## Inflation type one error [RSABE / ABEL]

Hi Mikalai,

» I am not a statistician […]

So am I.

» We basically do the same things as in the usual average bioequivalence where we are able to preserve TIE at 5%, [... ]

No, we aren’t. In ABE we have fixed limits of the acceptance range, i.e. a pre-specified Null Hypothesis. In ABEL the limits are random variables or in other words, the Null is generated ‘in face of the data’. That means that each study sets it own standards and if we have a couple of HVDPs, each of them was approved according to different rules.

» What is behind this inflation, philosophically and mathematically?

Maybe this presentation helps. In short: Reference-scaling is based on the true population parameters (hence the Greek letters $$\theta_s,\,\mu_T,\,\mu_R,\,\sigma_{wR}$$). The true standard deviation $$\sigma_{wR}$$ of the reference is unknown. We have only its estimate $$s_{wR}$$ from the study. Imagine: The true within-subject CV of the reference is 27%. Hence, it is not an HVD(P) and we should use the conventional limits of 80.00-125.00%. However, by chance in our study we get an estimate of 35% and we expand the limits. Since the PE and the 90% are not affected it means that the chance of passing BE increases. The chance to falsely not accepting the Null increases and this is the inflated type I error.

» I also bumped into this discussion where some ever argue about whether this concept even exists. https://daniellakens.blogspot.com/2016/12/why-type-1-errors-are-more-important.html I assume this is not related to multiple testing.

Nice one. Your assumption is correct.

» Also we have a statistical concept, but do we have any real proof of this concept? Does any» W know products that were initially registered and then withdrawn from the market because their initial bioequivalence had been due to the inflation TIE?

No (twice). But these questions diserve a detailed discussion. More when I’ll be back from Athens.

Dif-tor heh smusma 🖖
Helmut Schütz

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