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khaoula
Junior

Algeria,
2014-09-27 11:14

Posting: # 13600
Views: 12,136
 

 minimum number of subject in bioequivalence study [Power / Sample Size]

Hi everybody,

I have two questions:
  • Why the minimum simple size fixed by all regulatory authorities is 12? because when we consult the table of Sample Size for Schuirmann’s Two One-Sided t-Tests Procedure, we note that for low CV <15% the number of subject required is < 12?
  • in pilot study, we need small simple size, but could it be greater than 12?
thank you
ElMaestro
Hero

Denmark,
2014-09-27 11:26

@ khaoula
Posting: # 13601
Views: 10,819
 

 minimum number of subject in bioequivalence study

Hello Khaoula,

» – Why the minimum simple size fixed by all regulatory authorities is 12? because when we consult the table of Sample Size for Schuirmann’s Two One-Sided t-Tests Procedure, we note that for low CV <15% the number of subject required is <12?

You're right you might get good level of power for N<12 but regulators have decided to set a limit and they set that limit at 12. Not sure there is a really good reason, but that's just the way it is.

» – in pilot study, we need small simple size, but could it be greater than 12?

Pick any number you like. But be aware that the value of a pilot study tends to be limited if you have few subjects. In this regard it is impossible to tell what "few" really means - that would depend on the actual GMR, its CV and the purpose of the pilot. Therefore, I'd say use as many subjects in the pilot as you can within the meaning of ethics and budgets and everything else.

if (3) 4

Best regards,
ElMaestro

"(...) targeted cancer therapies will benefit fewer than 2 percent of the cancer patients they’re aimed at. That reality is often lost on consumers, who are being fed a steady diet of winning anecdotes about miracle cures." New York Times (ed.), June 9, 2018.
khaoula
Junior

Algeria,
2014-09-27 23:49

@ ElMaestro
Posting: # 13602
Views: 10,765
 

 minimum number of subject in bioequivalence study

thank you ElMaestro!!!!

for minimum number of subject: it's not about possible significant treatment effect with low nuber of subject, low CV?
Helmut
Hero
avatar
Homepage
Vienna, Austria,
2014-09-28 01:13

@ khaoula
Posting: # 13603
Views: 10,810
 

 “Overpowered” studies due to GLs

Hi Khaoula,

» for minimum number of subject: it's not about possible significant treatment effect with low nuber of subject, low CV?

Likely. Let’s assume a 2×2 cross-over, T/R-ratio 0.95, n=12. For any CV ≤15.63% power will be >80%, for CV ≤13.39% >90%, for CV ≤9.85% >99%, etc. etc.
The lowest CVs I have seen so far were 5–7% (AUCs of valproic acid, methylphenidate). If you perform a study with a drug showing a CV of 6% in 12 subjects, power will be 99.99993%. In other words, a significant treatment effect is highly probable. See this presentation (slide 9): The red diamonds are sample sizes to reach at least 80% power. If you keep the sample size at 12 for low CVs, power will increase extremely (blue line).

BTW, the minimum sample size of 12 is arbitrary; some tables1,2 go down to 4.


  1. Diletti E, Hauschke D, Steinijans VW. Sample size determination for bioequivalence assessment by means of confidence intervals. Int J Clin Pharm Ther Toxicol. 1991;29(1): 1–8. PMID 2004861.
  2. Hauschke D, Steinijans VW, Diletti E, Burke M. Sample Size Determination for Bioequivalence Assessment Using a Multiplicative Model. J Pharmacokin Biopharm. 1992;20(5):557–61. PMID 1287202.

Cheers,
Helmut Schütz
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khaoula
Junior

Algeria,
2014-09-28 22:36

@ Helmut
Posting: # 13610
Views: 10,647
 

 “Overpowered” studies due to GLs

Hi Helmut,
thank you for your answer, so 12 subjects it's a sure way to have "sufficient" and large power, if perhaps CV of the study is larger than planed (for small values of CV), the number of subject will be sufficient to prove bioequivalence
Helmut
Hero
avatar
Homepage
Vienna, Austria,
2014-09-29 03:51

@ khaoula
Posting: # 13612
Views: 10,695
 

 “Overpowered” studies due to GLs

Hi Khaoula,

» […] so 12 subjects it's a sure way to have "sufficient" and large power, if perhaps CV of the study is larger than planed (for small values of CV), the number of subject will be sufficient to prove bioequivalence

Correct. On the other hand it will allow to show BE with a PE far away from 100%. With a CV of 6% in 12 subjects we will still have 70% power to demonstrate BE with a PE of 84.7%… I don’t comment on whether this is a good idea.
Regulators move in mysterious ways.

Cheers,
Helmut Schütz
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mreyes
Junior

México,
2014-11-07 19:47
(edited by mreyes on 2014-11-07 19:57)

@ Helmut
Posting: # 13843
Views: 10,273
 

 Scientific Validation for the Sample Size Formula

Dear Helmut and everybody! Sorry if I posted my question on the wrong place (first time posting on this forum). I used the formula presented on slides 25-26 (link below) on a clinical protocol as justification for sample size calculation and the mexican regulatory agency asked for a scientific justification or a bibliography where the robustness of the formula can be proved/demosntrated. Do you have the specific reference of this? Thanks in advance, regards

Monica

» See this presentation (slide 9)
Helmut
Hero
avatar
Homepage
Vienna, Austria,
2014-11-07 20:09

@ mreyes
Posting: # 13844
Views: 10,263
 

 Basic maths

Hi Monica,

» Sorry if I posted my question on the wrong place (first time posting on this forum).

No problem; welcome to the club!

» I used the formula presented on slides 25-26 on a clinical protocol as justification for sample size calculation and the mexican regulatory agency asked for a scientific justification …

Oh no! I derived it on my own ages ago. That’s 8th grade maths. Any 14 year old kid should be able to do it. I’m not aware of any reference.

» … or a bibliography where the robustness of the formula can be proved/demosntrated.

The formula is exact if the study is balanced (nTR = nRT = ½N). Sometimes you don’t know whether a study was balanced (only the total number of completers given). If N is odd, it was imbalanced for sure. If N is even, you have no clue. Have a look at my example (slide 29). The study was extremely imbalanced (16:8) and the true CV 24.74%. But you don’t know that (only N 24 given). For any given combination of subjects in sequences you would estimate a CV which is higher than the true one. In other words, if you plan a study based on the estimate the sample size will be higher than required. You loose money, but don’t risk to be underpowered.

Cheers,
Helmut Schütz
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mreyes
Junior

México,
2014-11-07 20:47

@ Helmut
Posting: # 13845
Views: 10,223
 

 Basic maths

Thank you Helmut for your soon and kind answer.! ;-)

» » Sorry if I posted my question on the wrong place (first time posting on this forum).
»
» No problem; welcome to the club!
Helmut
Hero
avatar
Homepage
Vienna, Austria,
2014-12-14 01:51

@ mreyes
Posting: # 14070
Views: 9,911
 

 Reference for CI ⇒ MSE

Hi Monica,

» […] the mexican regulatory agency asked for a scientific justification or a bibliography where the robustness of the formula can be proved/demosntrated. Do you have the specific reference of this?

Nothing about robustness yet, but by chance I found a reference* in my files “[…] how to retrieve residual intrasubject mean squared error from historical summary results in the literature.” ;-)
Given in the Examples 2–4: 90% CI 0.83–1.15, N 30
  • paired design; calculated intrasubject MSE 0.1381.
  • 2×2 crossover; calculated intrasubject MSE 0.1378.
  • 6×3 Williams’ design; calculated intrasubject MSE 0.1425.
Detlew Labes implemented my formulas in the R package PowerTOST, function CI2CV(). With this little code

library(PowerTOST)
LL  <- 0.83
UL  <- 1.15
N   <- 30
des <- c("paired", "2x2x2", "3x6x3")
for (j in seq_along(des)) {
  cat(sprintf("%6s design: intrasubject MSE %.4f%s", des[j],
              CV2mse(CI2CV(lower=LL, upper=UL, n=N, design=des[j],
              alpha=0.05)), "\n"))
}


I got…

paired design: intrasubject MSE 0.1381
 2x2x2 design: intrasubject MSE 0.1378
 3x6x3 design: intrasubject MSE 0.1425


… matching results of the reference.

Hope it’s not too late for the authority…


  • Yuan J, Tong T, Tang M-L. Sample Size Calculation for Bioequivalence Studies Assessing Drug Effect and Food Effect at the Same Time With a 3-Treatment Williams Design. Ther Innov Regul Sci. 2013;47(2):242–7. doi:10.1177/2168479012474273.

Cheers,
Helmut Schütz
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mreyes
Junior

México,
2015-02-19 19:50

@ Helmut
Posting: # 14464
Views: 8,766
 

 Reference for CI ⇒ MSE

Ohh! Excellent example, I answered the authority request saying that this is a direct derivation from the original formula and added an example. Guess that was enough because I haven´t had any other comment.

Another question, Is it correct to use a reference with results out of the limits of IC 90%?, I mean not in 80-125% but with power > 80% for do the maths to get a simple size?

Thanks again!

Monica
Helmut
Hero
avatar
Homepage
Vienna, Austria,
2015-02-20 19:09

@ mreyes
Posting: # 14479
Views: 8,710
 

 Failed study: power <80%!

Hi Monica,

» Guess that was enough because I haven´t had any other comment.

Fine.

» Another question, Is it correct to use a reference with results out of the limits of IC 90%?, I mean not in 80-125% but with power > 80% for do the maths to get a simple size?

I’m not sure whether I understand you correctly: Do you mean a study where at least one of the confidence limits is outside the acceptance range (e.g., 99–127%)? You could never get a power of 80% in such a case. However, the formula still works.

Cheers,
Helmut Schütz
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mreyes
Junior

México,
2015-02-23 17:07

@ Helmut
Posting: # 14490
Views: 8,602
 

 Failed study: power <80%!

Hi Helmut, thanks again for your soon answer!

» I’m not sure whether I understand you correctly: Do you mean a study where at least one of the confidence limits is outside the acceptance range (e.g., 99–127%)? You could never get a power of 80% in such a case. However, the formula still works.

I'm sorry if I didn't get it correctly, but this is what I mean
http://www.gsk-clinicalstudyregister.com/files2/b966a5e8-d233-41ed-8c23-adeefba4f782

Best regards,

Monica
Helmut
Hero
avatar
Homepage
Vienna, Austria,
2015-02-23 17:38

@ mreyes
Posting: # 14491
Views: 8,560
 

 Reported 99.98%, correct 1.4%

Hi Monica,

» I'm sorry if I didn't get it correctly, but this is what I mean […]

Excuse my French, but this synopsis is crap. The CV for free ezetimibe’s AUC0-t is 20.5% (assuming 25/24 subjects in the sequences). Bloody irrelevant post hoc power is ~1.4% – not 99.98%!

Try:

library(PowerTOST)
lower <- 0.7295
upper <- 0.8372
n     <- 49
GMR   <- sqrt(lower*upper)
CV    <- CI2CV(lower=lower, upper=upper, n=n)
cat(" CV =", round(CV*100, 1), "%\n",
"Power =", round(power.TOST(CV=CV, theta0=GMR, n=n)*100, 1), "%\n")


BTW, do you think that it makes sense to report the AUC with eight significant digits?

Cheers,
Helmut Schütz
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ElMaestro
Hero

Denmark,
2015-02-23 17:51

@ Helmut
Posting: # 14492
Views: 8,494
 

 Reported 99.98%, correct 1.4%

Hi mreyes,

I think I got your question. It is often safe enough to assume the CV from another trial when you believe you can match the conditions, but of course you should not make assumptions about your (true) GMR on basis of a literature reference.
Therefore, I would do a dissolution trial or whatever you have available and judge the GMR from it, and secondly I would make an assumption about the CV from a published document, regardless of whether that document involved a failed trial or a successful one. Of course if you have concern about the validity of the reported CV then don't use it.

Hi Hötzi,
» Excuse my French, but this synopsis is crap. The CV for free ezetimibe’s AUC0-t is 20.5% (assuming 25/24 subjects in the sequences). Bloody irrelevant post hoc power is ~1.4% – not 99.98%!

Completely correct. Crap is the proper diplomatic term. They used GMR=1.00 and the observed CV for their calculation of post-hoc power. Therefore I don't know what the figure means and I am not aware of any reasonable use of such a figure.
Common sense seems to be in short supply these days.

if (3) 4

Best regards,
ElMaestro

"(...) targeted cancer therapies will benefit fewer than 2 percent of the cancer patients they’re aimed at. That reality is often lost on consumers, who are being fed a steady diet of winning anecdotes about miracle cures." New York Times (ed.), June 9, 2018.
Helmut
Hero
avatar
Homepage
Vienna, Austria,
2015-02-24 01:33

@ ElMaestro
Posting: # 14494
Views: 8,517
 

 GMR ∉ AR ⇒ power <5%

Hi ElMaestro,

» Completely correct. Crap is the proper diplomatic term. […] Common sense seems to be in short supply these days.

Rule of thumb: GMR at acceptance limit, sample size = ∞, vari­ance = 0, power = type I error ≤ 5%. :-D

Cheers,
Helmut Schütz
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mreyes
Junior

México,
2015-02-24 17:34

@ Helmut
Posting: # 14503
Views: 8,479
 

 GMR ∉ AR ⇒ power <5%

Thank you very much Helmut and ElMaestro.

» » Completely correct. Crap is the proper diplomatic term. […] Common sense seems to be in short supply these days.

This has been very lightener.

» Rule of thumb: GMR at acceptance limit, sample size = ∞, vari­ance = 0, power = type I error ≤ 5%. :-D

Excuse me for my poor english thanks for the effort to understand me. All your comments on this and other topics have been very helpful in my job. Best regards,

Monica
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