Bioequivalence and Bioavailability Forum

Hi BEQool,

❝ So you would assume that Residual Mean Squares (MS) as the denominator was used because nothing is explicitly stated? If Subject MS was used instead as the denominator, you think that they would probably mention it?

yes.
The regulators are not trying to make our life easier. Yes, the model to be used is rarely presented. There are not so many exceptions (i.e. replicate designs for EMA or FDA).

❝ Is there any source or literature what to use as denominator when assessing Group*Treatment interaction? I cant find anything relevant. Nothing is mentioned about it in the new ICH M13A guideline

You are right. There's nothing. Note that when FDA published the code for 2*2*2 studies (a while ago), they did not mention in the text that a sequence should be tested against Subject MS, but just added a RANDOM statement in PROC GLM. Anyway, this decision had some reason.

In any sources with Group*Treatment interaction the denominator is not mentioned directly, but I think that without additional RANDOM statement (or ANOVA postprocessing) which SHOULD be mentioned if in use, the Residual MS is still valid. So you should prove why you modified your ANOVA to get F against Subject MS. The `famous` Sun et al. ^* paper states:

For each dataset, a Linear Mixed Model is fit with subgroup, sequence, subgroup-by-sequence, period nested within subgroup, treatment, treatment-by-subgroup as the fixed model and subject nested within subgroup and sequence as a random effect model (the same model can also be fit using the General Linear Model (GLM) with fixed effects only but with slight modification).

❝ Additionally, what if the significance between the denominator used differ?

yes, that's why it should be mentioned if the model/ANOVA was modified to use Subject MS

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• Wanjie Sun, Don Schuirmann & Stella Grosser (31 Oct 2022): Qualitative versus Quantitative Treatment-by-Subgroup Interaction in Equivalence Studies with Multiple Subgroups, Statistics in Biopharmaceutical Research, doi:10.1080/19466315.2022.2123385

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PS: Are you equipped with SAS to check the ANOVA tables for this model (using some dataset without dropouts?) It would be interesting to see what PROC MIXED thinks about this interaction. From this paper I assume they should be the same as PROC GLM. But who knows! I could be wrong with my claim...