Bioequivalence and Bioavailability Forum

Dear All,

from occasion of a recent post I would like to discuss again the question of designs for 3-treatments 3-periods.
Here in the forum it was repeatedly advocated that only a design with the full six sequences (let's letter!)
  ABC  Latin square 1
  BCA
  CAB
  -----
  ACB  Latin square 2
  BAC
  CBA
should be used.

Of course this design is balanced with respect to the conditions

1. Each formulation occurs only once with each subject.
   
2. Each formulation occurs the same number of times in each period.
   
3. The number of subjects who receive formulation i in some period followed by formulation j in the next period is the same for all i # j

as Helmut has stated here.

But I cannot understand why this is desirable, especially the last condition.

As far as I have understood until now: The balance under 3. is only necessary if one is willing to adopt the view of first-order (simple) carry-over and incorporate this effect also in the analysis model. Only in that case the full 6-sequence design has its merits.

Following the view of SENN¹⁾ that the model of simple carry-over is obsolet and not testing for it, especially in case of BE studies with appropriate wash-out (which view has found its way into the new EMEA DRAFT, one of the rare things I appreciate), what are then the benefits of using balance with respect to condition 1.-3., the so called Williams designs?

And why should regulators insist on it?

Has anybody factual experiences that studies were rejected if only balanced designs with respect to the conditions 1. and 2. (Latin square designs) were use?

BTW which guidance state the necessity of the full 3x3x6 (treatment/period/sequence) design?

¹⁾ S. Senn, Cross-over Trials in Clinical Research
John Wiley & Sons, Chichester, chapter 10