Bioequivalence and Bioavailability Forum

Hi BR,

❝ When I use such a model: Sequence+Period+Treatment+Group+Patient(Sequence) I get "Not estimable" in the results of ABE in WNL. Model is wrong? When I delete the "group" than error dissapears. Comments: it is BE cross over study in 3 groups and all effects are fixed.

As Simon noted already at Certara’s Forum, it’s the fixed effects model – not the software. Even without the group-term (i.e., the EMA’s sequence, subject(sequence), period, formulation) you will get an endless list of “Not estimables” simply because the requested combination does not exist in the data set. Example: All subjects are uni­quely coded (1, 2, …, n) and subject 1 is in sequence RT. You will get an estimate. Fine. But the model tries to estimate subject 1 in sequence TR as well. Not estimable! That’s correct because a datum with such a coding does not exist.

Since you are posting from Russia what do you want to achieve? Satisfy the «Экспертами» (see this post)? Every time I was in Moscow we had endless & fruitless debates about it… All relevant documents (2008 GL, 2013 “Red Book”, 2015 EEU GL) are more or less translations of the EMA’s GL (the EEU GL spiced with some parts of the WHO’s GL). What does the EMA’s GL say about groups (or more important sites)? Nothing! Only:

The precise model to be used for the analysis should be pre-specified in the protocol. The statistical analysis should take into account sources of variation that can be reasonably assumed to have an effect on the response variable.

Is it reasonable to assume such an effect if a study was performed in multiple groups due to logistic reasons (e.g., limited capacity of the clinical site)? I don’t think so. Hence, in the EU generally data are simply pooled and the common model (without a group term) is used.
Different sites are much more problematic. I recently saw a multi-site study where the sites clearly showed different results (averages differed tenfold). It was a cancer drug and some sites were pretty small. If (if!) all sites would have balanced sequences it would have been still no problem but this was not the case. Actually there was a highly significant (p <0.001) site-by-treatment interaction. If one would naïvely pool the sites the treatment effect would be biased.

OK, back to the EEU GL (the last paragraph of section 94):

Если предполагается проведение исследования в нескольких группах из логистических соображений, об этом необходимо явно указать в прото­коле исследования; при этом, если в отчете отсутствуют результаты статис­тического анализа, учитывающие многогрупповой характер исследования, необходимо представить научное обоснование отсутствия таких результатов.

My interpretion:

1. State already in the protocol that the study will be performed in multiple groups and give a justification that an effect on the treatment comparison can be reasonably ruled out (i.e., same site, same procedures, all subjects randomized before splitting, same batches of T and R, short time interval between groups, blahblah).
   
2. If you want to go the hard way: Modify the FDA’s multi-group models (i.e., mixed-effects ⇒ all effects fixed). More about that later.

I would always try #1. Whether the experts will swallow that is another story.
#2 can be nasty! Start with “Model 1” (fixed effects* in Phoenix-notation):

Group + Sequence + Sequence(Group) + Period(Group) + Treatment +
Treatment * Group + Subject(Sequence * Group)

1. If the term Treatment * Group (the treatment-by-group interaction) is not significant at the 0.1 (!) level remove this term and perform the analysis by “Model 2”. The between-group test is not very sensitive (sloppy: has low power). Therefore, the FDA requires testing at 0.1 (and not at 0.05).
   
2. If the test is significant, you are not allowed to pool the data and can only run the conventional model with the data of the largest group. Good luck! The loss of power likely will be extreme. Furthermore, you could expect false positives – and consequently throw away 10% of your studies…

“Model 2”:

Group + Sequence + Sequence(Group) + Period(Group) + Treatment +
Subject(Sequence*Group)

Yes, you will see an awful lot of “Not estimables”.

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• I have seen a data set (three groups: 19, 19, 18) where both fixed effects models did not converge (neither in Phoenix nor in SAS/JMP). No problem with the mixed-effects models (i.e., Subject(Sequence*Group) random)… The statistician of the MHRA accepted it.