Bioequivalence and Bioavailability Forum

Salam Mutasim,

❝ What is the explanation for …

Chance.

❝ … and the impact of having a significant group by sequence interaction in a study with 4 groups and 2 sequences and 4 periods (HVD).

If you are dealing with ABEL (the EMA’s method) chances than any (!) European agency will ask for a group-term in the analysis are close to nil. When I gave my first presentation about it in Budapest 2017 in front of European regulatory (!) statisticians they were asking in disbelieve “What the hell are you talking about?” See what the BE-GL states:

The study should be designed in such a way that the formulation effect can be distinguished from other effects.
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 that groups or sequences have an effect on the PK response? Heck, no way! Same inclusion-/exclusion-criteria and hence, similar demographics, same clinical site, same bioanalytical method. Hundreds (thousands?) of studies performed in multiple groups and accepted by European agencies based on pooled data. OK, I know of two cases where the EMA (centralised procdure) asked for something similar. Both were complicated drugs (a biosimilar and a liposomal product) and multi-centric. Hence, the EMA asked for a site term.*
This is in line what is stated in the Q&A document about Two-Stage Designs:

A model which also includes a term for a formulation*stage interaction would give equal weight to the two stages, even if the number of subjects in each stage is very different. The results can be very misleading hence such a model is not considered acceptable. […] this model assumes that the formulation effect is truly different in each stage. If such an assumption were true there is no single formulation effect that can be applied to the general population, and the estimate from the study has no real meaning.

Replace formulation*stage by formulation*group and you get the idea.

But all of this is about a group-by-treatment interaction. Sometimes in conventional 2×2×2 crossovers we see a significant sequence (better unequal carry-over) effect. Since it can only be avoided by design (sufficiently long wash­out) any test for it is futile. Check for eventual residual concentrations in higher period(s) and exclude subjects with pre-dose concentrations >5% of their C_max-values. In analogy the same can be said about the group-by-sequence interaction. Occasionally you will see a significant result. Ignore it.
Only if you prefer braces plus suspenders: Go with the FDA’s model II. But no pre-test and no interaction! The loss in power as compared to the pooled analysis is negligible.
Degrees of freedom in a 2×2×2 design:

Model III: n₁ + n₂ – 2
Model II:  n₁ + n₂ – (N_groups – 1) – 2

Or in the 4-period full replicate:

Model III: 3(n₁ + n₂) – 4
Model II:  3(n₁ + n₂) – (N_groups – 1) – 4

Am I right that you had to deal with 128 subjects? Then the 90% CI with model II will be just 0.002% (!) wider than the one with model III.
What you never ever should do: Evaluate groups separately. Power will be terrible. Even if you are extremely lucky and one of them passes, what will you do? Submit only this one? Any agency will ask for the others as well. Guess the outcome.

If you are thinking about the FDA’s group models I–III: There were very few deficiency letters (all with the same text) issued to US and Canadian companies. On the other hand, many European CROs have such letters collecting dust in archives. Politics? Even if you follow this track, model III (pooling) is justified since the conditions are practically always fulfilled. The sequential procedure (test for a group-by-treatment interaction at the 10% level) as any pre-test might inflate the type I error. I even have a statement from the EMA that such a procedure is not acceptable. Group-by-sequence interaction? Forget it.

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• Proposed all-fixed effects model:
  Site+Sequence+Sequence(Site)+Period(Site)+Subject(Sequence×Site)+Treatment