## Williams design 3-way [Design Issues]

Hi Brus,

❝ ❝ That’s not balanced for carryover.

❝ Why?

Sorry (see below).

❝ Eeach formulation is administered once per subject, occurs the same number of times in each period, and any formulation is preceded equally often by each of the other formulations. In this way it is a balanced design.

So far, so good. But: In your design you have to assume equal period effects. Let’s count how many times the treatments are administered in each period.

   1 2 3 ──────── A  1 2 1 B  1 2 1 C  2 0 2

❝ What benefit does williams design bring?

It’s also balanced for period effects, which is really important.

    1 2 3 ───────── s1  A B C s2  A C B s3  B A C s4  B C A s5  C A B s6  C B A ───────── A   2 2 2 B   2 2 2 C   2 2 2

❝ ❝ What is your idea behind such a design?

❝ Make a balanced design with as few sequences as possible.

Got it.

❝ ❝ Actually a simple Latin Square (ABC|BCA|CAB) would do as well. If you want to make European assessors happy, opt for the 6-sequence Williams’ design.

❝ Will Simple Latin Square be accepted by EMA assessors?

Possible. Statistically nothing speaks against it. We don’t have carryover in the model and it’s balanced for period effects.

❝ Will my proposal design be accepted by EMA assessors?

Unlikely. If you have true period effects, your estimates will be biased and you have no means to correct it.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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