'm not sure whether 't-value' should read 'table-value' or 'value of the t-distribution'...

To add my two pence: IMHO this calls directly for the ("obsolete") Lund test! :surprised:

As far as I remember and as far as I understood this test up to now Lund suggested to test the studentized residuals against an appropriate t-value (the residuals are assumed as approximately distributed according to a Student's t-distri).
However he suggests to test with a Bonferroni adjusted alpha, i.e. with quantil of the t-distribution
qt((1-alpha/(2*n)),df) where n is the number of residuals and df the error degrees of freedom.
Seems this is too conservative for the Canadians :-D

.

Lund, "Approximate Tables for Outliers in linear Models", Technometrics Vol.17/4, 473-476 (1975)

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2010-02-12 21:04
(5983 d 01:55 ago)

@ d_labes
Posting: # 4755
Views: 6,980

Lund!

Post reply

Dear D Labes!

❝ As far as I remember and as far as I understood this test up to now Lund suggested to test the studentized residuals against an appropriate t-value (the residuals are assumed as approximately distributed according to a Student's t-distri).

❝ However he suggests to test with a Bonferroni adjusted alpha, i.e. with quantil of the t-distribution qt((1-alpha/(2*n)),df) where n is the number of residuals and df the error degrees of freedom.

Hhm, are you sure about the way the Bonferroni-correction is applied? Do be honest, it's quite a long time ago, I used Lund's test. I did not really dwelve into the theory behind, but only tested the studentized residuals against his Table 1 values (at 0.05). I used q=5 for the effects in the model: sequence, treatment, period, subject(sequence) + intercept. Since there are a lot of missing rows for the number of residuals (n) in the table, I fitted an empirical function, rounded to two decimal places:
0.057979×ln(n)⁵-1.022492×ln(n)⁴+7.221331×ln(n)³-25.628487×ln(n)²+46.329654×ln(n)-31.856913
The empirical fit gives table values for n=9-70.

—
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

ElMaestro ★★★ Denmark, 2010-02-12 21:29 (5983 d 01:30 ago) @ Helmut Posting: # 4756 Views: 6,999	intercept Post reply
	Hi HS, ❝ I used q=5 for the effects in the model: sequence, treatment, period, subject(sequence) + intercept. How/why does the intercept count as an "effect"? Best regards and thanks for any insight, EM.

Helmut
★★★

Vienna, Austria,
2010-02-13 01:03
(5982 d 21:57 ago)

@ ElMaestro
Posting: # 4758
Views: 6,889

intercept

Post reply

Hi ElMaestro,

❝ ❝ I used q=5 for the effects in the model: sequence, treatment, period, subject(sequence) + intercept.

❝ How/why does the intercept count as an "effect"?

Well, cough... Lund's paper gives an example from a multiple regression model (Y on x₁, x₂) where the intercept is included. Therefore q=3 in the paper. Forgive my youthful abandon; maybe I called the test "obsolete" because I never understood it.

—
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

ElMaestro
★★★

Denmark,
2010-02-13 02:04
(5982 d 20:55 ago)

@ Helmut
Posting: # 4759
Views: 6,909

intercept

Post reply

Hi,

❝ Well, cough... Lund's paper gives an example from a multiple regression model (Y on x₁, x₂) where the intercept is included. Therefore q=3 in the paper. Forgive my youthful abandon; maybe I called the test "obsolete" because I never understood it.

I just took a look at the paper and the example you mention. My take on it after reading and understanding very little: q is the number of columns in the model matrix; in BE we -depending how we specify our model and/or which software is used- sometimes work with full rank matrices or deficient rank matrices. I am inclined to think q thereby can or must be understood as the rank of the model matrix.
In a 2,2,2-BE trial with m subjects: q= 2 for the treatments + 2 for the sequences + 2 for the periods + m for the subjects, then subtract one for each redundancy. I think this is in total q=m+2 (give or take, it is a little late).

Weird. Slaap lekker.

EM.

d_labes
★★★

Berlin, Germany,
2010-02-22 13:52
(5973 d 09:08 ago)

@ Helmut
Posting: # 4809
Views: 7,342

Lund's critical values, technically

Post reply

Dear Helmut!

❝ Hhm, are you sure about the way the Bonferroni-correction is applied?

Sorry for the delay, but I was lost in snow last week :-D

. Had very fine holidays in the Harz mountains in the middle of germany.

I must confess that I do not remember exactly what I figured out about Lund's test in the very past. Then later on I discarded my code because of the agreed rating in the BE community "Lund's test is obsolete for cross-over trials".

Now again I had to figure out what is written in Lund's paper (cryptic for me).
Have a look at http://en.wikipedia.org/wiki/Studentized_residual and you will find (like me) that

ISR² = rdf * t²/(t²+rdf-1)

where ISR is the internal standardized residual and rdf the residual degrees of freedom and t is student's t distributed with rdf-1 degrees of freedom.
This formula is identical to Lund page 473, right paneel, noticing that t² = F and rdf = n-p.

With that you can reproduce the Lund tables if you use the Bonferroni correction for determination of the t-quantiles. No need to fit approximating functions.

Here some beginners R-code for the first column in Table 1 of Lund's paper:

alpha <- 0.1

n <- c(5,6,7,8,9,10,12,14)

q <- 1

t <- qt((1-alpha/n/2),n-q-1)    # Bonferroni!

(isr2 <- (n-q)*(t^2)/(t^2+(n-q)-1))

sqrt(isr2) # this are Lund's critical values

Result:


n=    5        6        7        8        9        10       12       14

   1.868666 1.996032 2.093425 2.171927 2.237528 2.293777 2.386556 2.461181

   1.87     2.00     2.10     2.18     2.24     2.30     2.39     2.47

(last row from Lund's paper, used a Taylor series for the density function of Student's distri, see page 476)

For our BE studies take the residual degrees of freedom from the ANOVA and proceed accordingly. Eventually we had to consider that the residuals are not independent (correlated) on each subject and adjust n in the Bonferroni adjustment (1-alpha/(2*n)) to the number of independent residuals.

BTW: The externally studentized residuals are themselves t-distributed with n-p-1 degrees of freedom, if Wikipedia is true. So we can use the t-quantiles directly to test them.

—
Regards,

Detlew

ElMaestro
★★★

Denmark,
2010-02-25 15:22
(5970 d 07:37 ago)

@ d_labes
Posting: # 4817
Views: 6,816

R code

Post reply

Hmmm, this works on yours truly's machine:


Lund <- function (Linmo, alpha, Verbose)

{

  ## Linmo is the linear model object

  ## alpha is self explanatory

  ## Verbose: set to 1 for more info, otherwise 0



  q=qr(model.matrix(Linmo))$rank

  n=length(residuals(Linmo))

  FLAG=0

  t <- qt((1-alpha/n/2),n-q-1)           # code from d_labes

  isr2 <- (n-q)*(t^2)/(t^2+(n-q)-1)      # code from d_labes

  lcv=sqrt(isr2)                         # code from d_labes

  for (i in 1:n)

   if (abs(rstandard(Linmo)[i])>lcv)

   {

    FLAG=1

    if (Verbose==1) cat ("Stud. residual # ", i, " is ", rstandard(Linmo)[i], ", lcv is ", lcv, "\n")

   }

  if (FLAG==1) cat ("This datafit is not without outliers.\n")

}

EM.

Example - taken from Lund's paper.
y=c(64,60,71,61,54,77,81,93,93,51,76,96,77,93,95,54,168,99)
x1=c(0.4, 0.4, 3.1, 0.6, 4.7, 1.7, 9.4, 10.1, 11.6, 12.6, 10.9, 23.1, 23.1, 21.6, 23.1, 1.9, 26.8, 29.9)
x2=c(53,23,19,34,24,65,44,31,29,58,37,46,50,44,56,36,58,51)

Lm2=lm(y~x1+x2)
Lund(Lm2, 0.01,1)

d_labes ★★★ Berlin, Germany, 2010-02-25 17:34 (5970 d 05:25 ago) @ ElMaestro Posting: # 4819 Views: 6,788	R code quest Post reply
	Dear ElMaestro, ❝ Lund <- function (Linmo, alpha, Verbose) ❝ { ❝ ... ❝ q=qr(model.matrix(Linmo))$rank ❝ n=length(residuals(Linmo)) ❝ ... why did you use this here? Is there any hidden secret behind? I would do: `summary(Linmo)$df[2] # error degrees of freedom ... t <- qt((1-alpha/n/2),df-1) isr2 <- df*(t^2)/(t^2+df-1) ...` — Regards, Detlew

ElMaestro ★★★ Denmark, 2010-02-25 18:06 (5970 d 04:53 ago) @ d_labes Posting: # 4820 Views: 6,781	R code quest Post reply
	Dear d_labes, ❝ Is there any hidden secret behind? There's no deep secret. My basis was the model matrix (dimensions n x q) of which the interpretation of q was addressed above. I noted you also used n and q in your equations, so I tried to write elmaestrolophystic code reflecting that. Best regards EM.

Canada: Draft Guidances published [Regulatives / Guidelines]

Outlier

Outlier (tests?)

Outlier (tests?)

Outlier (tests?)

Outlier (tests?)

Outlier "im Quadrat"

Hotelling's T²

Lund!

Lund!

intercept

intercept

intercept

Lund's critical values, technically

R code

R code quest

R code quest