## Williams design 3-way [Design Issues]

❝ ❝ 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

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

Science Quotes

### Complete thread:

- Three-way crossover BABE Studies acfalcao 2007-09-16 22:34 [Design Issues]
- Three-way crossover example data set Helmut 2007-09-17 20:47
- Three-way crossover example data set acfalcao 2007-09-17 23:02
- Three-way crossover example data set Helmut 2007-09-18 12:47
- Three-way crossover (WinNonlin) Nirali 2007-09-21 06:49
- Three-way crossover (WinNonlin) Helmut 2007-09-21 13:04
- Three-way crossover (WinNonlin) Nirali 2007-09-25 08:05
- Three-way crossover (WinNonlin) Helmut 2007-09-25 13:15

- Three-way crossover (WinNonlin) Nirali 2007-09-25 08:05

- Three-way crossover (WinNonlin) Helmut 2007-09-21 13:04
- Three-way crossover example data set Irene_I 2018-06-07 11:09
- Three-way crossover example data set Helmut 2018-06-07 13:04
- Three-way crossover example data set Irene_I 2018-06-08 11:09
- Three-way crossover example data set Irene_I 2018-06-12 09:21
- Leave-One-Out (IBD) Helmut 2018-06-12 12:42
- Leave-One-Out (IBD) Irene_I 2018-06-13 05:02
- Impact of pooled variance (bias, CI) Helmut 2018-06-13 15:02

- carry (over?) d_labes 2018-06-13 15:31

- Leave-One-Out (IBD) Irene_I 2018-06-13 05:02

- Leave-One-Out (IBD) Helmut 2018-06-12 12:42

- Three-way crossover example data set Helmut 2018-06-07 13:04

- Three-way crossover (WinNonlin) Nirali 2007-09-21 06:49

- Three-way crossover example data set Helmut 2007-09-18 12:47
- Pseudo-periods ElAlumno 2019-03-14 23:40
- Pseudo-periods Helmut 2019-03-15 00:47
- Two‐at‐a‐Time analysis in R ElAlumno 2019-03-22 21:59
- fixed & mixed (dammit!) and a request to SASians Helmut 2019-03-23 01:03
- Pooled vs IBD T-R in SAS from non-SASian mittyri 2019-03-23 23:13
- Pooled vs IBD T-R in SAS from non-SASian Helmut 2019-03-23 23:36

- mixed in R mittyri 2019-03-23 23:50
- mixed in R (EMA B ≠ FDA) Helmut 2019-03-24 01:23

- Pooled vs IBD T-R in SAS from non-SASian mittyri 2019-03-23 23:13

- fixed & mixed (dammit!) and a request to SASians Helmut 2019-03-23 01:03

- Two‐at‐a‐Time analysis in R ElAlumno 2019-03-22 21:59

- Pseudo-periods Helmut 2019-03-15 00:47
- Williams design 3-way Brus 2021-06-09 16:48
- Williams design 3-way Helmut 2021-06-09 17:48
- Williams design 3-way Brus 2021-06-10 14:33
- Williams design 3-wayHelmut 2021-06-10 15:03
- Williams design 3-way vezz 2021-06-10 17:23
- Williams design 3-way Helmut 2021-06-10 20:14
- Williams design 3-way vezz 2021-06-11 09:11
- Williams design 3-way Brus 2021-06-11 12:19
- Williams design 3-way Relaxation 2021-06-11 12:42
- Period effects in general Helmut 2021-06-11 15:41
- Williams design 3-way vezz 2021-06-11 16:56

- Williams design 3-way vezz 2021-06-11 09:11

- Williams design 3-way Helmut 2021-06-10 20:14

- Williams design 3-way vezz 2021-06-10 17:23

- Williams design 3-wayHelmut 2021-06-10 15:03

- Williams design 3-way Brus 2021-06-10 14:33

- Williams design 3-way Helmut 2021-06-09 17:48

- Three-way crossover example data set acfalcao 2007-09-17 23:02

- Three-way crossover example data set Helmut 2007-09-17 20:47