d_labes ★★★ Berlin, Germany, 20101005 15:09 Posting: # 5997 Views: 10,311 

Dear all, I have been questioned about the following design: The sponsor/experimenter has no sufficient information about CV and point estimate ('true' value) to be able to make an "educated" guess of the sample size for a BE study. Some distinct shift in the point estimator is expected. To save resources (its a fixed combination drug with 3 constituents, analytical expensive) he is not willing to do a pilot study and based on this a pivotal with BE decision not using the data from the pilot. Thus the design shall be a 2stage design. A first group of subjects (conception is 812) shall be dosed, analyzed and statistical evaluated. Based on the data (CV and point estimate) a final sample size shall be derived which will be utilized for the second stage. There is the idea of a formal extreme small alpha to spend after the first stage =0.001 (to conform EMA guideline). This will ensure with great probability that the second stage will be reached. Practical no stopping will occur by that. The only stopping rule is a maximum sample size constraint N_{max} the sponsor is willing to fund. If the estimated sample size after stage 1 is greater the second stage will not performed. Any body out there who knows how to handle such a design? Is there something to do to protect the overall alpha (lower nominal alpha at second stage)? Is the sample size estimation done as usually? Any input will be highly appreciated. — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20101025 19:16 @ Jack Posting: # 6078 Views: 9,468 

Dear Jack! » this is quite a complex question… True. » … to which I will add some more questions. Well, I think the applicability of commonly used methods is questionable, because of the different way the Null is formulated in BE studies. Just a quote from Potvin et al.,* after referring different approaches: Regardless, none of the methods are validated for crossover studies and two onesided ttests, so there is a need to start from the beginning in considering these approaches.
— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20101026 13:28 (edited by d_labes on 20101026 13:45) @ Jack Posting: # 6080 Views: 9,363 

Dear Jack, » this is quite a complex question ... Sure! Otherwise I had not asked . » The first and most important question in my mind is why not consider a single stage design with a sample size review at interim? So basically not allowing for the study to stop early (besides the sponsors constraint). This was the intention of the design described. But why do you call it single stage? The reason behind it was that for some constituent (its a FDC) the variability is not known at all. Each assumption about is only a delusion. Not to waste resources the pilot, usually performed in such circumstances, should included in the study (sometimes called internal pilot). The 'extreme' alpha to spend at stage 1 is only for compliance with the new EMA guidance which calls definitely for it, statistical sound or not. Just to cite page 16 to 17: "Twostage design ... If this approach is adopted appropriate steps must be taken to preserve the overall type I error of the experiment and the stopping criteria should be clearly defined prior to the study. The analysis of the first stage data should be treated as an interim analysis and both analyses conducted at adjusted significance levels (with the confidence intervals accordingly using an adjusted coverage probability which will be higher than 90%) ..." » The second choice one needs to make is if the sample size review is going to be blinded or not (note that I am ignoring any knowledge about a possible shift in point estimates). I'm not sure about this. Usually BE studies are performed with administration of the study medications in an open fashion. Why then make a blinded evaluation at interim? The interim sample size estimation is highly influenced by a shift in the point estimator. Especially the futility bound: Can we expect to prove BE with a N_{max} of 120 subjects with some prespecified power? An apriori difference in Cmax is expected due to the nature of the study products. Not considering it is like "Mit offenen Augen gegen eine Wand fahren" (to drive against a wall with open eyes). I'm on the same point of view as Helmut above. All I've read in the meantime is for groupsequential or adaptive designs for superiority trials with parallel groups, or at best some rare papers for noninferiority. Since the role of the Null and the Alternative are reversed in equivalence trials compared to superiority it is likely that the results obtained do not apply. Nevertheless, thanks for your input. — Regards, Detlew 
d_labes ★★★ Berlin, Germany, 20101027 16:01 @ Jack Posting: # 6090 Views: 9,260 

Dear Jack, » the reason I call this a onestage design is that I would not formally test for equivalence at the time were one does the sample size reestimation. Hence one would not need to spend any alpha at this time (as no testing is done and hence the EMA guide is not relevant) and hence no risk of the awkward situation that one could have to stop the trial early. I wonder if the EMA will seeing this the same way. Especially claiming that the EMA guideline is not relevant . » This is also the reason why doing the sample size reestimation in a blinded fashion can make sense as using unblinded data will question the onestage design. The questions is why? Can you explain why an unblinded evaluation will have any influence? All involved personal in an open study is unblinded. But the statistician should have a blindfold (this or better this one )? » As for the question: "Can we expect to prove BE with a N_{max} of 120 subjects with some prespecified power?" » » I dont really see the problem there. You are not arriving at a test decision about BE if you decide to stop because you would need more resources than you have and hence it is not impacting your typeIerror. Do you mean that the stopping the study due to exceeding N_{max} is not a decision about BE? I have thought up to now that this is equal to the decision: Given the data of the 'internal' pilot we can not expect to reject the Null: Bioinequivalence with reasonable resources. Thus we have to stay with the Null (aka accept H_{0}). In that direction I had understood hitting futility bounds in group sequential trials. Or am I here totally wrong? This is crucial in implementing a Monte Carlo simulation in which we would count 'BE' / 'not BE' to establish the type I and type II errors. As what shall I count hitting the futility criterion? 'Not BE' or a third answer? If you prefer a third, how to count them with respect to type I and type II errors (nominator/denominator)? — Regards, Detlew 
Ohlbe ★★★ France, 20101027 23:37 @ Jack Posting: # 6092 Views: 9,229 

Dear Jack, What's probably confusing to a number of people following this thread is what you exactly mean with "blind". In clinical trials this is usually meant as not knowing which treatment is administered to which patient/subject. In a BE trial this usually only applies to the bioanalytical lab. You can't run the statistical analysis without unblinding (even if you call the products A and B and don't tell the statistician which is the test and which is the reference, it won't make any difference). So to keep it short, a question from a nonstatistician: what do you exactly mean by blinded in this particular context ? Blinded to what ? Regards Ohlbe — Regards Ohlbe 
Astea ★ Russia, 20190530 10:37 @ Jack Posting: # 20305 Views: 2,410 

Dear Smart People! Digging forum posts I've found this 9year old question from Detlew. It turns out that the question can be now easily answered by the author after constructing Power2Stage. But can you clarify me the meaning of blindness in BE trials? I naively thought that blind interim analyses should not influence the typeone error. But comparing power.tsd.ssr(n1=10,CV=0.1,blind=FALSE,theta0=1.25) and power.tsd.ssr(n1=10,CV=0.1,blind=TRUE,theta0=1.25) it turns out that blinding may even worse the situation (5.01% vs 7.36%, TIE). It is connected with the unknown PE (cause for BLIND=TRUE s20s<mses ), but isn't it contrintuitive?Can it be true for parallel design also? Suppose we want to make a blind interim analyses after first stage with N subjects and recalculate sample size on fixed GMR=0.95 if total CV would be greater than initial suggestion. Will it cause any inflation? How to estimate it? — "We are such stuff as dreams are made on, and our little life, is rounded with a sleep" 
Helmut ★★★ Vienna, Austria, 20190530 12:56 @ Astea Posting: # 20306 Views: 2,378 

Hi Nastia, » But can you clarify me the meaning of blindness in BE trials? You know its meaning. Never seen ones, except for Health Canada: 2.4.2 Blinding That’s a funny idea if the products don’t look the same. » […] it turns out that blinding may even worse the situation (5.01% vs 7.36%, TIE). It is connected with the unknown PE (cause for BLIND=TRUE s20s<mses ), but isn't it contrintuitive?Yes and yes. Have a look at Figure 1 of Golkowski et al.* » Can it be true for parallel design also? Suppose we want to make a blind interim analyses after first stage with N subjects and recalculate sample size on fixed GMR=0.95 if total CV would be greater than initial suggestion. Will it cause any inflation? Possibly. » How to estimate it? Simulations… Might be tricky cause we have to think about unequal group sizes and/or variances. BTW, do you remember Paola Coppola’s presentation at last year’s BioBridges?
— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
Astea ★ Russia, 20190531 14:36 (edited by Astea on 20190531 22:51) @ Helmut Posting: # 20308 Views: 2,350 

Dear Helmut! Thank you for pointing on the article! I've tried to draw a graph similar to Figure 1 of Golkowski et al. by using power.tsd.ssr . It uses CV instead of N of the second size, but the tendency is pretty similar: low sample size of the first stage can significantly enlarge the TIE.» Simulations… Might be tricky cause we have to think about unequal group sizes and/or variances. Is it possible to do it with Power2Stage or some modifications? (As I understand power.tsd.p deals with unblind scheme?) The coauthors of the aforementioned article have also an article dedicated to the parlallel groups but relatively to noninferiority trials...— "We are such stuff as dreams are made on, and our little life, is rounded with a sleep" 
Helmut ★★★ Vienna, Austria, 20190602 20:14 @ Astea Posting: # 20311 Views: 2,302 

Hi Nastia, I don’t get your subject line. Do you mean that Golkowski’s Figure 4 resembles SaintExupéry’s Drawing № 2 in Le Petit Prince (cutoff a boa constrictor showing its last meal, an elephant)? Or are you referring to this one? With four parameters I can fit an elephant, and with five I can make him wiggle his trunk. John von Neumann — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
Astea ★ Russia, 20190603 01:47 @ Helmut Posting: # 20312 Views: 2,265 

Dear Helmut! » I don’t get your subject line. Do you mean that... I am very sorry for confusing! (neither of them, but I really love your way of thinking!!) It has to mean "Blind men and an elephant", a parable about how difficult is to find the truth if you have only limited data . That was about parallel blind studies. » Simulations… Might be tricky cause we have to think about unequal group sizes and/or variances. As far as I understood from an article by A. Fuglsang*, heteroscedasticity should not cause problems. But for blind studies CV_{average} (that is not distinguishing treatments) is not equal to CV_{pooled}, how to deal with it? Is there a way to prove a possibility of inflation in blind parallel studies?

d_labes ★★★ Berlin, Germany, 20190605 12:23 @ Astea Posting: # 20317 Views: 2,185 

Dear Astea, » ... But for blind studies CV_{average} (that is not distinguishing treatments) is not equal to CV_{pooled}, how to deal with it? Is there a way to prove a possibility of inflation in blind parallel studies? Not with the tools available in Power2Stage. But others have done the Job for you. Friede T., Kieser M. Sample size adjustment in clinical trials for proving equivalence Drug Information Journal, Vol. 35, pp. 1401–1408, 2001 doi:00928615/2001 Citing page 1407: ... the computation of the actual level of the onesided tests can be done following the lines of Kieser and Friede (unpublished data; 2001). The basic idea is the same as in the unblinded case. However, calculations are more complex and will, therefore, be omitted here. In all situations considered in Kieser and Friede (unpublished data, 2001), the inflation of the significance level was smaller than 0.0001. Therefore, no adjustment of the nominal significance level is necessary for the two onesided tests procedure in case of blinded sample size adjustment. It's a little bit annoying that they reference themselves and with "unpublished data" but nevertheless ... — Regards, Detlew 
Astea ★ Russia, 20190606 00:55 @ d_labes Posting: # 20318 Views: 2,149 

Dear Detlew! » It's a little bit annoying that they reference themselves and with "unpublished data" but nevertheless ... Thank you very much for the article! Ok, let us trust the authors until someone will prove it independently! By the way, I've found another article of this series, dedicated not to equivalence but to equality, as I understood: Bristol D.R., Shurzinske L. Blinded Sample Size Adjustment. Drug Information Journal, Vol. 35, pp. 1123–1130, 2001. doi:10.1177/009286150103500409. Disclaiment: the subject line of the post doesn't intend to confuse anyone and should refers to Pieter Bruegel the Elder and another parable about blindness and the truth :) 