## Terrible… [RSABE / ABEL]

Hi Mikalai,

» » […] see there
»
» 1. In the case of going by ABEL path (see the decision tree), I assume we do not use any population parameters and just compare concentration from samples.

Nope. Scaled ABE (in both of its flavors ABEL and RSABE) is formulated in the unknown population parameters (see the linked slide above). For ABEL we have
• the fixed regulatory standardized variation $$\sigma_0=\sqrt{\log_{e}(0.30^2+1)}=0.2935604\ldots$$
• which leads to the switching condition $$\theta_s=\frac{\log_{e}(1.25)}{\sigma_0}\small{=0.7601283\ldots}$$ (given in the guideline as k and for reasons beyond my intellectual reach rounded to 0.760).
• The expanded limits are $$[L,U]=\text{e}^{\mp \theta_s\cdot \sigma_{wR}}$$.
• At the end we assess whether the 90% CI of $$\mu_T-\mu_R$$ lies entirely within $$[L,U]$$.
Note the Greek letters all over the place. What we get from the study are only estimates of the parameters.

» There is no inflation TIE? Is it correct?

No it isn’t. On the contrary, the inflated TIE arises from a misspecification of CVwR. We think that the drug/drug product is highly variable, expand the limits and pass. But the true CVwR is <30%, i.e., not a HVD(P) and we would have failed ABE. That’s it.

» And we do not use RR for the ref drug in our calculation. Is it correct?

If you mean by ‘we’ Elena’s approach, and stop since you showed ABE, no.

» 2. But if the study fails, we then calculate RR and a new bioequivalence interval if CV is higher than 30%. That is when we use RR and where TIE can be inflated. Is it correct?

Yes.

» But we do not recalculate our new CI we just use that from ABEL to compare with a new or the old CI. In the latter case, we basically fail the study. Is it correct?

I try to repeat Elena’s procedure. You make a lot of decisions (any of them can be wrong):
1. Assess ABE with α 0.05.
• If the 90% CI entirely outside 80.00–125.00%, stop (bioinequivalent).
• If the 90% CI within 80.00–125.00%, stop (pass).
• If not, calculate CVwR (and the stupid outlier check)
2. ABEL branch
• ≤30% → stop (fail).
• >30% → expand the limits.
• If the 90% CI is not entirely within [L,U] → stop (fail).
• Otherwise, check additionally whether the PE is within 80.00–125.00%.
If no, fail.
If yes, pass.
Apart from the issues with the misspecification of CVwR, if you proceed with this approach to the second step the TIE will be inflated for sure. The entire nominal α is already ‘consumed’ in step #1 – there is simply nothing ‘left’ for step #2. I would never use such a framework. Even if you use Bonferroni’s 0.025 in the first step, there might still an inflation due to CVwR. Check out again slide 15. In this approach the CI is only calculated once.

» The identical decision tree was used in the BS of rasagiline (registration required) and was accepted by EMA. https://clinicaldata.ema.europa.eu/web/cdp/home

This site is a pain in the back (refuses my credentials, send as a reminder the user name I just typed in, etc.). If this procedure was really accepted, that’s even worse than the ‘usual’ inflation of up to ~0.09… Oh dear!
Maybe I’ll set up simulations, time allowing. I expect the worst.

» If I am correct, in my view it is a preferable solution to minimize the inflation TIE.

Sorry, not at all.

Dif-tor heh smusma 🖖
Helmut Schütz

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