khaoula Junior Algeria, 20140927 11:14 Posting: # 13600 Views: 11,284 

Hi everybody, I have two questions:

ElMaestro Hero Denmark, 20140927 11:26 @ khaoula Posting: # 13601 Views: 9,998 

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 OneSided tTests 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. — I could be wrong, but… Best regards, ElMaestro  Bootstrapping for dissolution data is a relatively new hobby of mine. 
khaoula Junior Algeria, 20140927 23:49 @ ElMaestro Posting: # 13602 Views: 9,930 

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 Vienna, Austria, 20140928 01:13 @ khaoula Posting: # 13603 Views: 9,971 

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 crossover, T/Rratio 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 tables^{1,2} go down to 4.
— Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
khaoula Junior Algeria, 20140928 22:36 @ Helmut Posting: # 13610 Views: 9,823 

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 Vienna, Austria, 20140929 03:51 @ khaoula Posting: # 13612 Views: 9,869 

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. — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
mreyes Junior México, 20141107 19:47 (edited by mreyes on 20141107 19:57) @ Helmut Posting: # 13843 Views: 9,445 

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 2526 (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 Vienna, Austria, 20141107 20:09 @ mreyes Posting: # 13844 Views: 9,444 

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 2526 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 8^{th} 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 (n_{TR} = n_{RT} = 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. — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
mreyes Junior México, 20141107 20:47 @ Helmut Posting: # 13845 Views: 9,391 

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 Vienna, Austria, 20141214 01:51 @ mreyes Posting: # 14070 Views: 9,073 

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
PowerTOST , function CI2CV() . With this little code
I got…
… matching results of the reference. Hope it’s not too late for the authority…
— Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
mreyes Junior México, 20150219 19:50 @ Helmut Posting: # 14464 Views: 7,946 

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 80125% but with power > 80% for do the maths to get a simple size? Thanks again! Monica 
Helmut Hero Vienna, Austria, 20150220 19:09 @ mreyes Posting: # 14479 Views: 7,887 

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 80125% 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. — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
mreyes Junior México, 20150223 17:07 @ Helmut Posting: # 14490 Views: 7,770 

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.gskclinicalstudyregister.com/files2/b966a5e8d23341ed8c23adeefba4f782 Best regards, Monica 
Helmut Hero Vienna, Austria, 20150223 17:38 @ mreyes Posting: # 14491 Views: 7,728 

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 AUC_{0t} is 20.5% (assuming 25/24 subjects in the sequences). Bloody irrelevant post hoc power is ~1.4% – not 99.98%! Try:
BTW, do you think that it makes sense to report the AUC with eight significant digits? — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
ElMaestro Hero Denmark, 20150223 17:51 @ Helmut Posting: # 14492 Views: 7,672 

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 AUC_{0t} 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 posthoc 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. — I could be wrong, but… Best regards, ElMaestro  Bootstrapping for dissolution data is a relatively new hobby of mine. 
Helmut Hero Vienna, Austria, 20150224 01:33 @ ElMaestro Posting: # 14494 Views: 7,698 

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%. — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
mreyes Junior México, 20150224 17:34 @ Helmut Posting: # 14503 Views: 7,650 

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%. 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 