Bioequivalence and Bioavailability Forum

Dear Ben,

Lets come to your original questions (beside PowerTOST issues).
I will only deal with carry-over. Others may be more qualified for your other issues.

❝ The main argument is that it (the 3x6x3 design) is variance balanced and balanced for (first order) carry-over effects. Let us consider the latter property: What exactly does it mean? Does it mean that on average the effect of carry-over cancels out (as with the period effect)?

For the latter you are mistaken. A period effect only cancels out if you have it in your evaluation model. Otherwise it will be incorporated into the treatment effect and into the error term (at least partially) and and will affect your 90% confidence intervals.

The same applies to to carry over also.

But carry-over evaluation in cross-over designs, if any, suffer from another fact. It is usually modeled as so called "first order" carry-over or "simple carry over". The main feature of such modeling is that the carry-over effect lasts only from the treatment given in the previous period.
This model is extremely oversimplified and not in accordance with pharmacokinetic and pharmacodynamic conceptions. (see Steven Senn, Cross-over Trials in Clinical Research, John Wiley & Sons, Chichester, chapter 10)

Therefore Senn considered this model as obsolete.
Thus the advantage of Williams designs, which are optimal with respect to such an carry-over model, vanish as you by yourself noticed.

Hope this helps.