d_labes
★★★

Berlin, Germany,
2010-03-05 10:51

Posting: # 4864
Views: 21,666

## EMA: ANOVA and replicate studies [RSABE / ABEL]

Dear all,

after reading the tons of answers to the comments regarding the DRAFT of the new EMA Guidance I am more and more confused.

As Helmut has already noted they insists on using ANOVA, ANOVA, ANOVA ... and nothing else in the statistical evaluation of bioequivalence (in SAS speak Proc GLM or for Rusers function lm()). And more over all effects in the ANOVA as fixed!

Beside their joke "It is out of the scope of the guideline to give details on how to analyse the data of a replicate design, since it is standard statistical analysis " in the comments I would ask the community:
• How do we formulate an ANOVA for replicate designs (or partial replicate)? Some code highly appreciated, SAS or not SAS is not the question!
• How do we get the right ("appropriate") tests for the effects in the ANOVA with all effects fixed? In fixed effects models the denominator is always the MS(error) term as far as I know.
• From where do we get the intra-individual variabilities within Test or Reference? One of the ANOVA assumptions is equal variabilities within groups I think.
• Can we have an evaluation that is not only EMA accepted? FDA suggests mixed models in their statistical guidance.
I had used the FDA code for replicate designs up to now. But it relies definitely on mixed model (i.e. assuming subject as a random effect, factor) and thus on more elaborate and sophistic statistical method, but lacking anything that looks like ANOVA table. But this now obsolete in the light of the new EMA guidance!
So how to react? How to proceed with replicate studies practically, technically ... to be EMA conform?

Regards,

Detlew
Helmut
★★★

Vienna, Austria,
2010-03-05 14:17

@ d_labes
Posting: # 4866
Views: 19,547

## EMA: ANOVA and replicate studies

Dear D Labes!

» • From where do we get the intra-individual variabilities within Test or
»   Reference? One of the ANOVA assumptions is equal variabilities within
»   groups I think.

In a 2×2 design that's a main assumption. In replicate designs I'm not sure.

» • Can we have an evaluation that is not only EMA accepted?

I don't think so.

» […] mixed model […] obsolete in the light of the new EMA guidance!
» So how to react? How to proceed with replicate studies practically, technically ... to be EMA conform?

To be honest: not the slightest idea.
I'm still trying to track down where the ANOVA comes from. Tóthfalusi et al. (2009) wrote in Section 6.1 (p 737):

  The statistical models underlying the calculations make several assumptions. Relaxation and modifications of these assumptions can lead to different analyses and results. The issue of the multiplicity of models is particularly troublesome when parameters are estimated from replicate designs (with three or more periods), because each model corresponds to a different statistical and computational procedure and provides different final estimates and conclusions. Bioequivalence studies are not powered sufficiently to check the validity of most of the model assumptions, and thus the different assumptions can lead to multiple solutions. Each of the solutions can be correct statistically, but it is problematic if the different solutions suggest contradictory regulatory decisions. In the case of simple two-by-two bioequivalence studies, the data are analysed in a straightforward manner, and the computational procedure is simple and unique. This is not true for replicate crossover trials. Statistical models of a replicate crossover trial can be written in different ways. In borderline cases, this requires that regulatory agencies clearly specify their preferred method of analysis. As an alternative, Hsuan and Reeve have described a unique ANOVA type of estimation method.

Note the last two sentences! But as a statistical amateur I don't get the point looking at the referred paper:

Hsuan FC, Reeve R. Assessing individual bioequivalence with high-order cross-over designs: a unified procedure. Stat Med. 2003;22:2847–60.

From the summary:

The U.S. FDA's newly issued guidance on bioequivalence recommends the use of individual bioequivalence (IBE) for highly variable drugs and possibly for modified release dosage forms. The recommended approach to the analysis is to follow the methodology of Hyslop, Hsuan and Holder (HHH), based on a linear mixed model. A limitation of the HHH method is that it works only for uniform designs, such as RTRT/TRTR. In this paper, we present an alternative approach based on a multivariate model. The multivariate model is shown to be a strict superset of the linear mixed model and can successfully model data where the mixed model fails. Our multivariate approach coincides with the HHH method where the HHH method applies, but generalizes to any high-order cross-over design, such as the Balaam design, RTR/TRT, and TRSS/RSTT/STRR.

My emphasis. And on page 2858:

  The method we proposed here has been implemented in a Pharsight™ product, WinNonlin® (version 3.2 or later).

Too bad that WinNonlin's output states on top of each page

WINNONLIN LINEAR MIXED EFFECTS MODELING / BIOEQUIVALENCE

Maybe I write a one-line SOP: "In the core output replace 'LINEAR MIXED EFFECTS MODELING' by 'MULTIVARIATE ANOVA'; save file."

Cheers,
Helmut Schütz

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

Berlin, Germany,
2010-03-09 09:33

@ Helmut
Posting: # 4882
Views: 19,081

## Orouboros mixed up

Dear Helmut!

Oh, oh the orouboros has beaten again!

» ... But as a statistical amateur I don't get the point looking at the referred paper:
» Hsuan FC, Reeve R. Assessing individual bioequivalence with high-order cross-over designs: a unified procedure. Stat Med. 2003;22:2847–60.

I must confess that I had not understand this paper at all, thus being less than an amateur
("Blutiger Laie" = raw recruit ).

» The method we proposed here has been implemented in a Pharsight™ product, WinNonlin® (version 3.2 or later).

Too bad I do not own WinNonlin.
Can you eventually show some output of this method?

J.-P. Liu
Statist. Med. 14, 1067-1078 (1995)

It has ANOVA tables but Liu term his model underlying the analysis "Mixed"!
Mixed effects for subject and subject*formulation interaction.
Without mixed effects the corresponding F-Tests would be others, I think.

Regards,

Detlew
Helmut
★★★

Vienna, Austria,
2010-03-09 14:55

@ d_labes
Posting: # 4885
Views: 19,084

## Orouboros mixed up

Dear D Labes!

» Too bad I do not own WinNonlin.
» Can you eventually show some output of this method?

Well, we had a comparison following this post.

»
» J.-P. Liu
» Statist. Med. 14, 1067-1078 (1995)

Hhm, I don’t have it in my files yet.

» It has ANOVA tables but Liu term his model underlying the analysis "Mixed"!
» Mixed effects for subject and subject*formulation interaction.
» Without mixed effects the corresponding F-Tests would be others, I think.

Mixed is the taboo-word!

Edit: Got the paper. It’s definitely a mixed effects-model.

Cheers,
Helmut Schütz

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

Berlin, Germany,
2010-03-11 11:07
(edited by d_labes on 2010-03-11 11:25)

@ Helmut
Posting: # 4894
Views: 19,458

## Liu ANOVA PtC

Dear Helmut, dear All,

Meanwhile I have experimented a little bit with the ANOVA described in the Liu paper. I have taken Example 4.4 from the book

Patterson, Jones
"BIOEQUIVALENCE and STATISTICS in CLINICAL PHARMACOLOGY"
Chapman & Hall / CRC 2006

a 4-period study with the sequences TRTR and RTRT as the dataset (to be found here).
[edit: /CRC WEB PAGE/chapter4/exam44.dat (Helmut)]

The subjects with missing data were left out from the analyses.

It took me some headache (and some beer ) to figure out how to formulate a Proc GLM ANOVA with the effects sequence, subject (within sequence), formulation, period and subject-by-formulation interaction. "Simple" attempts catched me often in the Type III sum-of-squares trap.

Here comes the code that worked without curiosities:
 Proc GLM data=four;   class sequence subject period formula;   model ln_AUC = sequence subject(sequence) formula period                  subject(sequence*formula) / CLparm alpha=0.1;   random subject(sequence) subject(sequence*formula) /Test;   Estimate 'T-R' formula -1 1; *without subjects with missings;  where subject not in(3 27); quit;

The random statement is only for letting SAS figure out the "appropriate" F-tests for the effects, because we all know meanwhile that Proc GLM is fitting the model as if all effects are fixed and the random statement only affects the F-tests, which in an all-fixed model always have MS(error) as denominator.

Results:
...                              The GLM Procedure Dependent Variable: ln_auc                                    Sum of  Source                  DF       Squares   Mean Square  F Value  Pr > F  Model                  105   55.42179511    0.52782662     5.33  <.0001  Error                  102   10.10810776    0.09909910  Corrected Total        207   65.52990287            R-Square     Coeff Var      Root MSE    ln_auc Mean            0.845748      5.349792      0.314800       5.884343 *----------------------------------------------------------------------- the all effects fixed part;  Source                    DF     Type I SS   Mean Square  F Value  Pr > F  sequence                   1    0.17364001    0.17364001     1.75  0.1886  subject(sequence)         50   49.37630741    0.98752615     9.97  <.0001  formula                    1    0.56857602    0.56857602     5.74  0.0184  period                     3    0.30656009    0.10218670     1.03  0.3821  subje(sequen*formul)      50    4.99671158    0.09993423     1.01  0.4752  Source                    DF   Type III SS   Mean Square  F Value  Pr > F  sequence                   1    0.17364001    0.17364001     1.75  0.1886  subject(sequence)         50   49.37630741    0.98752615     9.97  <.0001  formula                    1    0.56857602    0.56857602     5.74  0.0184  period                     2    0.27974027    0.13987013     1.41  0.2485  subje(sequen*formul)      50    4.99671158    0.09993423     1.01  0.4752 *----------------------------------------------------------------------- expected mean square from the MIXED model; Source                Type III Expected Mean Square sequence              Var(Error) + 2 Var(subje(sequen*formul)) +                       4 Var(subject(sequence)) + Q(sequence) subject(sequence)     Var(Error) + 2 Var(subje(sequen*formul)) +                       4 Var(subject(sequence)) formula               Var(Error) + 2 Var(subje(sequen*formul)) + Q(formula) period                Var(Error) + Q(period) subje(sequen*formul)  Var(Error) + 2 Var(subje(sequen*formul)) *---------------------------------------------------------------------- appropriate (for the MIXED model) F-tests;          Tests of Hypotheses for Mixed Model Analysis of Variance Dependent Variable: ln_auc  Source                    DF   Type III SS   Mean Square  F Value  Pr > F  sequence                   1      0.173640      0.173640     0.18  0.6768  Error                     50     49.376307      0.987526  Error: MS(subject(sequence))  subject(sequence)         50     49.376307      0.987526     9.88  <.0001  formula                    1      0.568576      0.568576     5.69  0.0209  Error                     50      4.996712      0.099934  Error: MS(subje(sequen*formul))  period                     2      0.279740      0.139870     1.41  0.2485  subje(sequen*formul)      50      4.996712      0.099934     1.01  0.4752  Error: MS(Error)         102     10.108108      0.099099 *-------------------------------------------------------------- estimated treatment effect, 90% CIs in log domain Parameter  Estimate       Error    t Value    Pr > |t| 90% Confidence Limits T-R      0.10456651    0.04365492   2.40      0.0184   0.03210240   0.17703061 ...

Some points to consider:
• The "appropriate" F-tests will only be obtained if the model is formulated with some random effects.
• If there is no subject-by-formulation interaction the model reduces to the classical GLM-ANOVA used for the 2x2 crossover (the Bear way, but there estimation with "real" mixed model software lme()).
• The appropriate error term for the formula (treatment) effect is the MS(subject-by-formulation) if mixed model is used! This is the meaning of sInt not known in this thread in connection with SABE in replicate design.
• The estimate statement is not affected by the random statement and uses the MS(error) as the error term. This can be show if the random statement is deleted (results not shown here).
Thus it treats all effects as fixed. (EM: Now I understand you, from now on I will call it also bogus! )
• This is in most cases anti-conservative. You can verify this in looking at the expected mean square for MS(SxF) and noticing that it is the sum of the error variance + variance from subject-by-treatment interaction. Thus you will get wider CIs for the treatment diffs in the mixed model, even more if you look at the associated degrees of freedom.
But this anti-conservative method is what is required by the new EMA guidance (or do we err?)! BTW: This is different to the classical 2x2 design where the correct error term is due to missing SxF interaction always MS(error)(subject as random effect or not).
• The different intra-individual variabilities are not part of the Proc GLM output and have to calculate in a additional step (using method of moments?).
• Somehow curious for me is the period effect df. Don't know if this is a SAS curiosity. It is different from the Liu paper, but the Liu design is also different (2 periods with 2 replicates within periods).

BTW: Excuse this very long post, but I had no idea how to shorten.
BTW2: The fixed effects story gets more and more curious for me.
BTW3: If this ANOVA would be sufficient for the EMA we had also in SAS to follow Helmut's SOP with the adaption "delete Mixed model" .

Regards,

Detlew
d_labes
★★★

Berlin, Germany,
2010-03-26 14:01

@ Helmut
Posting: # 4977
Views: 18,932

## A walk on the wild side - the Bear way

Dear All!

This should read in connection with my previous post in this thread.
Helmut, I have posted to you because I otherwise had to post to myself.

After touting the anti-conservatism of the all-fixed-effects-approach of the Liu ANOVA and noticing the fact that omitting SxF results in the classical model, hopefully with SxF incorporated in the error term.
I was interested in going the Bear way for replicate designs because meanwhile I hazard a guess that EMA is expecting this from us.

Some little evidence:
• EMA comments, page 139: Q: "What is the suggested statistical model for crossover designs with more than 2 periods in BE studies?
EMA comment: "The model is the same for designs with more than 2 periods."
• 3x3 and 4x4 cross-over curiosity in the guidance (extract common 2x2 studies)
• EMA comments, page 185: Q: "How to evaluate a replicate design in an average BE approach?"
EMA comment: "... it is standard statistical analysis."
• Mixed model curiosity (Nothing other then common ANOVA, ANOVA, ANOVA ...)
• The Old s.. story.
But then I remembered a paper coming under my eyes some times ago:

S.A. Willavize, E.A. Morgenthin
Comparison of models for average bioequivalence in replicate cross-over designs
Pharm. Stat. Volume 5 Issue 3, Pages 201 - 211 (2006)
Published Online: 24 May 2006

The authors have simulated data of a TRTR/RTRT design distributed exactly according to the models underlying the evaluation methods, namely according to the classical model without any SxF interaction and some variants of including such an interaction. Various values of the involved variabilities were employed. For each setting 1500 datasets were simulated with 24 subjects.
These data were then evaluated with each evaluation method.

Here is a part of the results of evaluations with the classical model, also Proc Mixed was employed instead of Proc GLM (the Bear way):
  Probability of concluding BE at T/R = 0.8 (=alpha) Data model1       0.041 ... 0.054 Data model2       0.047 ... 0.174  sic!  Data model3       0.047 ... 0.129
model1=classical model
model2=FDA model with SxF
model3=Ekbohm-Melander (very similar to the Liu ANOVA)

Although not mentioned exactly in the paper I suppose that the greatest anti-conservatism / alpha-inflation occurred with drastic values of the SxF interaction.
Seems the SxF component can not always incorporated into the error term of the simple classical evaluation.

Of course the impact of these results depend on the belief if the SxF is a real phenomenon in bioequivalence studies. For instance in

Endrenyi, Tothfalusi
Subject-by-formulation interaction in determination of individual bioequivalence: Bias and prevalence
Pharm. Res. 16 (1999), 186-190

and others it is strongly argued against it in showing that the datasets used by FDA during evaluation of IBE are compatible with a SxF=0.

Regards,

Detlew
d_labes
★★★

Berlin, Germany,
2010-03-29 16:17

@ d_labes
Posting: # 4986
Views: 18,818

## New adventures from the Bear way

Dear All!

Talking a little bit with myself for psycho-hygiene.

After walking a while on the bear way, sun was shining , all was good, suddenly I came into a dark wood, to a big dark hole in which the three-headed hydra resides.
She was horrible looking, totally out of balance and equipped with dreadful mixed (un)expected means and (non)integer degrees of freedom .

Quick I employed the famous bogus RANDOM statement of Proc GLM, which I was preventively armed with during this adventure, to inspect the expected mean squares of the data and to perform the 'appropriate' F-tests for banishing that beast arosen from the depth of moria .
(Unfortunately the mightier Proc Mixed was prohibited to me by the custodians of the bear-way on EMA territory.)

Here the result: evaluation of example 4.2 from Patterson/Jones, a dataset from a 3-period-2-sequence replicate crossover design with the sequences RTT (39 subjects) and TRR (35 subjects), without missing data.
                       Classical Proc GLM, Cmax                              The GLM Procedure Source                Type III Expected Mean Square formula            Var(Error) + Q(formula) period             Var(Error) + Q(period) sequence           Var(Error) + 2.6667 Var(subject(sequence)) + Q(sequence) subject(sequence)  Var(Error) + 3 Var(subject(sequence)) *-------------------------------------------------------------------------                              The GLM Procedure          Tests of Hypotheses for Mixed Model Analysis of Variance Dependent Variable: ln_cmax  Source                 DF   Type III SS   Mean Square  F Value  Pr > F  formula                 1      0.829991      0.829991     4.89  0.0286  period                  2      0.331868      0.165934     0.98  0.3786  subject(sequence)      72    190.981556      2.652522    15.63  <.0001  Error: MS(Error)      145     24.606438      0.169700  Source                 DF   Type III SS   Mean Square  F Value  Pr > F  sequence                1      2.490853      2.490853     1.05  0.3093  Error              73.154    173.861309      2.376652  Error: 0.8889*MS(subject(sequence)) + 0.1111*MS(Error) 

After I had survived this beastly monster due to my extra-power-to-know I had questions:
• Somebody out there which had similar "Close Encounters of the Third Kind"?
• Or was this only Morgan le Fay confusing me while looking through my rose-tinted ®SAS® glasses?
• Can we also survive equipped with other arms not so expensive (especially R)?
BTW: Non-integer df due to Satterthwait approximation due to mixture of MS'ses. Again the result of defining subject nested within sequence as the expatriated random effect.

Regards,

Detlew
ElMaestro
★★★

Belgium?,
2010-03-29 17:26

@ d_labes
Posting: # 4987
Views: 18,708

## New adventures from the Bear way

Dear d_labes

» She was horrible looking, totally out of balance and equipped with dreadful mixed (un)expected means and (non)integer degrees of freedom .

Hmmm, have you been smoking Schuetzomycin?

» Here the result: evaluation of example 4.2 from Patterson/Jones, a dataset from a 3-period-2-sequence replicate crossover design with the sequences RTT (39 subjects) and TRR (35 subjects), without missing data. (...)

I am completely lost, simply not at your level of insight. I don't know how to understand all this. Could you explain to a novice like me in slowmotion what you investigated and what you conclude and why?

Best regards,
EM.
Helmut
★★★

Vienna, Austria,
2010-03-29 18:41

@ ElMaestro
Posting: # 4988
Views: 18,951

## Posology

Ahoy!

» Hmmm, have you been smoking Schuetzomycin?

What?! Schützomycin is an esoteric (aka undocumented) ingredient of modern preparations of Flying Ointment. You don't smoke it, honey – its use is dermal & delicate; believe me.

» » Here the result: evaluation of example 4.2 from Patterson/Jones, a dataset from a 3-period-2-sequence replicate crossover design (...)
»
» I am completely lost

Well, Detlew is referring to a dataset we played with in the past. Since I’m not equipped with I’m lost in the details as well. Rumors are going that he’s on the track of evaluating a replicate study without a mixed model and all effects fixed.

Cheers,
Helmut Schütz

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

Berlin, Germany,
2010-03-30 09:20
(edited by d_labes on 2010-03-30 09:50)

@ Helmut
Posting: # 4992
Views: 18,916

## Lost on the Bear way

Gents!

» ... Schützomycin is an esoteric (aka undocumented) ingredient of modern preparations of Flying Ointment. You don’t smoke it, honey – its use is dermal & delicate; believe me.

Ok, on my next leg along the Bear way I will take some dose of Schützomycin with me. Hopefully this will escape me from some more serious situations.

» ... Rumors are going that he’s on the track of evaluating a replicate study without a mixed model and all effects fixed.

Yessss Sir, this is the Bear way, without lme() but rather lm() also known to SAS'lers as Proc GLM .

And what I have observed in this adventure along the Bear way was to evaluate my original question Q2 above in this thread: How can we get the 'appropriate' tests (new BE guidance, page 16 "The ANOVA tables, including the appropriate statistical tests of all effects in the model, should be submitted.") within an ANOVA style evaluation.

And I was very surprised with that finding as a statistical raw recruit.

If it is real, and the right answer to a false question, it prevents us from using a test by hand of the sequence effect using simply the subject(sequence) MS as the error term because the mixture observed above depends on the degree of imbalance.
Just to cite ElMaestro above, ooouch ..., below: "You still can get the effects right ... by considering all effects fixed. but you will have to do some manual brain-work still."
I employed the RANDOM statement to save my small brain.

I suppose a big amount of serious headache! For every new study, if using 3-period-whatever-sequence replicate design, if not totally balanced! Schützomycin to the rescue?

BTW: In a bizarre twist, it's not all-fixed but rather mixed as usual, but ANOVA, ANOVA, ANOVA ...
BTW2: The Bear model is also used in Chow/Liu, Chapter 9 but evaluated with GLM (see for instance page 274). Also the various formula given there (casually also for the within-subject variabilities!) then heavily rely on within-subject contrasts.

Regards,

Detlew
ElMaestro
★★★

Belgium?,
2010-03-30 16:01

@ d_labes
Posting: # 4993
Views: 18,750

## Lost on the Bear way

Ahoy,

» I suppose a big amount of serious headache! For every new study, if using 3-period-whatever-sequence replicate design, if not totally balanced!

Section 6.2.3.1.2.5.7.2: Statistical handling of volunteers
Each subject will be stratified into one of three sequences.

Section 8.4.9.8.3.5.1.5: Statistics
The full analysis set consists of the 14 volunteers that first complete sequence ABB, plus the 14 volunteers that first complete sequence BAB, plus plus the 14 volunteers that first complete sequence BBA.

» Schützomycin to the rescue?

Not sure. It has recently come to my attention that Schützomycin, although it's a wonderful drug, also has a few shortcomings. On board my boat I usually give my men a large dose before we make port as a preventive measure. This is because I know that once they get on land after 3 months at sea the first thing they do is [DELETED BY THE FORUM ADMINISTRATOR] after which they [DELETED BY THE FORUM ADMINISTRATOR] and frequently they will even [DELETED BY THE FORUM ADMINISTRATOR]. After such events a brief visit to the local police authority (with a stack of cash in a suitcase) and/or the consulate is now and then called for.

Best regards
EM.
d_labes
★★★

Berlin, Germany,
2010-04-01 15:20

@ ElMaestro
Posting: # 4995
Views: 18,716

## Nice looking three-headed hydra mutant

Ahoy Old Sailor,

» Section 6.2.3.1.2.5.7.2: Statistical handling of volunteers
» Each subject will be stratified into one of three sequences.
»
» Section 8.4.9.8.3.5.1.5: Statistics
» The full analysis set consists of the 14 volunteers that first complete sequence ABB, plus the 14 volunteers that first complete sequence BAB, plus plus the 14 volunteers that first complete sequence BBA.

Nice idea, as always: ElMaestro to the rescue!

Meanwhile I have inspected the Extra-reference three-headed hydra, captured on my last journey on the Bear way using some Schützomycin for immobilizing (a paradox effect, which occurs only for hydras).

Whatever imbalance I put on it, the expected mean squares always show that the error term for the sequence effect is simply subject(sequence), as my bogus little RANDOM friend tells me.

BTW: Played with the data set
Le Roux et.al
"Use of repeated cross-over design in assessing bioequivalence: (within and between subjects variability - Schuirmann confidence intervals estimation)"
Eur. J. Drug Metab. Pharmacokin. 23(2), 339-345 (1998)

Have a nice Easter.

Regards,

Detlew
ElMaestro
★★★

Belgium?,
2010-03-05 23:02

@ d_labes
Posting: # 4869
Views: 19,341

## EMA: ANOVA and replicate studies

Dear d_labes,

» • How do we formulate an ANOVA for replicate designs (or partial
»   replicate)? Some code highly appreciated, SAS or not SAS is not the
»   question!

Go to church, pray, and hope for a miracle. Or go to the EMA at their upcoming event for people interested in this guideline and ask the question.

» • How do we get the right ("appropriate") tests for the effects in the
»   ANOVA with all effects fixed? In fixed effects models the denominator
»   is always the MS(error) term as far as I know.

Disagree. You still can get the effects right (in particular we talk sequence, right?) by considering all effects fixed. but you will have to do some manual brain-work still. By the way, there is even in this case a non-trivial issue with that effect. One can rightfully claim it must be null for a type III SS, because type III SS for Seq reflects a model with Per Trt and Subj, and since Subj is nested in Seq, one does not achieve anything by this single term deletion. Compare R's "drop1" with Proc GLM and see the difference.

» • From where do we get the intra-individual variabilities within Test or
»   Reference? One of the ANOVA assumptions is equal variabilities within
»   groups I think.

Mixed models or nothing. Church or EMA.
I am not competent to tell if there is a potential gain in the Method of Moments, but I have not seen it working in bioequivalence.

» • Can we have an evaluation that is not only EMA accepted? FDA suggests
»   mixed models in their statistical guidance.

FDA got it right. It's standard.

» I had used the FDA code for replicate designs up to now. But it relies definitely on mixed model (i.e. assuming subject as a random effect, factor) and thus on more elaborate and sophistic statistical method, but lacking anything that looks like ANOVA table. But this now obsolete in the light of the new EMA guidance!
» So how to react? How to proceed with replicate studies practically, technically ... to be EMA conform?

Church or EMA.

When you figure out the answers, please inform us all. I completely agree with your disorientation and I think this is a lapse in the guidance that merits a correction (better sooner than later).
EM.
d_labes
★★★

Berlin, Germany,
2010-03-09 09:02

@ ElMaestro
Posting: # 4881
Views: 19,047

## Prayers quest

Dear Großer Meister,

» Go to church, pray, and hope for a miracle.

I know that the world is full of miracles.
But I don't believe in .

Moreover the Oracle has answered already: "It is out of the scope of the guideline to give details on how to analyse the data of a replicate design, since it is standard statistical analysis". (emphases by me)

So once again: Any idea how to do that? The Bear way, i.e same model as for 2x2? Helmuts suggestion? Any other?

Regards,

Detlew
ElMaestro
★★★

Belgium?,
2010-03-09 19:02

@ d_labes
Posting: # 4886
Views: 19,086

## Go for the referral

Dear d_labes,

» So once again: Any idea how to do that? The Bear way, i.e same model as for 2x2? Helmuts suggestion? Any other?

Neither. If I had to do something with a dossier based on a replicated study it would be the following:
1. Carry on with a linear mixed model.
2. Construct the CI's and stuff as you ordinarily did before this guidance document was published.
3. Wait and see!
If anyone has the guts to trigger an EU referral, this would still be a good outcome. Not the quickest way for the product in question, but it would be good to have this issue debated at CMD and, much better, at CHMP.
So if the product is referred to CMD, there will be limited scientific discussion there because CMD is mainly a regulatory comittee. They are highly skilled in all procedural problems, but they are not statisticians or pharmacokinetophystians or what it's called (they can bring experts, but there is a limitation to that, too). So either approval or referral to the CHMP. This would be a great chance for you. Because you can openly address it and ask them to show you how one can analyse replicated studies without a mixed model and still get unbiased separate withins for T and R. Gotcha!

I have the greatest respect for the PK-subgroup, the CMD, the CHMP and EU regulators in general for all the work they undertake. But in this specific case I think the PK-subgroup has produced a document that is self-contradictory and not on par with current standards and which may result in rejection of equivalent products if the word of the guideline is followed. For that reason, I think that medicine consumers in Europe would have a potential benefit if someone like you engages the regulators in a game of chicken. It is only one sentence that needs to be changed in the guidance in order for everything to be ok.

Best regards
EM.
yjlee168
★★

Kaohsiung, Taiwan,
2010-03-08 03:23

@ d_labes
Posting: # 4874
Views: 19,147

## EMA: ANOVA and replicate studies

Dear d_labes,

» the community:
» • How do we formulate an ANOVA for replicate designs (or partial
»   replicate)? Some code highly appreciated, SAS or not SAS is not the
»   question!

With R codes, I don't know if this method is applicable to a replicate BE? Scroll down the webpage to browse "Mixed (between and Within) designs". However, it's not lm() function. Thanks.

All the best,
-- Yung-jin Lee
bear v2.8.7:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear
d_labes
★★★

Berlin, Germany,
2010-03-09 08:52

@ yjlee168
Posting: # 4880
Views: 19,719

## R: aov(), lm() and what does it mean?

Dear Yung-jin,

Thanks for pointing me to this WEB site.
But my R speak is not good enough to figure out what the difference between aov() and lm() is.
Moreover I don't understand their data.

Eventually there is someone out to enlighten me?

Regards,

Detlew