## Bias correction unveiled [BE/BA News]

Hi Achievwin,

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

In the respective next lines you find

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.

❝ ❝ 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;`

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.- Troubles likely if one naïvely implements the formulas in another software…

- This formula is used in all papers of Endrényi and Tóthfalusi.

—

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!_{}Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- FDA guideline on BE, draft August 2021 ElMaestro 2021-08-23 14:42 [BE/BA News]
- FDA guideline on BE, draft August 2021 Helmut 2021-08-23 15:31
- FDA guideline on BE, draft August 2021 Achievwin 2021-09-08 04:09
- Bias correction unveiledHelmut 2021-09-10 20:47

- FDA guideline on BE, draft August 2021 Achievwin 2021-09-08 04:09
- FDA guideline on BE, draft August 2021 Achievwin 2021-08-23 21:35
- FDA guideline on BE, draft August 2021 Helmut 2021-08-23 23:46

- FDA guideline on BE, draft August 2021 Helmut 2021-08-23 15:31