Bioequivalence and Bioavailability Forum • Never eaten Cadmium deliberately

Never eaten Cadmium deliberately [🇷 for BE/BA]

posted by d_labes – Berlin, Germany, 2011-01-20 16:00 (4837 d 20:14 ago) – Posting: # 6456
Views: 28,952

Ahoy dear "Der Meister",

sorry but I must confess that I'm totally confused and that I can't follow your points and reasoning :confused:

❝ If I get you right you are looking for the answer to this question:

❝ If we have a power of P at T/R=soandso and CV being thisorthat, then what should the accetance range be if the CV is not thisorthat but blahblah?

I never asked that question (they never came into my mind!) and I can't imagine what the results of I_Eat_Cadmium() are. Eventually hard poisoning with some side effects on the CNS :-D

?

What I meant with my sentence is that using the original scaled ABE criterion
(µT-µR)²/s²WR < (theta/sw0)²
would let to power calculations that are independent from the variabilities, at least at true µT-µR=0.
This is well known for using the "effect size" in superiority studies.
But this can only be proven for BE within the classical 2x2 design because in case of others the distribution of the test statistics are not known exactly.

See f.i.
L. Tothfalusi, L. Endrenyi and A. Garcia Arieta
"Evaluation of Bioequivalence for Highly Variable Drugs with Scaled Average Bioequivalence"
Clin Pharmacokinet 2009; 48 (11): 725-743

The use of the widened acceptance limits according to the EMA guidance is only an approximation to the original problem (as well as the linearized criterion with approximate upper 95% CI in the FDA Progesterone guidance).

Power calculations for the EMA widened acceptance limits can be done naively by inserting the widened limits depending on the assumed CV into the classical power formulas.
I had thought that Your feature request is going in that direction.

Lets see what happens with this approach:

require(PowerTOST)

#regulatory constant

k <- (log(1.25)/CV2se(0.3))



CVs <- c(0.3,0.35,0.4,0.45,0.5,0.55,0.6)

#restrict widening to CV=50%

CVr <- ifelse(CVs>0.5,0.5,CVs)

#widened limits

theta1 <- ifelse(CVr>=0.3, exp(-k*CV2se(CVr)), 0.8)



# GMR =1

pow <- vector("numeric",length=length(CVs))

for (i in seq_along(CVs)){

  pow[i] <- power.TOST(n=20, CV=CVs[i], theta0=1, theta1=theta1[i], design='2x2x4')

}



# GMR = 0.95

pow <- vector("numeric",length=length(CVs))

for (i in seq_along(CVs)){

  pow[i] <- power.TOST(n=20, CV=CVs[i], theta0=0.95, theta1=theta1[i], design='2x2x4')

}

data.frame(CV=CVs, AccLimLo=theta1, AccLimHi=1/theta1, power=pow)

Results:


GMR=1

    CV  AccLimLo AccLimHi     power

1 0.30 0.8000000 1.250000 0.9132950

2 0.35 0.7722885 1.294853 0.9132950

3 0.40 0.7461401 1.340231 0.9132950

4 0.45 0.7215055 1.385991 0.9132950

5 0.50 0.6983255 1.431997 0.9132950

-----------------------------------

6 0.55 0.6983255 1.431997 0.8503237

7 0.60 0.6983255 1.431997 0.7759268



GMR=0.95

    CV  AccLimLo AccLimHi     power

1 0.30 0.8000000 1.250000 0.8202398

2 0.35 0.7722885 1.294853 0.8436856

3 0.40 0.7461401 1.340231 0.8590072

4 0.45 0.7215055 1.385991 0.8695570

5 0.50 0.6983255 1.431997 0.8771277

-----------------------------------

6 0.55 0.6983255 1.431997 0.8113771

7 0.60 0.6983255 1.431997 0.7380680

You see (if not you need glasses :cool:

Power is actually independent of the CV if GMR=1 up to the EMA cutoff CV=50%.
The power is dependent on the CV (variability) if GMR!=1.
The power increases with variability in the range 0.3 - 0.5 where scaling/widening is according to the magnitude of the CV. This is counter-intuitive!

Moreover the classical power formulas have nowhere the scABE constraint "point est. must be within 0.8-1.25" as presupposition.
Thus my encrypted babblings are nothing more then the statement: "I'm not convinced that we are actually calculating somefink that can be called power of scABE if we do it that way".

Long post but not any meaning :cool:

"Power Calculation - A guess masquerading as mathematics."
Guernsey McPearson

—
Regards,

Detlew

Complete thread:

Feature suggestion for bear and PowerTOST ElMaestro 2011-01-16 19:13 [🇷 for BE/BA]
- Sample size for widened scaled ABE limits d_labes 2011-01-17 13:19
  - 0.760 or... Helmut 2011-01-17 14:38
    - ... full precision is the question d_labes 2011-01-17 16:37
      - ... full precision is the question Helmut 2011-01-17 18:06
        
        OT: Number of horns on a unicorn d_labes 2011-01-18 08:32
        
        Goooogle Helmut 2011-01-18 11:44
  - Cadmium ElMaestro 2011-01-19 17:50
    - Never eaten Cadmium deliberatelyd_labes 2011-01-20 15:00
      - Never eaten Cadmium deliberately Helmut 2011-01-20 15:25
        
        Call of duty for simulants d_labes 2011-01-20 16:15
        
        Counterinuitive Helmut 2011-01-21 04:13
        
        Counterintuitive d_labes 2011-01-21 08:36
        
        Counterintuitive Helmut 2011-01-21 12:53
        
        Counterinuitive, but ... d_labes 2011-01-21 12:12
        
        Counterinuitive, but ... Helmut 2011-01-21 13:01
        
        Wow, Wow ... d_labes 2011-01-21 14:43
        
        Never eaten Cadmium deliberately ElMaestro 2011-01-21 12:59
        
        Simulants of the world, unite! Helmut 2011-01-21 14:05
        
        Simulants of the world, unite! ElMaestro 2011-01-21 14:52
        
        Hyslop, Howe, scaled ABE and that all d_labes 2011-01-21 15:28
        
        Hyslop, Howe, scaled ABE and that all ElMaestro 2011-01-21 15:45
        
        scABE and missings d_labes 2011-01-21 16:19
        
        Intuition Helmut 2011-01-21 18:41
      - Never eaten Cadmium deliberately ElMaestro 2011-01-20 15:34
        
        Use of Cadmium d_labes 2011-01-20 16:06
        
        Use of Cadmium ElMaestro 2011-01-20 16:52
        Use of Cadmium ElMaestro 2011-01-20 17:53