Bioequivalence and Bioavailability Forum

Williams design 3-way [Design Issues]

posted by Relaxation  – Germany, 2021-06-11 14:42 (1043 d 13:22 ago) – Posting: # 22409
Views: 8,548

Hi Stefano.

I was a little bit hesitant to answer, as I am and likely will remain a noob in the statistical background. Maybe I also misunderstand your question, which is quite possible.
But there are a lot of people around here to correct the answer, if necessary, and its SOP-Friday...

I think I get your point, but I also think that the period effect is implemented above.
The numbers already include both as mean=µ+π = treatment + period effect.

As an example:
the term s2p2 above is not the treatment mean for A in sequence 2 and period 2 (=1), it is the observed mean and includes the effect of period 2 (1-0.5=0.5).

If we would like to split that up into more detail, when sxpy is the treatment only (defined by combination of sequence and period), we can add Py as the period effect for more clarity.
Then:
A-C = ((s1p1 + P1) + (s2p2 + P2) + (s3p2 + P2) + (s4p3 + P3))
- ((s1p3 + P3) + (s2p3 + P3) + (s3p1 + P1) + (s4p1 + P1)).
See, as in Helmuts post, the period effects are implemented. But in the discussed design (P1+P2+P2+P3 = -0.5) and (P3+P3+P1+P1 = 1) do not completely eliminate each other as they would in a Latin Square. Thus treatment difference is biased (to +0.5 or 3.5/5=0.7) and not easily corrected.

Now, lets both wait and see, whether I got it right .

Best regards,

Relaxation.

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-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-wayRelaxation 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