## PE constraint and “politics” [R for BE/BA]

Hi GM,

» As this is a replicated study, there are only few articles for calculating the sample size.

If reference-scaling (RSABE, ABEL) is concerned, do you know any article except the two Lászlós’?

We need simulations because the methods are implicitly sequential. Like in any framework (following a decision scheme) an analytical solution for power does not exist.

However, the sample size estimation for ABE in replicate designs is straightforward (

» There is no clear information about this. So that, I suppose to understand concept through R-program.

Tóthfalusi

» I thought CVswitch=0.30 for both FDA and EMA, …

Correct.

» … r_const=0.25 and 0.760 for FDA and EMA respectively …

Not quite. The switching condition θ

Then \({\theta _s} = \log (1.25)/\sigma _{w0} = 0.8925742 \ldots \) (FDA) and \(0.7601283 \ldots \) (EMA).

Note that σ

» … and don't know about the pe_constr.

It was introduced by all agencies following suggestions by Les Benet (see this post). It is “political” and leads to statistical troubles (essentially we are truncating the distribution and the entire concept is built on sand).

» As this is a replicated study, there are only few articles for calculating the sample size.

If reference-scaling (RSABE, ABEL) is concerned, do you know any article except the two Lászlós’?

^{1}We need simulations because the methods are implicitly sequential. Like in any framework (following a decision scheme) an analytical solution for power does not exist.

- Estimate s
_{wR}.

If <0.294* (FDA) or \(C{V_{wR}} = 100\sqrt {{e^{s_{wR}^2}} - 1} \le 30\% \) (EMA) apply conventional, unscaled ABE.

Otherwise, continue with the respective reference-scaling method.

- For the EMA (and others) observe an upper cap of the CV
_{wR}(*i.e.*, don’t expand the limits beyond this point).

- Assess the point estimate restriction.

However, the sample size estimation for ABE in replicate designs is straightforward (

*i.e.*, does*not*require simulations). Use`sampleN.TOST()`

instead.» There is no clear information about this. So that, I suppose to understand concept through R-program.

Tóthfalusi

*et. al.*^{2}is a good starting point. Other references are given in the man-pages of`PowerTOST`

.» I thought CVswitch=0.30 for both FDA and EMA, …

Correct.

» … r_const=0.25 and 0.760 for FDA and EMA respectively …

Not quite. The switching condition θ

_{s}(aka regulatory constant) is based on the regulatory standardized variation σ_{w0}. For the FDA σ_{w0}= 0.25 and for the EMA based on CV_{wR}30% as \({\sigma _{w0}} = \sqrt {\log \left( {{{0.30}^2} + 1} \right)} = 0.2935604 \ldots \)Then \({\theta _s} = \log (1.25)/\sigma _{w0} = 0.8925742 \ldots \) (FDA) and \(0.7601283 \ldots \) (EMA).

Note that σ

_{w0}0.25 is explicitly given by the FDA and therefore, the regulatory constant in`PowerTOST`

is used in full precision.* On the other hand, the EMA requires the *rounded*0.760 (termed k in the GL) and an upper cap for scaling at CV_{wR}50% (EL 69.84–143.19%). Check the conditions:`library(PowerTOST)`

reg_const("FDA")

FDA regulatory settings

- CVswitch = 0.3

- no cap on scABEL

- regulatory constant = 0.8925742

- pe constraint applied

reg_const("EMA")

EMA regulatory settings

- CVswitch = 0.3

- cap on scABEL if CVw(R) > 0.5

- regulatory constant = 0.76

- pe constraint applied

» … and don't know about the pe_constr.

It was introduced by all agencies following suggestions by Les Benet (see this post). It is “political” and leads to statistical troubles (essentially we are truncating the distribution and the entire concept is built on sand).

- First we have to check whether a condition is fulfilled.

FDA: Upper 95% confidence bound of \((\overline{Y_T}-\overline{Y_R})-\theta\sigma^{2}_{wR}\leq 0\).

EMA: 90% CI within the expanded limits \([L,U]=\exp^{\mp k \cdot s_{wR}}\).

- If
*this*test passes, we have to*additionally*check whether the point estimate lies within 80.00–125.00%. Only*then*the study passes.

_{wR}57.38% (EL 66.7–150.0%). Try`reg_const("HC")`

.- Endrényi L, Tóthfalusi L.
*Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs.*J Pharm Pharmaceut Sci. 2011;15(1):73–84. free resource.

- Tóthfalusi L, Endrényi L, García-Arieta A.
*Evaluation of Bioequivalence for Highly Variable Drugs with Scaled Average Bioequivalence.*Clin Pharmacokinet. 2009;48(11):725–43. doi:10.2165/11318040-000000000-00000.

- The FDA gives σ
_{w0}0.25 and s_{wR}0.294 (rounded!). We decided to use s_{wR}in full precision.

@Detlew: Should we change for the FDA`CVswitch`

from 0.3 to`se2CV(0.294)`

?

—

Helmut Schütz

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

Science Quotes

*Dif-tor heh smusma*🖖Helmut Schütz

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

Science Quotes

### Complete thread:

- Functionality of sampleN.RSABE GM 2018-11-02 06:25 [R for BE/BA]
- Gutting PowerTOST Helmut 2018-11-02 10:50
- Gutting PowerTOST GM 2018-11-03 05:09
- PE constraint and “politics”Helmut 2018-11-03 13:04

- Gutting PowerTOST GM 2018-11-03 05:09

- Gutting PowerTOST Helmut 2018-11-02 10:50