Bioequivalence and Bioavailability Forum

Hi Nastia

❝ […] I have some doubts in logical equality of the inflation of TIE and consumer's risk. Can you please explain my faults in the following reasoning?

❝

❝ Suppose we expect drug A to be highly variable (in the previous study somewhere in Antarctica W. Oodendijk et al. have got CV>30% for the reference drug).

The problem starts already here. How reliable is Oodendijk’s result? Is it the only one? Did the agency agree that the drug is HV and wider limits can be used?

❝ Which of the following options should we prefer to write in the protocol in order to care of the customer:

❝

❝ a). Use pre-specified wider limits 75-133 for C_max (no inflation?)

❝ b). Use the GCC-GL approach (inflation up to 21%?)

The crucial point is what we consider a “clinically not relevant \(\small{\Delta}\)”. Muse a bit on these goodies:
$$\small{\Delta=20\%\implies\left\{\theta_1=80.00\%,\,\theta_2=125.00\%\right\}}\tag{1}$$ $$\small{\Delta=25\%\implies\left\{\theta_1=75.00\%,\,\theta_2=133.3\dot{3}\%\right\}}\tag{a}$$ $$\small{\Delta\: \overset{{\color{Red} ?}}{\rightarrow}\,\begin{vmatrix}
\widehat{CV_\textrm{wR}}\leq30\%\rightarrow \widehat{\Delta}=20\%\\
\widehat{CV_\textrm{wR}}>30\%\rightarrow \widehat{\Delta}=25\%
\end{vmatrix}\implies\begin{Bmatrix}
\theta_1=80.00\%,\,\theta_2=125.00\%\\
\theta_1=75.00\%,\,\theta_2=133.3\dot{3}\%
\end{Bmatrix}}\tag{b}$$ \(\small{(1)}\) and \(\small{(\textrm{a})}\) are straightforward. Fixed limits, type I error always ≤ the nominal \(\small{\alpha}\).
\(\small{(\textrm{b})}\) is data-driven (like ABEL and RSABE), since it depends on the estimated \(\small{CV_\textrm{wR}}\). The Null-hypothesis is like Schrödinger’s cat – or Wigner’s friend, if you prefer. The study (not based on clinical grounds by the applicant and regulator like in \(\small{(1)}\) and \(\small{(\textrm{a})}\)) “decides” which \(\small{\widehat{\Delta}}\) is acceptable for the patient. That’s not a particularly good idea. By definition (‼) any framework (or a pre-test) might lead to a false decision and hence, inflates the TIE. That’s a multiplicity problem, which – if not adjusted – will increase the familywise error rate.

❝ Suppose that at the end of the trial we get CV≤30% and CI within 75-133, but out of 80-125.

❝ Then for the a-approach we should conclude the drug BE, …

If (a) was stated in the protocol and accepted by the agency, fine. The CV is interesting though not relevant. Try the function CVCL() in PowerTOST. Might be pure chance (well include >30%).

❝ … for the b-approach - fail to conclude BE.

No risk, no fun.

❝ That is the risk of the customer to get a bad product is higher in the first approach if we define "a bad product" as a non-HVD with the limits out of 80-125.

Nope. In (a) you accept beforehand that \(\small{\Delta=25\%}\) is not relevant for the patient. But again: You don’t assess the CV at all. Maybe it is HV indeed (like in Antarctica).

❝ The difference is in the fact that in the first approach we proclaim the drug to be good if it is within the limits 75-133.

Correct.

❝ Until about 2013 there were a lot of studies in Russia with 75-133 limits for C_max even for non-HVD drugs.

Interesting. However:

library(PowerTOST)
CVCL(CV = 0.27, df = 3*40-4, side ="2-sided") # 4-period full replicate, n = 40

 lower CL  upper CL
0.2383666 0.3116013