Bioequivalence and Bioavailability Forum • Replicate design

Dr Andrew Leary
★

Ireland,
2011-04-21 13:50
(5119 d 19:56 ago)

Posting: # 6929
Views: 10,810

Replicate design [RSABE / ABEL]

Greetings Helmut et al from sunny Ireland! :-D

To my mind, it should be possible (in theory, at least) to make a BE comparison of Reference vs Reference (or Test vs Test) from the data derived from a BE study with a 4-period replicate design. Despite being a statistical epsilon semi-moron, I can still see that there must be a problem with the fact that in this design each volunteer receives the second dose of Reference after the first dose of Reference (doh!), whether they received the sequence TRTR or RTRT. In other words, there is only one sequence for Reference (or Test). Presumably this must interfere with proper determination of BE. How should one deal with this?

Kind regards

Andrew Leary

Edit: Category changed. [Helmut]

ElMaestro
★★★

Denmark,
2011-04-21 15:04
(5119 d 18:42 ago)

@ Dr Andrew Leary
Posting: # 6931
Views: 9,210

Replicate design

Post reply

Hello Andrew,

❝ To my mind, it should be possible (in theory, at least) to make a BE comparison of Reference vs Reference (or Test vs Test) from the data derived from a BE study with a 4-period replicate design. Despite being a statistical epsilon semi-moron, I can still see that there must be a problem with the fact that in this design each volunteer receives the second dose of Reference after the first dose of Reference (doh!), whether they received the sequence TRTR or RTRT. In other words, there is only one sequence for Reference (or Test). Presumably this must interfere with proper determination of BE. How should one deal with this?

"A cosmic mind-f#%&er" as one of my sailors would call it.
If I understand your post correctly, your worry seems to be whether patient X is in sequence RR or in sequence RR :-D

. Sequence, however, is a between-factor. Try and run the standard model without sequence as a factor on your ref data. And try for comparison to run a normal 2-period study without Sequence as a factor.

—
Pass or fail!
ElMaestro

Dr Andrew Leary ★ Ireland, 2011-04-21 23:53 (5119 d 09:53 ago) @ ElMaestro Posting: # 6934 Views: 9,191	Replicate design Post reply
	Many thanks, El Maestro!

Dr Andrew Leary
★

Ireland,
2011-04-27 14:21
(5113 d 19:25 ago)

@ ElMaestro
Posting: # 6946
Views: 9,046

Replicate design AGAIN

Post reply

Dear El Maestro

❝ If I understand your post correctly, your worry seems to be whether patient X is in sequence RR or in sequence RR :-D . Sequence, however, is a between-factor. Try and run the standard model without sequence as a factor on your ref data. And try for comparison to run a normal 2-period study without Sequence as a factor.

My data manager tells me that SAS will not allow sequence to be dropped from the regression (mixed effects?) model.

We've thus fallen at the first hurdle... :-(

Any other ideas?

Regards

Andrew

Helmut
★★★

Vienna, Austria,
2011-04-27 15:43
(5113 d 18:03 ago)

@ Dr Andrew Leary
Posting: # 6948
Views: 9,115

Replicate design limbo

Post reply

Dear Andrew!

❝ My data manager tells me that SAS will not allow sequence to be dropped from the regression (mixed effects?) model.

❝

❝ We've thus fallen at the first hurdle... :-(

No, your horse refused to jump the first fence, unseating the rider. ;-)

Try a conventional 2×2 without sequence: The CI (T/R) should be exactly the same.
In a 2×4 replicate I get differences in the 6^th significant figure.
In the EU you have to stick with EMA's crippled model anyhow.

BTW, you are not the first asking this question.
What you can do, is start with EMA's suggestion (throw away all test data), and recode periods to "occasion":
In sequence RTRT period 1 => occasion 1, period 3 => occasion 2
In sequence TRTR period 2 => occasion 1, period 4 => occasion 2
Set up a model with fixed effects occasion+subject, estimate "occasion 2-1"
With EMA's dataset I get (back-transformed):
Occasion 1: 2032, Occasion 2: 2249
Occasion 2/1: 110.64% (90% CI: 97.74 - 125.24%), CV 47.32% (which is identical to FDA's - referred by EMA as Method C).

—
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

Dr Andrew Leary
★

Ireland,
2011-04-27 18:11
(5113 d 15:35 ago)

@ Helmut
Posting: # 6949
Views: 9,015

Replicate design limbo

Post reply

Dear Helmut

❝ What you can do, is start with EMA's suggestion (throw away all test data), and recode periods to "occasion":

❝ In sequence RTRT period 1 => occasion 1, period 3 => occasion 2 In sequence TRTR period 2 => occasion 1, period 4 => occasion 2 Set up a model with fixed effects occasion+subject, estimate "occasion 2-1"

Now this looks simple, logical and elegant. I wonder what I'm missing! ;-)

Many thanks and kind regards

Andrew

Helmut
★★★

Vienna, Austria,
2011-04-27 18:52
(5113 d 14:54 ago)

@ Dr Andrew Leary
Posting: # 6950
Views: 9,086

Replicate design limbo

Post reply

Dear Andrew!

❝ Now this looks simple, logical and elegant. I wonder what I'm missing! ;-)

Well, I'm not sure whether the model makes sense, but it's somehow in line with EMA's simplifications. Test treatments are ignored, as is the fact that the first and second administrations of the reference occurred in different periods in sequences 1/2.

—
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,
2011-04-28 10:54
(5112 d 22:52 ago)

@ Helmut
Posting: # 6960
Views: 9,007

Replicate design Vienna waltz

Post reply

Dear Helmut, dear Andrew!

❝ Well, I'm not sure whether the model makes sense, but it's somehow in line with EMA's simplifications. Test treatments are ignored, as is the fact that the first and second administrations of the reference occurred in different periods in sequences 1/2.

What about recoding the treatments to T1, T2 and R1, R2 (numbers are Helmut's occasions or replicates) and evaluating the data as a 4x4 crossover with 2 sequences?

But which model ever, we make the assumption that the replicates are not the (random) result of the same formulation given at two occasions to the same subject, but something different. And that is to me not justifiable. Which effects should induce such a behaviour that we could separate the effects of the replicates? :lookaround:

To me a point estimate R2/R1 different from =1 does not make sense therefore.

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2011-04-28 16:17
(5112 d 17:29 ago)

@ d_labes
Posting: # 6964
Views: 9,203

Replicate design EMA Morris dance

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Dear D. Labes!

❝ But which model ever, we make the assumption that the replicates are not the (random) result of the same formulation given at two occasions to the same subject, but something different. And that is to me not justifiable. Which effects should induce such a behaviour that we could separate the effects of the replicates? :lookaround:

Well, that's a similar kind of folk dance like EMA's arbitrary discarding test administrations from the model (Q&A, Section 3.4). Let's read it again:

An advantage of Method C is that it directly calculates s²_wr. However, sometimes the algorithm fails to converge. For that reason the preferred way to get an unbiased estimate of sigma²_wr is using the data from the reference product only.

The following code removes all the test data from the data-set and then fits a model where the residual variance corresponds to the within subject variance for the test product.

Bonus questions:

Is the crippled model only preferred by EMA because Model C may not converge in all cases?
Is it acceptable to calculate s²_wr by Method C and only retreat to EMA's model if convergence is not reached (preferred # mandatory)?
Of course the evaluation for BE has to be done by Methods A or B ("compatible with CHMP guideline"). Can we perform the scaling based on s²_wr from the "advantageous" [sic!] Method C?
The last sentence is funny: within subject variance for the test product.

❝ To me a point estimate R2/R1 different from =1 does not make sense therefore.

OK, wrong model, but possible due to chance.

—
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,
2011-05-02 14:55
(5108 d 18:51 ago)

@ Helmut
Posting: # 6976
Views: 9,003

EMA Morris dance

Post reply

Dear Helmut!

❝ The following code removes all the test data from the data-set and then fits a model where the residual variance corresponds to the within subject variance for the test product.

Thanks for pointing me to this Gem I had read over up to now!
:rotfl:

Concerning your bonus questions:
No distinct answer from my side.

For our ongoing studies we have decided to go with the FDA model (both 90% CI and sigma_wR) because

we have written it down in the study protocols
We are convinced that it is the correct model, if not partial replicate

as the primary analysis and the EMA model as further analysis.

Lets see what our sponsors will do.

I am seeking for a compilation of arguments why the EMA model is inferior, which I will write down in my SAP.
Here my two cents:

The assumptions of the EMA recommended evaluation can not a-priori justified. Especially the evaluation of the average BE via a model assuming equal intra-subject variabilities of the Test and reference formulations (model A - Proc GLM evaluation same as for a 2x2 crossover) is contradictory to the reasons of use of a replicate crossover, namely the possibility to estimate separate intra-subject variabilities.
As the EMA Q&A already states "...This model (Model C - FDA model) will provide the same point estimate as methods A and B if all subjects provide data for all treatment periods. However it will generally give wider confidence intervals than those produced by methods A and B..."
This may lead to anticonservative behaviour with an inflation of the patients risk above 5%.
As Willavize and Morgenthien have shown by simulations¹⁾ especially the neglection of the subject-by-treatment interaction may result in a type I error inflation up to 17%.
It is well known that the least square estimates of the treatment effects are only unbiased if there are no missings in the data. From the dataset I of the EMA Q&A it is nevertheless obvious that these estimates should be used in case of missings.
The estimation of the intra-subject variance of the Reference formulation with a model neglecting the data for the Test formulation bears the danger of bias in the estimates of the period effects and presumable also the estimates of s²_wR.

¹⁾ Willavize, Morgenthien
"Comparision of models for average bioequivalence in replicated crossover designs"
Pharm. Stat. 2006 Jul-Sep;5(3):201-11.

Dear all! You are invited to contribute to this list and qualify it, preferably with literature, if you are also convinced that the FDA model is superior.

BTW: The Morrisk dance plays a prominent role in some of Terry Pratchett's "Discworld" novels. This Literature is highly recommended for people having contact with institutions like EMA for their mental health :-D

—
Regards,

Detlew