## Group by sequence interaction, an urban myth? [General Statistics]

❝ 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.

*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: *n*_{1} + *n*_{2} – 2

Model II: *n*_{1} + *n*_{2} – (*N*_{groups} – 1) – 2

Model III: 3(*n*_{1} + *n*_{2}) – 4

Model II: 3(*n*_{1} + *n*_{2}) – (*N*_{groups} – 1) – 4

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.

- Proposed all-fixed effects model:

Site+Sequence+Sequence(Site)+Period(Site)+Subject(Sequence×Site)+Treatment

*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

### Complete thread:

- Group by sequence interaction Mutasim 2019-08-07 13:16 [General Statistics]
- Group by sequence interaction, an urban myth?Helmut 2019-08-07 14:35
- pristine, genuine, holy, magnificent, inexplicable beautiful variation ElMaestro 2019-08-08 10:06
- I love your subject line! Helmut 2019-08-08 10:31
- Group effect, did you miss it? Astea 2019-12-21 14:12
- Group effect, did you miss it? PharmCat 2019-12-22 01:37
- Group effect: the endless story Helmut 2019-12-22 10:30
- Group effect: the endless river Astea 2019-12-22 21:23
- Group effect: the endless river PharmCat 2019-12-22 22:52
- replicateBE solution with interactions mittyri 2019-12-23 14:30
- replicateBE solution with interactions Astea 2019-12-23 17:26
- datasets issues mittyri 2019-12-24 10:53
- datasets Helmut 2019-12-24 11:03
- datasets Astea 2019-12-24 19:18
- lmer / lme Helmut 2019-12-25 19:12

- datasets Astea 2019-12-24 19:18

- replicateBE solution with interactions Astea 2019-12-23 17:26

- Group effect: the endless river Astea 2019-12-22 21:23
- What do you mean exactly? Beholder 2019-12-27 13:44
- What do you mean exactly? Astea 2019-12-29 21:59
- ANOVA acc. to GL Helmut 2019-12-30 12:32

- What do you mean exactly? Astea 2019-12-29 21:59

- Group effect, did you miss it? Astea 2019-12-21 14:12

- I love your subject line! Helmut 2019-08-08 10:31

- pristine, genuine, holy, magnificent, inexplicable beautiful variation ElMaestro 2019-08-08 10:06

- Group by sequence interaction, an urban myth?Helmut 2019-08-07 14:35