## Very tricky [General Sta­tis­tics]

Hi Researcher101,

» […] I wanna dose the participant T1 twice, T2 twice, R Twice as the drug is highly variable?
» The main goal is to check which formula ( T1 or T2 ) is more comparable to the reference drug

OK, you are planning a pilot study. With six periods you are draining volunteers (hope your bioanalytical method can deal with small sample volumes). Dropouts are also an issue. I have never seen a study with more than five periods so far.
I tried to find a balanced incomplete block design (with less than six periods) to no avail… Since you mentioned a Williams’ design in your original post: No idea.

One option would be a Latin Square:

$$\small{\begin{array}{ccccccc} \hline & p_1 & p_2 & p_3 & p_4 & p_5 & p_6\\ \hline s_1 & \text{T}_1 & \text{T}_1 & \text{T}_2 & \text{T}_2 & \text{R} & \text{R}\\ s_2 & \text{T}_1 & \text{T}_2 & \text{T}_2 & \text{R} & \text{R} & \text{T}_1\\ s_3 & \text{T}_2 & \text{T}_2 & \text{R} & \text{R} & \text{T}_1 & \text{T}_1\\ s_4 & \text{T}_2 & \text{R} & \text{R} & \text{T}_1 & \text{T}_1 & \text{T}_2\\ s_5 & \text{R} & \text{R} & \text{T}_1 & \text{T}_1 & \text{T}_2 & \text{T}_2\\ s_6 & \text{R} & \text{T}_1 & \text{T}_1 & \text{T}_2 & \text{T}_2 & \text{R}\\ \hline \end{array}}$$

Exclusions as usual:

$$\small{\begin{array}{ccccccc} \hline & p_1 & p_2 & p_3 & p_4 & p_5 & p_6\\ \hline s_1 & \text{T}_1 & \text{T}_1 & \bullet & \bullet & \text{R} & \text{R}\\ s_2 & \text{T}_1 & \bullet & \bullet & \text{R} & \text{R} & \text{T}_1\\ s_3 & \bullet & \bullet & \text{R} & \text{R} & \text{T}_1 & \text{T}_1\\ s_4 & \bullet & \text{R} & \text{R} & \text{T}_1 & \text{T}_1 & \bullet\\ s_5 & \text{R} & \text{R} & \text{T}_1 & \text{T}_1 & \bullet & \bullet\\ s_6 & \text{R} & \text{T}_1 & \text{T}_1 & \bullet & \bullet & \text{R}\\ \hline \end{array}}$$
$$\small{\begin{array}{ccccccc} \hline & p_1 & p_2 & p_3 & p_4 & p_5 & p_6\\ \hline s_1 & \bullet & \bullet & \text{T}_2 & \text{T}_2 & \text{R} & \text{R}\\ s_2 & \bullet & \text{T}_2 & \text{T}_2 & \text{R} & \text{R} & \bullet\\ s_3 & \text{T}_2 & \text{T}_2 & \text{R} & \text{R} & \bullet & \bullet\\ s_4 & \text{T}_2 & \text{R} & \text{R} & \bullet & \bullet & \text{T}_2\\ s_5 & \text{R} & \text{R} & \bullet & \bullet & \text{T}_2 & \text{T}_2\\ s_6 & \text{R} & \bullet & \bullet & \text{T}_2 & \text{T}_2 & \text{R}\\ \hline \end{array}}$$

Select the test with a PE closer to 100% (i.e., $$\small{\textrm{min}\left\{\left|\log_{e}\text{T}_1/\text{R} \right|,\left|\log_{e}\text{T}_2/\text{R} \right|\right\}}$$) for the pivotal study.
If PEs are similar – don’t ask me what “similar” is – opt for the one with lower CVwT.

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
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