Bioequivalence and Bioavailability Forum

Dear Detlew,

❝ IMHO this suggestion is an orouboros.

Oh dear, it is!

❝ Calculating the CV from the CI and using this CV to calculate the CI will give you always the CI used in the starting step. Regardless of the design used in both steps.

❝ As you has demonstrated with your calculations .

Shit. Not that easy. Second try with a simple example. My data:

sub per seq  trt   PK
 1   1  ACBD  A  1.0793
 1   2  ACBD  C  1.1324
 1   3  ACBD  B  0.9422
 1   4  ACBD  D  0.7828
 2   1  BADC  B  1.0005
 2   2  BADC  A  1.1138
 2   3  BADC  D  0.7245
 2   4  BADC  C  0.9690
 3   1  CDAB  C  0.8392
 3   2  CDAB  D  0.8110
 3   3  CDAB  A  1.1333
 3   4  CDAB  B  1.0058
 4   1  DBCA  D  0.7478
 4   2  DBCA  B  0.8006
 4   3  DBCA  C  1.1432
 4   4  DBCA  A  0.9911
 5   1  ACBD  A  1.4136
 5   2  ACBD  C  0.8082
 5   3  ACBD  B  1.3025
 5   4  ACBD  D  1.4506
 6   1  BADC  B  1.0167
 6   2  BADC  A  0.9470
 6   3  BADC  D  1.5021
 6   4  BADC  C  1.2398
 7   1  CDAB  C  1.3904
 7   2  CDAB  D  1.2809
 7   3  CDAB  A  1.3593
 7   4  CDAB  B  1.3605
 8   1  DBCA  D  1.0852
 8   2  DBCA  B  0.9390
 8   3  DBCA  C  1.2467
 8   4  DBCA  A  1.2721
 9   1  ACBD  A  1.3878
 9   2  ACBD  C  1.2703
 9   3  ACBD  B  1.5533
 9   4  ACBD  D  1.3324
10   1  BADC  B  1.1792
10   2  BADC  A  0.9035
10   3  BADC  D  1.1517
10   4  BADC  C  1.1225
11   1  CDAB  C  1.1025
11   2  CDAB  D  1.0596
11   3  CDAB  A  1.5024
11   4  CDAB  B  0.8432
12   1  DBCA  D  1.1236
12   2  DBCA  B  1.3696
12   3  DBCA  C  0.6106
12   4  DBCA  A  0.6973

Running the models gives in the comparisons vs A:

Test    Method        PE     90% CI     CVintra
 B   pooled ANOVA   96.62  83.41 111.91  21.45
     Two-at-a-Time  96.62  80.90 115.39  23.72
 C   pooled ANOVA   93.16  80.43 107.91  21.45
     Two-at-a-Time  93.16  82.48 105.23  16.15
 D   pooled ANOVA   93.79  80.97 108.64  21.45
     Two-at-a-Time  93.79  79.44 110.74  22.47

Say the CIs of the three comparisons are published but not the method. Two cases:

1. The analysis was performed by the pooled ANOVA.
   If we plug in the CIs of B/A, C/A, and D/A we get in all comparisons 21.45% for the pooled ANOVA and 20.06% for the Two-at-a-Time Principle (TaaTP).
   
2. The analysis was performed by the TaaTP.
   We get different results, namely for
   B/A: 26.05% and 24.35%
   C/A: 17.71% and 16.57%
   D/A: 24.32% and 22.73%

Now I think we have sumfink to work with. If we get identical results, it means that a pooled analysis was performed and the TaaTP otherwise.
What puzzles me is that in the latter case the calculated CVs don’t match the models’ (24.35↔23.72, 16.57↔16.15, 22.73↔22.47). Knapp vorbei ist auch daneben. Degrees of freedom?