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GM
Junior

India,
2018-11-02 06:25

Posting: # 19522
Views: 346
 

 Functionality of sampleN.RSABE [R for BE/BA]

Dear Dlabes,

I am trying to calculate the sample size for replicate design using R software with sampleN.RSABE.

With keen interest to know about the functionality of sampleN.RSABE, I have searched in the web. I got some backend code of this function from Github (see link).

I am a beginner of R software, but I tried to understand this. There are some intermediate functions like .sampleN0, .sampleN0.2, .power.RSABE are involved.

I got the informationn of first two functions from the same github. but not the third one.

As you are the auther of this function, am directly requesting you.

Kindly explain or suggest any link about this function.

Thank you in advance.

Best Regards,
GM
Helmut
Hero
avatar
Homepage
Vienna, Austria,
2018-11-02 10:50

@ GM
Posting: # 19523
Views: 309
 

 Gutting PowerTOST

Hi GM,

not Detlew but answering anyway. ;-)

» I am trying to calculate the sample size for replicate design using R software with sampleN.RSABE.

So why are you not simply using it?

library(PowerTOST)
sampleN.RSABE(CV=0.4, theta0=0.9, targetpower=0.8, design="2x2x4")

If you want further information about the arguments and their defaults, type ?sampleN.RSABE in the R-console / R-Studio’s console or consult the online manual.

» I am a beginner of R software

If you want to dive into the code, be aware of R’s steep learning curve.

» […] but I tried to understand this.

OK, this is a laudable.

» There are some intermediate functions like .sampleN0, .sampleN0.2, .power.RSABE are involved.
» I got the informationn of first two functions from the same github. but not the third one.

.power.RSABE is contained in power_RSABE2L_isc.R.

Cheers,
Helmut Schütz
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GM
Junior

India,
2018-11-03 05:09

@ Helmut
Posting: # 19525
Views: 276
 

 Gutting PowerTOST

Hi Helmut,

» not Detlew but answering anyway. ;-)

Thank you for quick reply at every time.:-)

» So why are you not simply using it?
»

library(PowerTOST)
» sampleN.RSABE(CV=0.4, theta0=0.9, targetpower=0.8, design="2x2x4")

If you want further information about the arguments and their defaults, type ?sampleN.RSABE in the R-console / R-Studio’s console or consult the online manual.

As this is a replicated study, there are only few articles for calculating the sample size.
There is no clear information about this. So that, I suppose to understand concept through R-program.

I have few more doubts, regarding the terms CVswitch, r_const and pe_constr.

I thought CVswitch=0.30 for both FDA and EMA, r_const=0.25 and 0.760 for FDA and EMA respectively and don't know about the pe_constr.

Kindly correct me if I am wrong...

Thank you in advance.

Best Regards,
GM
Helmut
Hero
avatar
Homepage
Vienna, Austria,
2018-11-03 13:04

@ GM
Posting: # 19526
Views: 262
 

 PE constraint and “politics”

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’?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.
  1. Estimate swR.
    If <0.294* (FDA) or CVwR (100√wR–1) ≤ 30% (EMA) apply conventional, unscaled ABE.
    Otherwise, continue with the respective reference-scaling method.
  2. For the EMA (and others) observe an upper cap of the CVwR (i.e., don’t expand the limits beyond this point).
  3. Assess the point estimate restriction.
We have two decision points for the FDA (a, c) and three (a, b, c) for the EMA…

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 θs (aka regulatory constant) is based on the regulatory standardized variation σw0. For the FDA σw0 = 0.25 and for the EMA based on CVwR 30% as σw0 = √log(0.30²+1) = 0.2935604. Then θs = log(1.25)/σw0 = 0.8925742 (FDA) and 0.7601283 (EMA).
Note that σw0 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 CVwR 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 (YTYR)–θs²wR ≤0.
    EMA: 90% CI within the expanded limits [L,U] = ℯ∓k·swR.
  • If this test passes, we have to additionally check whether the point estimate of the GMR lies within 80.00–125.00%. Only then the study passes.
Note that the EMA’s method is followed in many other jurisdictions (WHO, ANVISA, Russia, EEC, Australia, New Zealand, Egypt). Health Canada’s TGD requires an upper cap for scaling at CVwR 57.38% (EL 66.7–150.0%). Try reg_const("HC").


  1. Endrényi L, Tóthfalusi L. Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs. J Pharm Pharmaceut Sci. 2011;15(1):73–84. [image] free resource.
  2. 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 σw0 0.25 and swR 0.294 (rounded!). We decided to use swR in full precision.
    @Detlew: Should we change for the FDA CVswitch from 0.3 to se2CV(0.294)?

Cheers,
Helmut Schütz
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