Bioequivalence and Bioavailability Forum • Williams design 3-way

Williams design 3-way [Design Issues]

posted by Helmut – Vienna, Austria, 2021-06-10 22:14 (1211 d 12:57 ago) – Posting: # 22405
Views: 12,297

Hi vezz,

❝ ❝ Unlikely. If you have true period effects, your estimates will be biased and you have no means to correct it.

❝

❝ This is not to support the design proposed by Brus, but it seems to me that with those sequences we should still be able to obtain unbiased estimates of treatment effect also in presence of a period effect (based on the model suggested by the EMA Guideline on BE).

Nope. Let’s consider a simple example. A = B = C = 1, no carryover, additive model.

Latin Square
No period effects
p1 p2 p3 s1 A=1 B=1 C=1 s2 B=1 C=1 A=1 s3 C=1 A=1 B=1 A/C = (s1p1+s2p3+s3p2)/(s1p3+s2p2+s3p1)=(1+1+1)/(1+1+1) = 1 B/C = (s1p2+s2p1+s3p3)/(s1p3+s2p2+s3p1)=(1+1+1)/(1+1+1) = 1
Period effects (p2 = p1–0.5, p3 = p2+1)
p1 p2 p3 s1 A=1 B=0.5 C=1.5 s2 B=1 C=0.5 A=1.5 s3 C=1 A=0.5 B=1.5 A/C = (s1p1+s2p3+s3p2)/(s1p3+s2p2+s3p1)=(1+1.5+0.5)/(1.5+0.5+1) = 1 B/C = (s1p2+s2p1+s3p3)/(s1p3+s2p2+s3p1)=(0.5+1+1.5)/(1.5+0.5+1) = 1
Brus’ design
No period effects
p1 p2 p3 s1 A=1 B=1 C=1 s2 B=1 A=1 C=1 s3 C=1 A=1 B=1 s4 C=1 B=1 A=1 A/C = (s1p1+s2p2+s3p2+s4p3)/(s1p3+s2p3+s3p1+s4p1)=(1+1+1+1)/(1+1+1+1) = 1 B/C = (s1p2+s2p1+s3p3+s4p2)/(s1p3+s2p3+s3p1+s4p1)=(1+1+1+1)/(1+1+1+1) = 1
Period effects (p2 = p1–0.5, p3 = p2+1)
p1 p2 p3 s1 A=1 B=0.5 C=1.5 s2 B=1 A=0.5 C=1.5 s3 C=1 A=0.5 B=1.5 s4 C=1 B=0.5 A=1.5 A/C = (s1p1+s2p2+s3p2+s4p3)/(s1p3+s2p3+s3p1+s4p1)=(1+0.5+0.5+1.5)/(1.5+1.5+1+1) = 0.7 B/C = (s1p2+s2p1+s3p3+s4p2)/(s1p3+s2p3+s3p1+s4p1)=(0.5+1+1.5+0.5)/(1.5+1.5+1+1) = 0.7

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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 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
  - 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
  - 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-way Helmut 2021-06-10 15:03
        
        Williams design 3-way vezz 2021-06-10 17:23
        
        Williams design 3-wayHelmut 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