Bioequivalence and Bioavailability Forum

Hi Ratnakar,

I think that your approach is not optimal, and the sponsor’s one is simply wrong. Let’s start with the sponsor’s. If a concentration was measured at 74 hours one cannot simply shift it to 72 hours (the “as-if” approach) ⇒ AUC₇₂ will be biased. Guidelines require the actual time, not the scheduled one.

Your approach is better, but biased as well. Imagine that F=100% and t_last after reference was 72 hours and after test 74 hours. Naturally AUC₇₄ (apples) > AUC₇₂ (oranges). The apples-to-oranges ratio will be >1 and you get a positive bias for F. It is a weak argument that due to randomization this should happen equally often to T and R (~similar number of apples and oranges in the fruits’ basket) and therefore means out. Why not calculate AUC₇₂ for both? In Phoenix/WinNonlin request a partial AUC (Start Time 0, End Time 72). C₇₂ will be lin/log-interpolated between the timepoint preceeding t_last and t_last.
Example: t_½,abs 1 hour, t_½,el 36 hours, F 90%, lin-up/log-down trapezoidal rule.
  t          R       T
 0.00       0.00    0.00
 0.50      28.33   25.50
 1.00      48.09   43.28
 2.00      71.22   64.10
 3.00      81.89   73.70
 4.00      86.34   77.70
 5.50      87.74   78.97
 7.50      86.00   77.40
10.50      81.63   73.46
14.50      75.64   68.07
20.00      68.04   61.24
27.50      58.89   53.00
38.00      48.11   43.30
52.25      36.57   32.91
72.00      25.00    NA
74.00       NA     21.65
AUC52.25 3142.42 2831.29
AUC72    3744.03   NA
AUC74       NA   3416.11
F at 52.52 hours is 90.10% (bias +0.11%). If one uses AUC_last for both formulations (your method) one gets 91.24% (bias +1.38%). The sponsor’s “method” of shifting 21.65 measured at 74 hours forward to 72 hours would give 3362.33 (bias –0.22%). The interpolated concentration of test at 72 hours is 22.50 (note: 22.50/25.00=0.90!) and AUC₇₂ 3371.96 – which would give F 90.06% (bias +0.07%). If you don’t have suitable software, the interpolation formula is:

Ĉ = ℯ^{log(C_i–1)+|t_i–t_i–1|/(t_i+1–t_i–1)×log(C_i+1/C_i–1)}

Now for the nasty parts. The study failed if evaluated according to protocol. I don’t think that the FDA will accept the sponsor’s “method” – cherry-picking and simply wrong. BTW, I’m surprised to see such a large difference. You can present BE based on AUC₇₂ as a sensitivity analysis and discuss the impact on BE (if the conclusions differ). For the next studies describe what you intend to do in the protocol and stick to it. If you don’t feel comfortable with an estimated AUC₇₂ (i.e., prefer mixed fruits), decrease the time allowance window. As an example EMA requires for studies in steady-state (τ 24 hours) a maximum deviation of 10 minutes.