Bioequivalence and Bioavailability Forum

Hi Vaibhav,

» For modifed release formulation (Bioequivalence of partial AUC) […]
» Comparisons of HaVD and MDT can be evaluated by nonparametric calculations
» Which part of the curve bioequivalence needs to be established, upper or lower?
» Is it acceptable approach for EU submission.

Since you posted in the category Regulatives / Guidelines and asked specifically for a European submission:

• Both PK metrics have nothing to do with the partial AUCs mentioned in the EMA’s guideline as an option to waive the MD study. The cut-off time is τ/2, unless another one is justified. Hence, in the simple case pAUC_0–τ/2 and pAUC_τ/2–τ.
  
• European assessors are allergic to nonparametric statistics.
  Therefore, t_max (which is ordinal) was removed from the BE-GL in 2010.
  
• For none (see the funny figure). HaVD (Half Value Duration, aka Peak Occupancy Time 50 ‘POT-50’)¹ is the time between intersections of a horizontal line at 50% of C_max with the profile.
  You need to interpolate concentrations, where the method of interpolation should be consistent with the chosen calculation of AUC.
  • If you calculate the AUC by the linear trapezoidal rule (I hope you don’t), interpolate by \(\small{(1)}\). $$\small{\widehat{C}=\frac{C_1+C_2}{2}\tag{1}}$$
  • If you employ the linear-up / logarithmic down rule (my recommendation), interpolate if \(\small{C_2\geq C_1}\) by \(\small{(1)}\) and if \(\small{C_2<C_1}\) by \(\small{(2)}\). $$\small{\widehat{C}=\frac{C_1+C_2}{\log_{e}\left(\frac{C_2}{C_1}\right)}\tag{2}}$$
  If there are multiple peaks, HaVD is the sum of sections.
  The calculation of MDT is trivial. However, if there are multiple peaks, MDT is undefined.
  Only formerly in Russia and currently in Kazakhstan yet another metric, the ‘Plateau Time’² t_75% (aka Peak Occupancy Time 75 ‘POT-75’) was/is required.³
  
• No, it is not acceptable. In 40 years I had only one case of any antibiotic where the primary metrics were ‘Occu­pancy Times’ (times where the concentrations ≥ numerous MICs). In this particular case AUC and C_max were only descriptive.

Personally I agree with the ‘Two Lászlós’ and think that these metrics are valuable indeed (though I don’t concur that nonparametrics are necessary). If you want to discuss these metrics, let me know and I will move this thread to the category NCA / Sham.

PS: Why did you upload the figure seven times in the lousy JPG-format (see there)? I removed them and uploaded an 8 bit PNG including the legend instead.
PPS: A salutation in posts is polite and never hurts.

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1. Endrényi L, Tóthfalusi L. Metrics for the Evaluation of Bioequivalence of Modified-Release Formulations. AAPS J. 2012; 14(4): 813–9. doi:10.1208/s12248-012-9396-8. Free full text.
   
2. Steinijans VW, Sauter R, Diletti E. Shape Analysis in Single- and Multiple-Dose Studies of Modified Release Pro­ducts. In: Blume HH, Midha KK (ed’s). Bio-International 2. Stuttgart: medpharm Scientific Publishers; 1995. pp. 193–206.
   
3. Shohin IE, Roshdestvenskij DA, Medvedev VYu, Komarow TN, Grebenkin DYu. Russia, Belarus & Ka­sakh­stan. In: Kanfer I. (ed). Bioequivalence Requirements in Various Global Jurisdictions. Cham: Springer; 2017. pp. 199–227.