Bioequivalence and Bioavailability Forum

Hi randombadger!

❝ For higher order studies (i.e. 3x3, 4x4 etc) I understand that the PKWP want us to make comparisons using a data subset (e.g. T2 vs T1) excluding the data from the treatments that are not relevant for the comparison in question (e.g. T1).

Reading in between the lines it’s clear that EMA likes Williams’ designs (e.g., 6×3) – not Latin squares (3×3). See the GL p22: “[…] (3 treatment, 3 period, 6 sequence design).”

No recoding should be done. See the complied Q&A-document from last year’s joint EGA/EMA workshop:

Q In the case of a 3-arm study with two reference products what does “excluding the data” mean?
If the data from one (or more) treatment arm(s) is (are) removed from ANOVA (eg, removing the data for a USA comparator product) and thus effectively considering it as a two arm study then the true sequences and periods are modified.
Answer
In studies with more than two treatment arms (eg, a three period study including two references, one from the EU and another from the USA; or a four period study including test and reference in fed and fasted conditions; or 2 test products and one reference provided one of the test products is the final ‘to be marketed’ formulation), the analysis for each comparison should be conducted excluding the data from the treatments that are not relevant to the comparison in question. However, the treatment, groups, sequences and periods should have their original values maintained in the analysis, and not have the values modified. For example an observation made in period 3 should still be coded as period 3, not have the period changed to “2” because the results for that subject in one of the earlier periods has now be removed.

David Brown (MHRA) gave the following example:

If we exclude the (irrelevant) data from the US test product,
we get this data-set
SUB SEQ PRD FRM
1   1   1   T
1   1   2   A
2   3   1   A
2   3   2   T
3   6   2   A
3   6   3   T
4   2   1   T etc.
which can be analysed as usual in PROC GLM with terms for
sequence, subject (sequence), period and formulation. (© Crown copyright 2005)

❝ So, the analysis done is basically a 2-way crossover study for each treatment comparison.

Not really. I would call it three-way with missing observations. Not sure whether this approach (essentially ignoring part of the story) is valid. The jury is out; no verdict^* yet (search the forum).

Let’s look at an example (Chow & Liu, Table 10.3.13; 6×3 Williams’ design, analysis on log-data):
Sequence Subject Period  AUC Formulation
RT2T1       1       1   5.68     R
RT2T1       1       2   4.21     T2
RT2T1       1       3   6.83     T1
RT2T1       2       1   3.60     R
RT2T1       2       2   5.01     T2
RT2T1       2       3   5.78     T1
T1RT2       3       1   3.55     T1
T1RT2       3       2   5.07     R
T1RT2       3       3   4.49     T2
T1RT2       4       1   7.31     T1
T1RT2       4       2   7.42     R
T1RT2       4       3   7.86     T2
T2T1R       5       1   6.59     T2
T2T1R       5       2   7.72     T1
T2T1R       5       3   7.26     R
T2T1R       6       1   9.68     T2
T2T1R       6       2   8.91     T1
T2T1R       6       3   9.04     R
T1T2R       7       1   9.68     T1
T1T2R       7       2   8.91     T2
T1T2R       7       3   9.04     R
T1T2R       8       1   4.63     T1
T1T2R       8       2   7.23     T2
T1T2R       8       3   5.06     R
T2RT1       9       1   7.25     T2
T2RT1       9       2   7.88     R
T2RT1       9       3   9.02     T1
T2RT1      10       1   5.00     T2
T2RT1      10       2   7.84     R
T2RT1      10       3   7.79     T1
RT1T2      11       1   4.63     R
RT1T2      11       2   6.77     T1
RT1T2      11       3   5.72     T2
RT1T2      12       1   3.87     R
RT1T2      12       2   7.62     T1
RT1T2      12       3   6.74     T2

• Complete model (all effects fixed: Sequence+Subject(Sequence)+Period+Formulation)
  T1/R: 113.31% [101.35% – 126.67%] CI width 25.32%
T2/R: 104.38% [ 93.37% – 116.69%] CI width 23.32%
CV:   15.93%
GLSM: 6.08 (R), 6.89 (T1), 6.35 (T2)
  
• Formulation T2 or T1 excluded
  T1/R: 113.31% [103.44% – 124.12%] CI width 20.68%
CV:   12.23%
GLSM: 6.08 (R), 6.89 (T1)
T2/R: 104.38% [ 90.51% – 120.37%] CI width 29.87%
CV:   19.23%
GLSM: 6.08 (R), 6.35 (T2)

If I take the full model as the ‘Gold Standard’ results according to EMA’s method are liberal for T1 (passes, while BE in the full model fails) and conservative for T2.

That’s why I said »EMA is a serious risk to public health!« last year. Wasn’t diplomatic, I know.

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^* Innocent = conservative, guilty = liberal.