Researcher101
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Egypt,
2020-10-10 19:27
(593 d 00:10 ago)

Posting: # 21987
Views: 1,497
 

 Randomization Sequences in fully replicate williams’ design [General Sta­tis­tics]

Dear All, I wanna know what exactly the randomization sequences if I will go for fully replicate ( Four periods) with three arms/treatments ( T1, T2, R)

If i'm going for a four periods of two treatments I will go for TRTR and RTRT so if there are 3 treatments, How many and what are the sequences?


Edit: Category changed; see also this post #1[Helmut]
Helmut
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Vienna, Austria,
2020-10-10 20:06
(592 d 23:31 ago)

@ Researcher101
Posting: # 21988
Views: 1,297
 

 Tricky

Hi Researcher101,

» Dear All, I wanna know what exactly the randomization sequences if I will go for fully replicate ( Four periods) with three arms/treatments ( T1, T2, R)

You need four sequences.

\(\small{\begin{array}{ccccc}
\hline
& p_1 & p_2 & p_3 & p_4 \\
\hline
s_1 & \text{T}_1 & \text{R} & \text{T}_2 & \text{R}\\
s_2 & \text{R} & \text{T}_1 & \text{R} & \text{T}_2\\
s_3 & \text{T}_2 & \text{R} & \text{R} & \text{T}_1\\
s_4 & \text{R} & \text{T}_2 & \text{T}_1 & \text{R}\\
\hline
\end{array}}\)


For the evaluation exclude either \(\small{\text{T}_2}\) or \(\small{\text{T}_1}\) to obtain two partial replicate designs with missing (\(\small{\bullet}\)) observations.

\(\small{\begin{array}{ccccc}
\hline
& p_1 & p_2 & p_3 & p_4 \\
\hline
s_1 & \text{T}_1 & \text{R} & \bullet & \text{R}\\
s_2 & \text{R} & \text{T}_1 & \text{R} & \bullet\\
s_3 & \bullet & \text{R} & \text{R} & \text{T}_1\\
s_4 & \text{R} & \bullet & \text{T}_1 & \text{R}\\
\hline
\end{array}}\)

and

\(\small{\begin{array}{ccccc}
\hline
& p_1 & p_2 & p_3 & p_4 \\
\hline
s_1 & \bullet & \text{R} & \text{T}_2 & \text{R}\\
s_2 & \text{R} & \bullet & \text{R} & \text{T}_2\\
s_3 & \text{T}_2 & \text{R} & \text{R} & \bullet\\
s_4 & \text{R} & \text{T}_2 & \bullet & \text{R}\\
\hline
\end{array}}\)


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ElMaestro
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Denmark,
2020-10-10 20:53
(592 d 22:43 ago)

@ Helmut
Posting: # 21989
Views: 1,263
 

 Tricky

Hi,

wise words from Helmut.

» For the evaluation exclude either \(\small{\text{T}_2}\) or \(\small{\text{T}_1}\) to obtain two partial replicate designs with missing (\(\small{\bullet}\)) observations (...)

...and depending on the context this could be a case where alpha adjustment is appropriate (if you are claiming BE if either T1 or T2 show BE, but the devil is in the details as they say).

Pass or fail!
ElMaestro
Helmut
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Vienna, Austria,
2020-10-10 21:18
(592 d 22:18 ago)

@ ElMaestro
Posting: # 21990
Views: 1,258
 

 Tricky

Hi ElMaestro,

» ...and depending on the context this could be a case where alpha adjustment is appropriate (if you are claiming BE if either T1 or T2 show BE, but the devil is in the details as they say).

Heck, you were faster than I!
I just wanted to edit my post to add my usual question: What do you want to achieve?
@ Researcher101: See this presentation (slides 22–23).

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Researcher101
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Egypt,
2020-10-11 09:07
(592 d 10:29 ago)

@ Helmut
Posting: # 21991
Views: 1,236
 

 Tricky

Thank you so much, but what if 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


Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post #5[Helmut]
Helmut
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2020-10-11 10:57
(592 d 08:40 ago)

@ Researcher101
Posting: # 21992
Views: 1,247
 

 Very tricky

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.

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