Bioequivalence and Bioavailability Forum

Dear Oiinkie!

❝ First, I would like to compliment HS and all contributors with the BEBAC site and forum.

Thanks for the compliments!

❝ […] According to the protocol, BLQ values should be set to zero (indeed, from a mathematical perspective it would be much nicer to log-linearly extrapolate to t=72 h by using lambda z).

I would also prefer the latter.

❝ The CRO omitted t=72 h values for this subject and calculated AUC_(0-48) for this subject (in fact, according to the CRO, WinNonlin treated the data as such).

Right, this is the default definition of AUCt in WinNonlin.

❝ I kept the 72 h time point in, set it to zero and calculated AUC_(0-72) (i.e. an underestimation of “real” AUC_(0-72)). In my opinion, as the samples at t=72 h were actually drawn and concentrations were not zero but BLQ (i.e. “measurable” but not “quantifiable”, if you get my point), I would opt to keep the values at t=72 h in for this subject (also to have a straight comparison from a statistical perspective).

Well, as hard-core pharmacokineticists use to say: “There is only one concentration after a dose which we are certain that it does not exist: zero.” If you have stated to set all BLQ values to zero in the protocol, the CRO should have used Pharsight’s invention ‘AUCall’ which adds a triangle from the last time point where C > LLOQ to the next sampling time point.
See this post and followings.

❝ Indeed, the definition of AUC_(0-t) (i.e. “area under the plasma concentration curve from administration to last observed concentration at t”) can be explained in different ways, but I truly think that this time point has to be kept in the analysis.

Right. In your case the subject’s 72 h values were BLQ after both formulations. The ratio of AUC₄₈ will be unbiased (IR formulations = no flip-flop PK!). CV_inter will increase – but not affecting the BE assessment. It’s getting nasty if C₇₂ is BLQ after one treatment only. If we compare AUC_t the ratio (e.g., AUC₄₈/AUC₇₂) will be biased away from 100%. Apples-and-oranges-statistics. At least members of the PK group were not concerned about this issue, claiming that the estimate will be conservative (i.e., shifting the point estimate away from 100% – increasing producer’s risk). I’m not sure whether this is true. IMHO the shift holds only for this particular subject’s ratio but may bias the study’s PE in any direction.

❝ What is your opinion on this issue? Would you omit or include t=72 for subject x in the AUC_(0-t) calculation?

I would use the estimated AUC₇₂. Some people set the first concentration after the last measurable one to BQL/2 and consecutive ones to zero. There are such methods available in Phoenix/WinNonlin – the (in)famous ‘BQL-rules’. IMHO this is arbitrary and would make sense only if t_z – t_z-1 = t_½.

Just a hint from PopPK: There are papers published comparing three methods – omitting BQLs, BQL/2, and C=0. If I recall it right: omitting gave the least bias and BQL/2 and C=0 performed almost equally worse. In the PopPK world most people nowadays set these values to BQL and use a one-sided (upper) truncated error (=censored) model for these values.

---

Equivalence Trials – Proving that apples are pears
by comparing the weight. Stephen Senn (2009)