Very tricky [General Sta­tis­tics]

posted by Helmut Homepage – Vienna, Austria, 2020-10-11 10:57 (47 d 11:01 ago) – Posting: # 21992
Views: 426

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:

    P1  P2  P3  P4  P5  P6
S1  T1  T1  T2  T2   R   R
S2  T1  T2  T2   R   R  T1
S3  T2  T2   R   R  T1  T1
S4  T2   R   R  T1  T1  T2
S5   R   R  T1  T1  T2  T2
S6   R  T1  T1  T2  T2   R

    P1  P2  P3  P4  P5  P6
S1  T1  T1   •   •   R   R
S2  T1   •   •   R   R  T1
S3   •   •   R   R  T1  T1
S4   •   R   R  T1  T1   •
S5   R   R  T1  T1   •   •
S6   R  T1  T1   •   •   R

    P1  P2  P3  P4  P5  P6
S1   •   •  T2  T2   R   R
S2   •  T2  T2   R   R   •
S3  T2  T2   R   R   •   •
S4  T2   R   R   •   •  T2
S5   R   R   •   •  T2  T2
S6   R   •   •  T2  T2   R


Select the test with a PE closer to 100% (i.e., \(\small{\textrm{min}\left\{\left|\log_{e}T_1/R \right|,\left|\log_{e}T_2/R \right|\right\}}\)) for the pivotal study.
If PEs are similar – don’t ask me what “similar” is – opt for the one with lower CVwT.

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