Bioequivalence and Bioavailability Forum

Hi ElMaestro & all,

let’s consider the basics. We have a set of two equations

1. AUC_T = ƒ_T·D_T/CL_T
   
2. AUC_R = ƒ_R·D_R/CL_R

which consist of eight variables. We are interested to compare the bioavailabilities or ƒ_T/ƒ_R (not the individual values ƒ_T and ƒ_R), reducing the variables to seven. We have AUC_T and AUC_R. Can this set solved for ƒ_T/ƒ_R? Obviously not. We need two assumptions.

1. CL_T = CL_R
   
2. D_T = D_R

Only then we can cross them out in the set and walk away happily with ƒ_T/ƒ_R = AUC_T/AUC_R.

The first assumption is not that bad. Clearance is a property of the drug, not the formulation. If we face variability of inter-occasion clearances it increases the residual error. Nasty for HVDs but no big deal (increased sample size, patient’s risk not affected).

The second one is much more tricky. As you rightly stated BE by definition means administration of the same molar dose. Here trouble starts. Reference is made to the labeled content. OK, we try to find test and reference batches which are as close as possible. Stupid enough the analytical assay is not free of error.* That’s why nobody with a clear state of mind estimates the sample size with a T/R of 100% even if this comes out in the analyses. To complicate things for generics the method is only validated for the test product. You can only hope that it gives unbiased results for the reference as well. Asking the originator for a CoA is not option. Might be easy for a simple IR product but already difficult for some MR products and can get really nasty for creams and ointments…

Acc. to the Canadian guidances (1992) both analyses (original and adjusted for measured content) had to be presented. No idea what happened if a study passed one and failed the other. Acc. to the WHO’s draft (1995) it was possible to adjust if Δ >5% and stated in the protocol. Only one analysis decisive.
Let’s explore your example. CI 77–108% (say for true D_T = D_R = 100), combinations of Δ 5% (adjustment not allowed) or slightly above (closer batches can’t be found). The Δ is either split or entirely on one side. This gives:

 Δ    adj.   DT       DR       90% CI         
──────────────────────────────────────────────
0.00   no  100.00  100.00  77.00  108.00  fail
──────────────────────────────────────────────
5.00   no   97.50  102.50  77.00  108.00  fail
5.00   no  102.50   97.50  77.00  108.00  fail
5.00   no   95.00  100.00  77.00  108.00  fail
5.00   no  100.00  105.00  77.00  108.00  fail
5.00   no   95.00  100.00  77.00  108.00  fail
──────────────────────────────────────────────
5.01  yes   97.50  102.51  80.96  113.55  pass
5.01  yes  102.51   97.50  73.24  102.72  fail
5.01  yes   94.99  100.00  81.06  113.70  pass
5.01  yes  100.00  105.01  80.86  113.41  pass
5.01  yes   94.99  100.00  81.06  113.70  pass

If we adjust – with one exception – the test passes. When you ask for the relevance, that’s a philosophical question. I think that not adjusting is conservative. On the other hand, adjusting might be more realistic keeping assumption #2 in mind.
Of course, the 5% limit is arbitrary. Is there any upper limit? For most products the release-spec’s are ±10%. Then is would be possible to adjust for a 20% difference. That would match already Detlew’s example… Don’t know where to draw the line.

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• BTW, how representative is the mean of 6 or 12 units of a biobatch of 500,000? Content uniformity? Ha! When I started to explained the procedure “Take a blister, analyze 6 capsules,…” to a friend of mine (chemist in the cement industry) he interrupted me cause he was dying of laughter. Since the 1950s they have procedures to draw representative samples from a 5,000 tons batch. Start with about ~500 (!) from different locations, mixing, splitting, to end up with ~30. Books are written about that.
  From this perspective one could criticize biostudies in similar way (“Take a blister…”).