Bioequivalence and Bioavailability Forum

Dear beman!

❝ i try to generate sequences for a 5x5-crossover study including 12 subjects.

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❝ Using Wiliams-Desing i need 10 sequences, but i have only 12 subjects, so it is not possible to have a balanced design.

I’m traveling, so I’m referring to my (bad) memory. If I recall it correctly Jones & Kenward^* stated that it’s not possible to construct a fully variance balanced Williams’ design with five treatments. They give only an example of an ‘almost balanced one’. Can you post the sequences you have in mind and a reference?

❝ Do you have any idea how to solve the problem ? Using 4 or 5 sequences with the disadvantage of an unblanced design ? How can i minimize the disadvantage ?

It’s not a good idea to already start with an imbalanced design. Drop-outs will do that for you anyway. If ten sequences are enough (which I doubt) and you start the study with 12 (or 14) subjects it might well be that you are missing some sequences entirely. Might play havoc with the model (running out of degrees of free­dom). Give it a try: Fire up a random number generator and check whether the model collapses or not. Hint: TR|RT → TR (only 1 sequence left). Does it work or not?

What you could do is some variant of an incomplete block design (also saving periods). But these designs are less powerful.

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• Jones B and MG Kenward
  Design and Analysis of Cross-Over Trials
  Chapman & Hall/CRC, Boca Raton, Chapter 4 (2^nd ed. 2003)