Bioequivalence and Bioavailability Forum • Williams design 3-way

Williams design 3-way [Design Issues]

posted by Brus – Spain, 2021-06-09 18:48 (1216 d 18:30 ago) – Posting: # 22398
Views: 12,939

Dear Helmut,

I have a question on this topic that you mentioned a long time ago:

❝ A 6×3 design is needed in order to ‘extract’ two 2×2 tables, which are also balanced. Although the full 6×3 table will be used in the analysis of AUC and C_max, you will need these 2×2s for the nonparametric analysis of t_max (unfortunately there’s no confidence interval based nonparametric method available for more than two formulations/periods). The asterisks * denote pseudo-sequences and pseudo-periods, e.g. P1* means only that the treatment was given in a period prior to P2* – irrespective of the true study period:

❝ +----+------------+ --> +----+--------+ and +----+--------+

❝ | | P1 P2 P3 | | | P1* P2*| | | P1* P2*|

❝ +----+------------+ +----+--------+ +----+--------+

❝ | S1 | T R1 R2 | | S1*| T R1 | | S1*| T R2 |

❝ | S2 | R1 R2 T | | S2*| R1 T | | S2*| R2 T |

❝ | S3 | R2 T R1 | | S1*| T R1 | | S2*| R2 T |

❝ | S4 | T R2 R1 | | S1*| T R1 | | S1*| T R2 |

❝ | S5 | R1 T R2 | | S2*| R1 T | | S1*| T R2 |

❝ | S6 | R2 R1 T | | S2*| R1 T | | S2*| R2 T |

❝ +----+------------+ +----+--------+ +----+--------+


❝                             ^   balanced          ^   balanced

❝ A common mistake is to design the study as a set of 3×3 latin squares, which will lead (especially if the sample size is small and in the case of drop outs) to extremely imbalanced data sets:

❝ +----+------------+ --> +----+--------+ and +----+--------+

❝ | | P1 P2 P3 | | | P1* P2*| | | P1* P2*|

❝ +----+------------+ +----+--------+ +----+--------+

❝ | S1 | T R1 R2 | | S1*| T R1 | | S1*| T R2 |

❝ | S2 | R1 R2 T | | S2*| R1 T | | S2*| R2 T |

❝ | S3 | R2 T R1 | | S1*| T R1 | | S2*| R2 T |

❝ +----+------------+ +----+--------+ +----+--------+


❝                             ^ imbalanced          ^ imbalanced

According to what you said, 6 sequences had to be done with a 3-way study to get balanced sequences on the two 2x2 tablets. But, with following approach, balanced sequences would also be achieved:

ABC
BAC
CAB
CBA

It's possible? What problems would it have? It is not williams square design, right?

Best regards,

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-wayBrus 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-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