Bioequivalence and Bioavailability Forum

Dear all,

did you validate the software you are using to get PK metrics (by NCA)?

Recently I faced a question from a European agency (don’t want to be more specific). In 2000 (!) I cross-validated the software against the one I had written myself in the early eighties. The agency asked for cross-validation against “commercial software like WinNonlin”. First I thought that this would be an easy task, but it turned out to need detective-work. I’m only aware of the data sets by Sauter et al.¹, which I used already in cross-validating software for 2×2×2 crossover studies. The single dose data set contains the intervals used for estimation of λ_z, the observed and estimated C_z (AUC_0–∞ was estimated based on the latter),
Clicked some buttons, got exactly the same eliminations and – not even the AUC_0–tz matched in most cases… What?! I forgot that Sauter et al. used a method which was proposed by Schulz and Steinijans in 1991.² This method went down the drain and therefore, it is not implemented in any software I know. I figured out to set it up in PHX/WNL, but it was not that easy. Let’s have a look at an example (Subject 8, test):

 t    C  
 0  <0.06
 1   0.19
 2   1.27
 3   2.75
 4   3.23
 5   3.36
 6   3.29
 7   3.89
 8   3.25
10   2.73
12   2.12
14   1.53
16   1.21
18   0.95
20   0.68
22   0.54
24   0.42
28   0.19
36   0.15
40   0.10
44  <0.06
48  <0.06
60  <0.06
72  <0.06

λ_z was estimated in the interval 10–28 hours. Don’t ask me why. Reference data set = take what you get. Looks like this:

Let’s zoom into the last/lower range. The two methods which are implemented in all versions of WinNonlin:

1. Use all values (irrespective whether they are used in the estimation of λ_z or not), extrapolation based on the observed last concentration (0.1 mg/mL).
   
   
   
   AUC_0–tz 45.875 h×mg/L, AUC_0–∞ 46.574 h×mg/L.
   
   
2. Like 1. but extrapolation based on the estimated last concentration (0.04 mg/L).
   
   
   
   AUC_0–tz 45.875 h×mg/L, AUC_0–∞ 46.147 h×mg/L.

Sauter et al. reported AUC_0–tz 44.07 h×mg/L and AUC_0–∞ 45.58 h×mg/L. Why does not even the AUC_0–tz match? Simsalabim:

Starting with 28 hours all values are dropped from NCA. At 28 hours the measured concentration (2.78 mg/L) is replaced by its estimate (2.83 mg/L), which is also the last value for the trapezoidal rule.

Quoting the paper: “Subtle problems such as […] the AUC extrapolation to infinity in single-dose studies have been dealt with. As pointed out in the previous paper [Schulz and Steinijans 1991] there is this occasional ambiguity in estimating the terminal half-life and its effect on the extrapolated AUC. As, presumably, there is no definite answer to this problem, it is important to document all steps of analysis as it has been done in Tables 4a and 4b of this paper. This will facilitate independent verifications of results by third party such as quality assurance, licensees, reviewers of journals or health authorities.”

Lessons learned: Even if reference data are published, surprises may happen.

---

1. Sauter R, Steinijans VW, Diletti E, Böhm E, Schulz H-U. Presentation of results from bioequivalence studies. Int J Clin Pharm Ther Toxicol 1992;30(Suppl.1):S7–30.
   
2. Schulz H-U, Steinijans, VW. Striving for standards in bioequivalence assessment: a review. Int J Clin Pharm Ther Toxicol 1991;29(8):293–8.