Bioequivalence and Bioavailability Forum

Dear Frieda!

❝ […] The combination A + B is hereafter called the test T and A + placebo the reference R.

I kept this line as a reference.
PK interaction studies are similar to BE studies, but not equal. Let's start with the fundamental pharmacokinetic relationship
  f_a x D = AUC x CL
or, rewritten
         f_a × D
  AUC = ————
          CL
In BE testing we are relying on two assumptions (unfortunatelly many people are not aware of #1):
  (1) CL remains constant during the study
  (2) D is the same (no potency correction)

For two formulations (T, R) we have
  AUC_T   f_T × D_T × CL_R
  ——— = ————————
  AUC_R   f_R × D_R ×CL_T
applying assumptions (1) and (2) we get
       AUC_T
  f_rel = ———
       AUC_R

In a PK interaction study assumption #1 (constant clearances) may not hold!
Contrary to BE studies, where the AUC-ratio is only a measure of the absorption characteristics of formulations, the concomitant treatment of drug B may influence the clearance of drug A (AUC therefore is a composite parameter consiting of extent of absorption and clearance). See the pioneering paper published in 1994 by Schall et al.^[1] and the chapter ‘Analysis of pharmacokinetic interactions’ in Hauschke et al. (2007).^[2]
If the CI falls with the commonly applied acceptance range (AR) ‘lack of interaction’ is likely (because a ratio close to unity would imply either no influence of T on f_R and CL_R or an influence on both f_R and CL_R in opposite directions to the same degree – which is considered improbable).
The authors suggest in any case no further analyses, but to include such an possible influence on the clearance in the wording of the conclusion, like
  ‘the amount of drug A available in the systemic circulation is not affected
  by concomitant administration of drug B’
rather than
  ‘drug B does not affect the absorption of drug A’.
If an influence is observed (CI not within AR), the authors suggest a second step in the analysis, namely
  (1) the elimination half life of drug A,
  (2) the ratio AUC/t_½ (or AUC × k_el).
The second metric was also proposed by Abdallah (1998)^[3] in another context (to ‘reduce variability’ of HVDs).

This is only an entry point from my side; though you didn’t see residual concentrations after the washout, some residual effects of T on the PK cannot be excluded (higher concentration of the reference in the TR group - this was also ElMaestro’s idea in his post). IMHO I would go with the second part of the analysis notwithstanding you have already shown a CI within the AR. Anyhow, from both clinical and regulatory points of view for a combination product any demonstrated PK interaction will go into the labeling (US) / SmPC (EU).
Must sleep over it…

1. Schall R, Hundt HKL and HG Luus
   Pharmacokinetic characteristics for extent of absorption and clearance in drug/drug interaction studies
   Int J Clin Pharmacol Ther 32/12, 633-637 (1994)
   
2. Hauschke D, Steinijans V and I Pigeot
   Bioequivalence Studies in Drug Development
   John Wiley, Chichester, pp 175-203 (2007)
   
3. HY Abdallah
   An Area Correction Method To Reduce Intrasubject Variability In Bioequivalence Studies
   J Pharm Pharmaceut Sci 1(2), 60-65 (1998)