mittyri
★★  

Russia,
2016-02-01 23:33
(2977 d 22:19 ago)

Posting: # 15912
Views: 5,570
 

 PowerTOST CV Power EMA 3 periods discontinuity [🇷 for BE/BA]

Dear All,

Could you please enlighten me about the following issue. May be it was discussed somewhere but I didn't find.
Some R code:
x1 <- seq(0.25, 0.5, length.out=100)
y1 <- vector("numeric", length=length(x1))
y2 <- vector("numeric", length=length(x1))
des = c("2x3x3", "2x2x3")
n<-48
GMR <- 0.95
for (j in seq_along(x1)) {
  if (x1[j] > 0.3) {
    y1[j] <- power.scABEL(CV=x1[j], theta0=GMR, n=n, des=des[1], reg="EMA")
    y2[j] <- power.scABEL(CV=x1[j], theta0=GMR, n=n, des=des[2], reg="EMA")
  }
  if (x1[j] <= 0.3) {
    y1[j] <- power.TOST(CV=x1[j], theta0=GMR, n=n, des= des[1])
    y2[j] <- power.TOST(CV=x1[j], theta0=GMR, n=n, des= des[2])
  }
}
plot(x1, y2,type="p",col="red", xlab="CV", ylab="Power")
lines(x1, y1,col="green")
legend('topright', c("TRT RTR", "TRR RRT RTR"), lty =1, col = c('red', 'green'))

The resulted plot:
[image]
There is a discontinuity at CV=0.3. I cannot figure out the reason. The limits are widening smoothly from this point.

PS: some intersection with Shuanghe's post :cool:


Edit: Category changed. [Helmut]

Kind regards,
Mittyri
Helmut
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Homepage
Vienna, Austria,
2016-02-02 01:23
(2977 d 20:28 ago)

@ mittyri
Posting: # 15913
Views: 4,657
 

 Discontinuity = artifact

Hi Mittyri,

❝ There is a discontinuity at CV=0.3. I cannot figure out the reason.


You introduced it yourself with the highlighted parts of the code:

  if (x1[j] > 0.3) {

❝     y1[j] <- power.scABEL(CV=x1[j], theta0=GMR, n=n, des=des[1], reg="EMA")
❝     y2[j] <- power.scABEL(CV=x1[j], theta0=GMR, n=n, des=des[2], reg="EMA")
❝   }
❝   if (x1[j] <= 0.3) {
❝     y1[j] <- power.TOST(CV=x1[j], theta0=GMR, n=n, des= des[1])
❝     y2[j] <- power.TOST(CV=x1[j], theta0=GMR, n=n, des= des[2])
❝   }


If you indend to go with reference-scaling you have to state that in the protocol. Based on that you perform the sample size estimation, but always with sampleN.scABEL(). Once the study is done, you may scale or not (dependent on CVwR). Hence, the only fair comparison would be ABE (power.TOST if you don’t intend to scale) with ABEL (power.scABEL) over the entire range of CVs, like this:

library(PowerTOST)
CV       <- seq(0.25, 0.55, 0.01)
pwr.ABEL <- vector()
pwr.ABE  <- pwr.ABEL
for (j in seq_along(CV)) {
  pwr.ABEL[j] <- power.scABEL(CV=CV[j], theta0=0.95,
                              n=48, design="2x2x3")
  pwr.ABE[j]  <- power.TOST(CV=CV[j], theta0=0.95,
                            n=48, design="2x2x3")
}
plot(CV, pwr.ABEL, type="l", col="blue", lwd=2,
  ylim=c(0.90, 1), ylab="power", las=1)
lines(CV, pwr.ABE, col="red", lwd=2)
abline(v=c(0.3, 0.5), lty=3)
legend("topright", legend=c("ABEL", "ABE"),
  col=c("blue", "red"), lwd=rep(2, 2))

or
[image]

With your code you would jump at 0.30 from the red line (ABE) to the blue line (ABEL). Note that even at CV 0.25 power of ABEL is slightly larger than the one of ABE since there is small chance that you are allowed to scale. That’s the tricky part with reference scaling. The simulation – as the scaling model itself* – is based on the true (but unknown) θ0 and σwR. By pure chance (CVwR >0.30) you will be allowed to scale although the drug is not highly variable (σwR ≤0.2936). This is the (main?) reason behind the inflation of the type I error. Another story.


  • ln(0.80) / σw0 ≤ [ln(μT) – ln(μR)] / σwR ≤ ln(1.25) / σw0
    Only parameters here, not their estimates

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ElMaestro
★★★

Denmark,
2016-02-02 17:28
(2977 d 04:24 ago)

@ mittyri
Posting: # 15916
Views: 4,540
 

 2x Laszlo

And now we might not even need simulations - see here.

Pass or fail!
ElMaestro
Helmut
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Homepage
Vienna, Austria,
2016-02-02 17:39
(2977 d 04:13 ago)

@ ElMaestro
Posting: # 15917
Views: 4,529
 

 2x Laszlo

Hi ElMaestro,

❝ And now we might not even need simulations - see here.


Did you read it? Interesting comparison, but all restrictions (on the PE, 50% cap for the EMA) were lifted. Some of their simulations (hey, in R!) had run-times of more than 24 hours…

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Helmut Schütz
[image]

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
ElMaestro
★★★

Denmark,
2016-02-02 18:09
(2977 d 03:43 ago)

@ Helmut
Posting: # 15918
Views: 4,508
 

 2x Laszlo

Hi Hötzi,

❝ Did you read it? Interesting comparison, but all restrictions (on the PE, 50% cap for the EMA) were lifted. Some of their simulations (hey, in R!) had run-times of more than 24 hours…


No I have not read it. I am busy with stuff, and reckoning that I might not understand it anyway this paper has not made it to the top of my to-do list. But I will give it a go, I think.

Pass or fail!
ElMaestro
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