Bioequivalence and Bioavailability Forum

Servus Franz,

welcome to the forum!

That’s very interesting, inasmuch the progesterone guidance specifically states:

For detailed information on this approach, please refer to the published book chapter, Davit B, Conner D. Reference-scaled average bioequivalence approach. In: Kanfer I, Shargel L, eds. Generic Drug Product Development – International Regulatory Requirements for Bioequivalence. New York, NY: Informa Healthcare, 2010: 271-272.

❝ I cross-checked the L. Endrenyi/L Tothfalusi chapter in Kanfer/Shargel’s book “Generic Drug Product Development”…

I don’t have this book; stupid question: Are you sure that you are dealing with the right chapter (see above)?

❝ … and found a difference …

❝ I tried now to simulate data in EXCEL to find out, which one is correct and calculated a “third” way of concluding BE: simply the exponentiated CI for the difference of the means using the SE of the differences.

❝ Instead of solving the problem, I have now 3 (slightly) differing results; This might be due to simple programming mistake but I couldn’t find them up to now;

With EMA’s full replicate data set I got in Phoenix/WinNonlin (6.3 beta RC3):

FDA’s code
Estimate   0.143765
StdError   0.0490802
sWR        0.446446 >0.294, scaling allowed
pointest   1.15461
x          0.0182596
boundx     0.0509076
critbound -0.0920763 ≤0, RSABE demonstrated
Of course we could calculate a 90% CI of the PE (1.06386–1.25311) but this doesn’t help – there’s no widening of the acceptance range like for the EMA. FDA’s unscaled mixed effects model gives 1.0710–1.2489; EMA’s Method A 1.0711–1.2489 and Method B 1.0711–1.2497.

Now let’s see:

\(E_m=(\mu_T-\mu_R)^2\)
\(E_s={\theta_{s}}^{2}\cdot {\sigma_{w}}^{2}\) (the FDA’s switching condition \({\theta_{s}}^{2}\) is 0.893 = CV of ~25.83%!)
\(C_m=(|m_T - m_R|+t_{\alpha,N-S}\cdot SE)^2\)
\(C_s={\theta_{s}}^{2} \cdot (N-S) \cdot {\sigma_{w}}^{2}/{\chi_{\alpha,N-S}}^{2}\)
\(L_m=(C_m-E_m)^2\)
\(L_s=(C_s-E_s)^2\)
\(CL=E_m-E_s+\sqrt{(L_m+L_s)}\)

I got (quick and dirty as always):
Em 0.0206685
Es 0.148147
Cs 0.113948
Cm 0.0509076
Lm 0.000914403
Ls 0.00116952
CL 0.214465 (ℯ^0.214465 = 1.23920)