Helmut
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Vienna, Austria,
2015-02-27 03:03
(3317 d 20:59 ago)

Posting: # 14508
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 Advanced example (futi­l­ity for GMR) [Two-Stage / GS Designs]

Dear all,

I want to share with you a recent example. Endogenous drug, baseline with circadian rhythm. Borderline highly variable, both for Cmax and AUC. Previous studies contradictory; CV reported with ~20–40%. Since for an European submission scaling AUC is not possible and the CV was unclear we considered various TSDs (“type 1”: T/R 0.95, target power 80% with optimized adjusted α for n1 16–66, CV 15–60%). We were also exploring the impact of various futility rules. Left panels empiric Type I error, right panels % power (lower surface in the first stage and upper one overall).

I.    α 0.0302 (93.96% CI), no futility criterion

[image]

II.    α 0.0306 (93.88% CI), futility criterion ]0.8000–1.2500[

[image]

III.    α 0.0313 (93.74% CI), futility criterion ]0.8250–1.2121[

[image]

IV.    α 0.0327 (93.46% CI), futility criterion ]0.8500–1.1765[

[image]



TIEmax-values are 0.05003 (I), 0.04995 (II), 0.05000 (III), and 0.05005 (IV).

TIE-surfaces show the shape common to “type 1” TSDs. With futility rules the methods become in­creas­ingly conservative at the extreme combinations of n1/CV.
Trivial observation: Increasingly restrictive futility rules prevent more studies from proceeding to the second stage. Therefore, we need less adjustment of α.
Hey, wider CIs! Are we more likely too pass and/or pay a smaller sample size penalty? On the contrary. Anders1 already showed last year that futility rules on the total sample size may substantially deteriorate power. For an example of the full adaptive methods proposed by Karalis/Macheras see the recent review.2 We get a similar effect for the GMR here. In the right panels white lines show the intersection with the plane of 80% power. With increasingly restrictive futility rules only small changes in the first stage’s power but overall the surface is lower and tilted down.
  1. Without a futility rule overall power is generally ≥80% – unless the first stage was small and one will be hit by a high CV. The 80%-border runs almost linear from n1 16 / CV 33% to n1 46 / CV 60%. However, even for n1 16 and CV 60% power is still 75.2%. For such a stupidly low n1 one deserves it to be punished by an average total sample size of 159… Don’t go there.
  2. A futility of ]0.8–1.25[ (as proposed by Peter Armitage) is still suitable – if the sample size is not too small for the “best guess” CV.
  3. With ]0.8250–1.2121[ we enter a slippery field. For moderate sample sizes it may be difficult to maintain the desired power.
  4. A futility of ]0.8500–1.1765[ (proposed by Charles Bon) makes only sense if one is willing to start in a relatively large sample size and is confident that the CV will not be too high…
We must not forget that in my example we had to deal with a borderline HVD, Assuming a T/R of 0.95 is nice, but who knows? Remember that the two Lászlós recommend a T/R of 0.90 for RSABE. Our final design was (based on a “best guess” CV of 30%) a sample size of 46 and an FC of ]0.8250–1.2121[. We expect for this CV a power in the first stage of 80.9% and 67.2% for a CV of 35%. Chances to proceed to the second stage are 10.1% and 28.2%. Overall-power is expected with 85.3% and 83.2%. We will have still 80% power for a CV up to 46% (very unlikely, anyhow). In this extreme case the average total sample size will be 79. Let’s see. ;-)


  1. Fuglsang A. Futility rules in bioequivalence trials with sequential designs. AAPS J. 2014;16(1):79–82. doi:10.1208/s12248-013-9540-0
  2. Schütz H. Two-stage designs in bioequivalence trials. Eur J Clin Pharmacol. 2015;71(3):271-81. doi:10.1007/s00228-015-1806-2

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d_labes
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Berlin, Germany,
2015-02-27 10:55
(3317 d 13:08 ago)

@ Helmut
Posting: # 14509
Views: 5,340
 

 Advanced example (futi­l­ity for GMR)

Dear Helmut,

❝ ... Borderline highly variable, both for Cmax and AUC. Previous studies contradictory; CV reported with ~20–40%. Since for an European submission scaling AUC is not possible and the CV was unclear we considered various TSDs (“type 2”: T/R 0.95, target power 80% with optimized adjusted α for n1 16–66, CV 15–60%).


From that I assume that you aimed for an European submission.
But then I wonder: Type 2 aka Potvin C? No longer regulatory caveats expected for this?

❝ ... Our final design was (based on a “best guess” CV of 30%) a sample size of 46 and an FC of ]0.8250–1.2121[. We expect for this CV a power in the first stage of 80.3% and 61.3% for a CV of 35%. Chances to proceed to the second stage are 10.1% and 28.2%. Overall-power is expected with 85.3% and 83.2%. We will have still 80% power for a CV up to 46% (very unlikely, anyhow). In this extreme case the average total sample size will be 79. Let’s see. ;-)


Sorry, I can't reproduce your numbers. Could you please write down the power.2stage.fC() call?

Regards,

Detlew
Helmut
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Vienna, Austria,
2015-02-27 11:43
(3317 d 12:20 ago)

@ d_labes
Posting: # 14510
Views: 5,341
 

 Advanced example (futi­l­ity for GMR)

Dear Detlew,

❝ ❝ ... we considered various TSDs (“type 2”: :blahblah:).


❝ From that I assume that you aimed for an European submission.

❝ But then I wonder: Type 2 aka Potvin C? No longer regulatory caveats expected for this?


Bloody typo (I will correct it). I preferred “type 2” but my client wanted “type 1”.

❝ Sorry, I can't reproduce your numbers. Could you please write down the power.2stage.fC() call?


power.2stage.fC(alpha=rep(0.0313, 2), n1=46, CV=0.3, GMR=0.95,
  targetpower=0.8, fCrit="PE", fClower=0.825, theta0=0.95,
  npct=c(0.05, 0.25, 0.5, 0.75, 0.95))
Method Bf: alpha (s1/s2)= 0.0313 0.0313
Interim power monitoring step included.
Target power in power monitoring and sample size est. = 0.8
BE margins = 0.8 ... 1.25
CV = 0.3; n(stage 1) = 46; GMR = 0.95
GMR = 0.95 and mse of stage 1 in sample size est. used.
Futility criterion for PE = outside 0.825 ... 1.212121

1e+05 sims at theta0= 0.95 (p(BE)='power').
p(BE)    = 0.85284
p(BE) s1 = 0.80877
Studies in stage 2 = 10.1%

Distribution of n(total)
- mean (range) = 47 (46 ... 96)
- percentiles
 5% 25% 50% 75% 95%
 46  46  46  46  54


I will check my original post for eventual other typos.

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d_labes
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Berlin, Germany,
2015-02-27 12:03
(3317 d 11:59 ago)

@ Helmut
Posting: # 14511
Views: 5,307
 

 Numbers

Dear Helmut,

power.2stage.fC(alpha=rep(0.0313, 2), n1=46, CV=0.3, GMR=0.95, targetpower=0.8,

❝   fCrit="PE", fClower=0.825, theta0=0.95, npct=c(0.05, 0.25, 0.5, 0.75, 0.95))

Ok, that was also mine, except npct.

...

❝ p(BE)    = 0.85284

❝ p(BE) s1 = 0.80877


That was my concern. And also the same for CV=0.35.

Regards,

Detlew
Helmut
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Vienna, Austria,
2015-02-27 12:22
(3317 d 11:41 ago)

@ d_labes
Posting: # 14512
Views: 5,368
 

 Typos

Dear Detlew,

❝ ❝ ...

❝ ❝ p(BE)    = 0.85284

❝ ❝ p(BE) s1 = 0.80877


❝ That was my concern. And also the same for CV=0.35.


THX – I got it! Looked at wrong rows of a gigantic table. Hopefully all typos are corrected now… Sorry.

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