Bioequivalence and Bioavailability Forum

Dear D. Labes!

❝ The study was long ago. So I don't remember exactly what was going on. But I have occasionally found that the variability of PTF was high if PTF was low. In a additive model this makes immediately sense:

❝    CV=sd/Mean

❝ is increasing if the mean is decreasing.

Sounds plausible. But only if the sd would stay constant. I would guess that the sd also decreases.
Remember the good old days of 'the flatter is better'?
Imagine two formulations (IR, MR) in steady state, AUC 2400. We get e.g.:
   Cmax  Cmin  %PTF
IR  100    10   90
MR   60    40   20
I would guess that the variability of %PTF of the MR is lower, despite the lower value itself. But this assumption depends mainly on the variability of C_min, which should be lower if moving upwards from the critical zone. The rest is silence (or the law of error propagation).

❝ BTW: For me it's questionable if a logarithmic transformation could and should be applied for this metric (also I do because of regulators).

Right. I had a conversation with Regulator XY,^* where he expressed also strong doubts about the distributional assumption. In our conversation we talked about C_max/AUC in SD. We assume both AUC and C_max follow lognormal - so what's the distribution of the ratio of two lognormal distributions? The same holds for %PTF (just see what happens if no accumulation occurs and C_min=0). On the other hand Martin (who is on the contrary to myself a professional statistician) told me that this is no problem. He talked about monotonous transformations, but a little bit too much beer was involved that evening...

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* Anonymized upon request; 2010-01-18 [Helmut]