Bioequivalence and Bioavailability Forum

Hi Achievwin,

❝ ❝ Furthermore, we need the standard error \(\small{s_\textrm{d}}\) of the point estimate

❝

❝ I did not find this one in the guidance can you point out to me what line number this is in the new guidance?

That’s a little bit tricky. I’ll try again.

We have the regulatory constant $$\small{\theta_\textrm{s}=\frac{\log_{e}1.25}{\sigma_\textrm{w0}}=0.89257\ldots}\tag{1}$$
In the guidance line 998 the scaled average BE limit is given by $$\small{\theta\equiv\left(\frac{\log_{e}1.25}{\sigma_\textrm{w0}}\right)^2\tag{2}}$$which is simply what I used in my previous post by $$\small{\theta=\theta_\textrm{s}^2}\tag{3}$$ Of course, $$\small{\left(\widehat{Y}_T-\widehat{Y}_R\right)^2=PE^2}\tag{4}$$ In the guidance line 1003 we have $$\small{crit=\left(\widehat{Y}_T-\widehat{Y}_R\right)^2-\theta\cdot s_\textrm{wR}^2}\tag{5}$$ That’s the same as $$\small{crit=PE^2-\theta_\textrm{s}^2\cdot s_\textrm{wR}^2}\tag{6}$$Here the confusion starts. You find my \({\color{Red}{s_\textrm{d}}} \) in lines 1083 and 1219 as the stderr of the difference.

In the respective next lines you find

x=estimate**2–stderr**2;

where it acts as a bias correction of the point estimate.

Hence, actually not \((5)\) or \((6)\) has to be used but $$\small{\begin{matrix}
crit=PE^2-{\color{Red}{s_\textrm{d}^2}}-\theta_\textrm{s}^2\cdot s_\textrm{wR}^2 =\\
\left(\widehat{Y}_T-\widehat{Y}_R\right)^2-{\color{Red}{se^2}}-\theta \cdot s_\textrm{wR}^2
\end{matrix}}\tag{7}$$ The bias correction is not mentioned anywhere in the guidance and therefore, \((5)\) without one is extremely misleading.^1,2 It is evident only if you inspect the SAS code. See Detlew’s post about the background given by Donald Schuirmann in 2016.

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1. Troubles likely if one naïvely implements the formulas in another software…
   
2. This formula is used in all papers of Endrényi and Tóthfalusi.