Bioequivalence and Bioavailability Forum

Dear Croosov,

welcome to the club.

❝ What test would you use for tmax if you have a 3 period + 3 treatment design or 4 period + 4 treatment design with one treatment as a reference.

Have a look at the papers cited in this relative old post.
They deal with 3-period-3treatment crossover designs with six sequences, but the ideas may be extended to 4x4 designs also.
The only thing to worry is the null-distribution of the tests if you need an exact solution. This is not an easy task, but approximate solutions are easily obtained.

Search the Forum's category Nonparametrics and you will find some more discussions on this topic.

If you have a study for submitting to the European regulatory body EMA you don't need any test for Tmax. Just to cite the EMA guidance:
"A statistical evaluation of tmax is not required. However, if rapid release is claimed to be clinically relevant and of importance for onset of action or is related to adverse events, there should be no apparent difference in median tmax and its variability between test and reference product." page 15

Moreover non-parametric test are not honoured by the EMA:
"A non-parametric analysis is not acceptable." page 15.

What else they expect for the second part of the quote above is not clear. Seems some sort of descriptive statistics.
Again search the forum to find numerous discussions on this topic.

Hope this helps.

BTW: WMW = Wilcoxon-Mann-Whitney test.