Researcher101
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Egypt,
2020-10-10 19:27
(17 d 15:59 ago)

Posting: # 21987
Views: 383
 

 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
(17 d 15:20 ago)

@ Researcher101
Posting: # 21988
Views: 364
 

 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; in your case

    P1  P2  P3  P4
S1  T1   R  T2   R
S2   R  T1   R  T2
S3  T2   R   R  T1
S4   R  T2  T1   R

For the evaluation exclude either T2 or T1 to obtain two partial replicate designs with missing () observations:

    P1  P2  P3  P4
S1  T1   R   •   R
S2   R  T1   R   •
S3   •   R   R  T1
S4   R   •  T1   R

    P1  P2  P3  P4
S1  •    R  T2   R
S2   R   •   R  T2
S3  T2   R   R   •
S4   R  T2   •   R


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Helmut Schütz
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ElMaestro
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Belgium?,
2020-10-10 20:53
(17 d 14:33 ago)

@ Helmut
Posting: # 21989
Views: 346
 

 Tricky

Hi,

wise words from Helmut.

» For the evaluation exclude either T2 or T1 to obtain two partial replicate designs with missing () 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).

I could be wrong, but...

Best regards,
ElMaestro

No, of course you do not need to audit your CRO if it was inspected in 1968 by the agency of Crabongostan.
Helmut
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2020-10-10 21:18
(17 d 14:08 ago)

@ ElMaestro
Posting: # 21990
Views: 341
 

 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
(17 d 02:18 ago)

@ Helmut
Posting: # 21991
Views: 322
 

 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
(17 d 00:29 ago)

@ Researcher101
Posting: # 21992
Views: 315
 

 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:

    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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