Helmut
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2014-10-23 22:11
(3443 d 13:35 ago)

Posting: # 13781
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 Riddle [Surveys]

Only for specialists!

Can you guess what these plots might represent? If yes, can you name the guideline(s) leading to them?  :cool:

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2014-10-23 22:37
(3443 d 13:09 ago)

@ Helmut
Posting: # 13782
Views: 10,461
 

 Riddle

Not a specialist, but: two-stage design, alpha max inflation, depending on sample size in stage 1 and 2?

Kindest regards, nobody
Helmut
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2014-10-23 22:58
(3443 d 12:48 ago)

@ nobody
Posting: # 13783
Views: 10,482
 

 Riddle

Ὀδυσσεύς

Not a specialist, but: two-stage design, alpha max inflation, depending on sample size in stage 1 and 2?


Nice try. ;-) Two-Stage Designs are never that bad like the upper panel. Hint:

\(\small{\alpha=0.05,\;k=2}\)
\(\small{p_1=1-(1-\alpha)^k}\)
\(\small{p_2=1-(1-\alpha/k)^k}\)


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ElMaestro
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Denmark,
2014-10-24 00:47
(3443 d 10:58 ago)

@ Helmut
Posting: # 13784
Views: 10,401
 

 A wild guess

Hi Hötzi,

A wild guess: I think you are fiddling around with WHO Technical Report Series, No. 937, annex 7 (Multisource BlahDeeBlah),
specifically you might be looking at section 6.3.2: "If the bioequivalence study was performed with the appropriate number of subjects but bioequivalence cannot be demonstrated because of a larger than expected random variation or a relative difference, an add-on subject study can be performed using not less than half the number of subjects in the initial study, provided this eventuality was anticipated and provided for in the study protocol."
as well as 6.11.3: "the total sample size of the initial bioequivalence study is not less than 20 (n = 10/group) or pooled sample size of the initial and add-on subject studies is not less than 30;"

-which lend from the PMDA guidelines section 2.5.
In a nutshell you are trying to figure out how the overall alpha behaves for various scenarios, incl. adjusted alphas, anticipated to comply with the Japanese add-on recommendations.

Pass or fail!
ElMaestro
Helmut
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2014-10-24 01:08
(3443 d 10:38 ago)

@ ElMaestro
Posting: # 13785
Views: 10,400
 

 Partly solved

Ahoy!

❝ A wild guess: […]



Bingo!

❝ In a nutshell you are trying to figure out how the overall alpha behaves for various scenarios, incl. adjusted alphas, anticipated to comply with the Japanese add-on recommendations.


That is not correct. No adjustment in 日本. Tried to convince them. No success.

So you got 50/100 points. What about the lower panel?

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ElMaestro
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Denmark,
2014-10-24 01:19
(3443 d 10:27 ago)

@ Helmut
Posting: # 13786
Views: 10,481
 

 Partly solved

Oh...

That is not correct. No adjustment in 日本. Tried to convince them. No success.


❝ So you got 50/100 points. What about the lower panel?


Oh...lemmefink.... so you did not adjust alpha but did just use 0.05 and 0.025...Upper versus lower panels show that if you pick a common alpha for both the main and the add-on then the applicable alpha will fall between 0.05 and 0.025 if convergence towards 0.05 is a goal. Paste some curves to show us how Pocock's alpha of ~0.0294 or somethink like that will give curves that converge towards 0.05 overall, please?

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ElMaestro
Helmut
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2014-10-24 01:27
(3443 d 10:19 ago)

@ ElMaestro
Posting: # 13787
Views: 10,387
 

 Partly solved

O-hoy!

❝ so you did not adjust alpha but did just use 0.05 and 0.025...

[image]

❝ Upper versus lower panels show that if you pick a common alpha for both the main and the add-on

[image]

❝ then the applicable alpha will fall between 0.05 and 0.025 if convergence towards 0.05 is a goal.

[image]

Read the second sentence of my OP again.

❝ Paste some curves to show us how Pocock's alpha of ~0.0294 or somethink like that will give curves that converge towards 0.05 overall, please?

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ElMaestro
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Denmark,
2014-10-24 01:37
(3443 d 10:09 ago)

@ Helmut
Posting: # 13789
Views: 10,304
 

 Partly solved

Hmmm,

❝ ❝ then the applicable alpha will fall between 0.05 and 0.025 if convergence towards 0.05 is a goal.

[image]


I still believe that conclusion would be valid if the purpose were to identify the common alpha level that would preserve convergence at overall alpha 0.05, even though your perspective happens to be another (assuming your curves are correct, of course).
What second sentence - are we missing some guideline stuff?

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ElMaestro
Helmut
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2014-10-24 02:20
(3443 d 09:26 ago)

@ ElMaestro
Posting: # 13791
Views: 10,394
 

 Partly solved

Hoho-hoy!

❝ ❝ ❝ then the applicable alpha will fall between 0.05 and 0.025 if convergence towards 0.05 is a goal.

❝ ❝ [image]


❝ I still believe that conclusion would be valid if the purpose were to identify the common alpha level that would preserve convergence at overall alpha 0.05,…


Yep. But this is an answer to a question I didn’t ask.

❝ … even though your perspective happens to be another (assuming your curves are correct, of course).


Well, the second one would lead to Bonferroni’s correction, which is related to…

❝ … are we missing some guideline stuff?


Now you got it. The first GL (upper panel) screws up whereas the second one (lower panel) doesn’t.

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d_labes
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Berlin, Germany,
2014-10-24 15:13
(3442 d 20:33 ago)

@ Helmut
Posting: # 13797
Views: 10,262
 

 Solved?

Dear Helmut,

❝ ... The first GL (upper panel) screws up whereas the second one (lower panel) doesn’t.


Let me try:
Second one: Canada.

Regards,

Detlew
Helmut
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2014-10-24 15:19
(3442 d 20:27 ago)

@ d_labes
Posting: # 13798
Views: 10,378
 

 99 points!

Dear Detlew,

❝ Let me try:

❝ Second one: Canada.


99 p(o)ints! It was stated in the 2009 draft, but they dropped it in the current (2012) guidance.

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ElMaestro
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Denmark,
2014-10-24 16:19
(3442 d 19:27 ago)

@ Helmut
Posting: # 13799
Views: 10,404
 

 For the tough

Hi all,

to round this off, can it be mathematically proven that upper type 1 error asymptotes exist for any level of common alpha smaller than 1?

I bet that should be possible, too. I'd love to see how. I imagine that to deliver the proof one would have to one way or another get aorund to Owen's Q and non-central t. So I am very certain that would improve yours truly's understanding of statistics for BE.

Pass or fail!
ElMaestro
Helmut
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2014-10-24 16:54
(3442 d 18:52 ago)

@ ElMaestro
Posting: # 13801
Views: 10,334
 

 For the tough ones

Hi ElMaestro,

❝ to round this off, can it be mathematically proven that upper type 1 error asymptotes exist


Yes. At least this is what my stats friends told me. Note that Bonferroni is the most conservative method in adjusting for multiplicity.*
IMHO, you could gain a little solving the quadratic equation \(\small{1-(1-x)^2=\alpha}\), which leads for α 0.05 to \(\small{(2-\sqrt{4-4\alpha})/2=0.02532057\ldots}\)
Others (f.i. Holm, Hochberg) are less conservative but may lead to a CI which doesn’t include the PE any more. Counterintuitive, but my stats friends just smile about it. See also EMA’s 2012 workshop on multiplicity. If you – really! – have nothing better to do, watch the six (‼) hours of video.

❝ for any level of common alpha smaller than 1?


Smaller than one?

❝ I bet that should be possible, too. I'd love to see how. I imagine that to deliver the proof one would have to one way or another get aorund to Owen's Q and non-central t. So I am very certain that would improve yours truly's understanding of statistics for BE.


Yep. People are working on it (for three years now)…


  • Since I’m not gifted with enough knowledge to proof anything I can only offer extreme simulations:

    library(Power2Stage)
    power.2stage.GS(alpha=rep(0.025, 2), n=c(10, 100000),
      CV=0.05, theta0=1.25, fCrit="PE", fClower=0, nsims=1e7)

    TSD with 2x2 crossover
     non-adaptive group sequential with
    alpha (s1/s2) = 0.025 0.025
    No futility criterion
    BE acceptance range = 0.8 ... 1.25

    CV= 0.05; n(s1, s2)= 10 1e+05

    1e+07 sims at theta0 = 1.25 (p(BE) = TIE 'alpha').
    p(BE)    =
    0.0493985
    p(BE) s1 = 0.0250372
    Studies in stage 2 = 97.5%


    That’s pretty close to what we would expect from Bonferroni (0.049375).
    The Japanese stuff gives me 0.0975317 (expected 0.0975).

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2014-10-24 16:25
(3442 d 19:21 ago)

@ Helmut
Posting: # 13800
Views: 10,305
 

 99 points!

Bonferroni in a Guidance! Wow! Didn't know that!

Kindest regards, nobody
Helmut
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2014-10-24 17:01
(3442 d 18:45 ago)

@ nobody
Posting: # 13802
Views: 10,251
 

 99 points!

❝ Bonferroni in a Guidance! Wow! Didn't know that!


Gone with the Wind…

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