Dr_Dan ★★ 20150624 13:55 Posting: # 14974 Views: 20,970 

Dear all From a leading European regulatory authority I just recieved the information that a 3period full replicate design (two sequences: TRT and RTR) for a bioequivalence study will not be accepted. The reason is that for a full replicate design R as well as T need to be replicated and this is only possible with the respective sequences (so TTRR etc.). A 3period full replicate design would result only in two parallel separate groups (one which – apart from the integrated 2period crossover– only get Test and the other only Reference); an evaluation would probably only possible as a general 2period crossover study. Please excuse the confusing explanation but the text set in italic is the verbal translation from what I received.My interest is just of academic nature: What should one reply to this attitude? Looking forward to your replies and to a fruitful discussion. Kind regards Dr_Dan Edit: Category changed from Design Issues. I think this category fits better – especially if one is interested in referencescaling. [Helmut] — Kind regards and have a nice day Dr_Dan 
ElMaestro ★★★ Denmark, 20150624 14:11 @ Dr_Dan Posting: # 14975 Views: 19,371 

Hi Dr_Dan, » My interest is just of academic nature: What should one reply to this attitude? How about something like: "From a statistical perspective the added value of a fully replicated trial, in contrast to a semireplicated trial, is that it contributes direct information about the withinsubject variability for the Test product. This information has, however, in its own right no regulatory use because:
— I could be wrong, but... Best regards, ElMaestro 
Helmut ★★★ Vienna, Austria, 20150624 14:29 @ Dr_Dan Posting: # 14976 Views: 19,590 

Dear Dan, this statement is outright bizarre (politely speaking). » What should one reply to this attitude? Suggest the “leading European regulatory authority” to read some stuff (»Lesen bildet!«). One of the authors (László Tóthfalusi) is a former member of the PKWP and another one (Alfredo GarcíaArieta) still is:
Edit (after reading the authority’s statement again): » A 3period full replicate design would result only in two parallel separate groups (one which […] only get Test and the other only Reference) […] I beg your pardon? _{} Sequence 1: TRT only Test? Sequence 2: RTR only Reference? » an evaluation would probably only possible as a general 2period crossover study What? Throw away the data of the third period? They don’t get the terminology right and mix up groups with sequences. If I follow this logic, they could also say: A 2period crossover design would result in two separate groups (one which gets Test and Reference in the order TR and the other one in the order RT); an evaluation would probably only possible as two separate paired designs – assuming no period effects. Gimme a break.— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
d_labes ★★★ Berlin, Germany, 20150624 14:38 @ Dr_Dan Posting: # 14977 Views: 19,335 

Dear Dr_Dan! » From a leading European regulatory authority I just recieved the information that a 3period full replicate design (two sequences: TRT and RTR) for a bioequivalence study will not be accepted. The reason is that for a full replicate design R as well as T need to be repclicated and this is only possible with the respective sequences (so TTRR etc.) ... Seems the story "Potvin C is not valid in Europe" is duplicated here on another field! The full replicate 3period design has the sequences TRT / RTR as is stated in your post and of course has T and R replicated. Not in each subject, but if balanced in half of ntotal each. And this design of course allows the evaluation of the intrasubject variabilities of T and R separately.So what's the problem of the "leading European regulatory authority"? Especially in the light of ElMaestro's remark that only the intrasubject variability of R is of any regulatory concern if scaled ABE is aimed for . — Regards, Detlew 
Dr_Dan ★★ 20150624 16:43 @ d_labes Posting: # 14978 Views: 19,261 

Dear Detlew » The full replicate 3period design has the sequences TRT / RTR as is stated in your post and of course has T and R replicated. Not in each subject, but if balanced in half of ntotal each. And this design of course allows the evaluation of the intrasubject variabilities of T and R separately.I think the question is whether a replication in only half of ntotal is sufficient in order to scale or ??? » So what's the problem of the "leading European regulatory authority"? » Especially in the light of ElMaestro's remark that only the intrasubject variability of R is of any regulatory concern if scaled ABE is aimed for . With regard to ElMaestro's reply: in a former statement the "leading European regulatory authority" had no problem with full replicate design (=4 periods and 6 possible sequences) and half replicate designs (3 periods and 3 sequences). A full replicate 3period design would not work according to their argumentation since a 3 period design implicity needs 3 sequences. I do not know why. Maybe you have an idea? Kind regards Dr_Dan — Kind regards and have a nice day Dr_Dan 
Helmut ★★★ Vienna, Austria, 20150624 18:00 @ Dr_Dan Posting: # 14979 Views: 19,499 

Dear Dan et alii, » I think the question is whether a replication in only half of ntotal is sufficient in order to scale or ??? Yes it is. Sometimes (!) you’ll need (slightly) more subjects.
Note that the partial replicate is a crappy design and sample size estimations are approximate at its best. For details see Detlew’s tractatus in your Rinstallion folder …\library\PowerTOST\Implementation_scaledABE_sims.pdf See also this thread. » in a former statement the "leading European regulatory authority" had no problem with full replicate design (=4 periods and 6 possible sequences)… Four periods and six sequences? Common are two (RTRTTRTR). Four were explored in the dark ages of PBE/IBE (RTRTTRTRRTTRTRRT). The analysis was tricky. Of course you could go even beyond that: RTRTTRTRRTTRTRRTRRTTTTRR. Have you really done that? » … and half replicate designs (3 periods and 3 sequences). Sure. That’s what they seem to believe to be the only possible one. » A full replicate 3period design would not work according to their argumentation since a 3 period design implicity needs 3 sequences. Crap. » I do not know why. You are not alone. » Maybe you have an idea? Maybe because the TRTRTR is not mentioned in the Q&A? Probably the “leading European regulatory authority” didn’t realize that the two designs given there are nothing more than examples. To illustrate [sic] these approaches, […] data from a fourperiod unbalanced study […] and data from a threeperiod balanced study […] were analysed. BTW, I disagree with our Captn’s arguments. » » From the perspective of the trial subject the burden associated with the fully replicated design is higher. Only if we compare a 4period design to 3period designs. The burden of particular subjects in the partial replicate and the fully replicated 3period is identical. Given the table above there are cases where less subjects are required in the fully replicated if compared to the partial replicate. » » Since the additional information obtained in a fully replicated trial does not contribute towards the average bioequivalence conclusion […] it is contended that the fully replicate design is associated with added risk but not additional benefit. In accordance with GCP clause 2.2 the fully replicated design therefore has no obvious merit. Well, that would imply:
— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
ElMaestro ★★★ Denmark, 20150624 18:11 @ Helmut Posting: # 14980 Views: 19,259 

Hi Hötzi and all, » BTW, I can’t follow our Captn’s arguments. I was too fast, I thought full replicate = four periods, and semireplicate = three periods (RTR, RRT, TRR) but I see now this was not the designs discussed here. I did not consider the option of full replicate in three periods. Consider my post above a highly relevant answer to a question that noone asked, please Who's got some publications about the performance of RTR / TRT? Do they exist? — I could be wrong, but... Best regards, ElMaestro 
Helmut ★★★ Vienna, Austria, 20150624 18:25 @ ElMaestro Posting: # 14981 Views: 19,432 

Ahoy! » I was too fast, A privilege of the youth. Note that the BEGL does not state a specific design, only: If an applicant suspects that a drug product can be considered as highly variable […], a replicate crossover design study can be carried out. » Who's got some publications about the performance of RTR / TRT? Do they exist? See the ones mentioned above. AFAIK, the last one was the basis for EMA’s approach; the paper introduced the term “ABEL” = Average Bioequivalence with Expanding Limits. All (!) simulations were performed for TRTRTR (for an example plot see this post). The TRTRTR is also mentioned in FDA’s Guidance (Appendix C, Table 3) in the context of IBE. Write a letter to László Endrényi asking him what he thinks about the partial replicate. Honestly, I don’t know why the partial replicate entered the European scene. Just because it was examined by the FDA before? Edit: After the concept paper on HVDs/HVDPs* was published in 2006, I suggested at conferences that agencies should collect real data and explore the performance of different methods. The data exist, since the prespecied widening of the acceptance range for C_{max} to 0.75–1.3333 also required a replicate design. Reaction: Nada, Zero, Τίποτα. The same people don’t getting tired to say “I don’t believe in simulations”, in the case of referencescaling do exactly this – rely entirely on them. OK, fine with me. But the sim’s were done for 3 and 4period fully replicated designs! @Dan: Ask the agency for the background of their statement.
‘Who controls the past,’ ran the Party slogan, — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
d_labes ★★★ Berlin, Germany, 20150625 08:52 @ Helmut Posting: # 14983 Views: 19,067 

Dear Helmut et al. I think it's a waste of time to discuss this bizarre opinion of a "leading European regulatory authority" in detail. Scientifically there is IMHO not a single argument to underpin this opinion. All details in Dan's quote are simply not true. Full stop. Unfortunately it seems that scientific arguments don't play a big role in some regulators "opinions". And much, much more unfortunately regulators don't have to justify their judgements . So what's left? Your tip: "Don’t select them as a RMS!" Another possibility would be to reactivate our Ol' pirate as a regulator BTW: The handling of the Concept paper on HVDs/HVDPs is revealing ... — Regards, Detlew 
ElMaestro ★★★ Denmark, 20150625 10:37 @ d_labes Posting: # 14985 Views: 19,016 

Haha, » So what's left? Your tip: "Don’t select them as a RMS!" » Another possibility would be to reactivate our Ol' pirate as a regulator I am already a bit reactivated but not in a role where I write the assessment reports. Perhaps that day will arrive, though... — I could be wrong, but... Best regards, ElMaestro 
d_labes ★★★ Berlin, Germany, 20150625 11:20 @ ElMaestro Posting: # 14988 Views: 19,058 

Dear ElMaestro, » I am already a bit reactivated ... Define a bit. Is it like a bit pregnant? — Regards, Detlew 
ElMaestro ★★★ Denmark, 20150625 11:54 (edited by ElMaestro on 20150625 12:16) @ d_labes Posting: # 14989 Views: 19,084 

Dear d_labes, » Define a bit. Is it like a bit pregnant? Yes. Of course there are rules for Conflicts of Interest. And they need to be observed and that is just ... not a problem at all despite the bureaucracy. The real challenge is that bureaucracy aside, in certain parts of the system (and pardon me, I will not define what that means in relation to this post) what matters is possibly not whether you are competent but whether you have the right friends. I have several times read reg. 2010/1235 (and of course also 2001/83 in its entirety) and so far without identifying clauses that allow interpersonal relations to prevail over science. Odd. Let it be said, that since I prefer not to define "system" above it is entirely possible that I am just reading the wrong legal framework. Besides, I am quite possibly not very competent myself. So I guess the answer is yes I am a little bit pregnant. Would like to add: There are many people on the inside who are really trying very hard and very wholeheartedly to keep the administration principles scientific. I feel we owe them our expression of gratitude – often they do not get the thanks they deserve. — I could be wrong, but... Best regards, ElMaestro 
d_labes ★★★ Berlin, Germany, 20150625 13:51 @ ElMaestro Posting: # 14990 Views: 19,043 

Dear ElMaestro, » So I guess the answer is yes I am a little bit pregnant. Many beer drinking people suffer from this. Especially man. Earlier or later ... » ... There are many people on the inside who are really trying very hard and very wholeheartedly to keep the administration principles scientific. I feel we owe them our expression of gratitude – often they do not get the thanks they deserve. Full ACK! — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20150626 13:51 @ Dr_Dan Posting: # 14993 Views: 19,301 

Dear Dan, » […] the question is whether a replication in only half of ntotal is sufficient in order to scale or ??? Adding to this post in the spirit of this thread: We could calculate the width of the confidence interval of the CV taking into account the sample size to achieve the desired power. Try this one (with the default T/R 0.9 and target power 0.8)… library(PowerTOST) … which gives
CV% 2×3×3: n  df  width 2×2×3: n  df  width 2×2×4: n  df  width Since the partial replicate (2×3×3) and the 3period full replicate (2×2×3) have the same degrees of freedom (2n–3), the winner (i.e., narrower width of the CI) is always the one with the larger sample size. The “best” designs (highest dfs ⇒ narrowest CI) formated in green (including the 4period full replicate, where df = 3n–4). But as Detlew correctly pointed out, the “precision” of the CV is not a requirement of the GL and all designs perform pretty similar. BTW, comparing variances (additionally to means) would need much higher sample sizes. This was one of the reasons why IBE was abandoned and the discussion point of the concept paper (see the end of this post) likely was not followed any further. The comparison of standard errors entered through the backdoor in FDA’s RSABE for NTIDs. Not only the acceptance range is scaled – which would mean 12 subjects for a CV of 7% (AR ~0.9–1.11), T/R 0.975, power 0.8… library(PowerTOST) … but the ratio of σ_{WT}/σ_{WR} must not exceed 2.5. Try library(PowerTOST) Due to the additional requirement and different implied limits (based on CV_{WR}) the sample size almost doubles to 22 – even if CVs are equal (σ_{WT} = σ_{WR} = 0.0699). If the ratio with 2 is close to the limit (σ_{WT} = 0.0884, σ_{WR} = 0.0442), we would need 142! Only if the test is much better (reversed ratio), the penalty almost vanishes (14 subjects). swt swr swt/swr CVwt CVwr CVwt/CVwr impl. limits n power Of course you could as well assume that only the CV_{WT} changes: swt swr swt/swr CVwt CVwr CVwt/CVwr impl. limits n power — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
d_labes ★★★ Berlin, Germany, 20150702 09:09 @ Helmut Posting: # 15014 Views: 18,474 

Dear Helmut! » library(PowerTOST) » CV < 0.07 » sep2s < function(CV, ratio=1) { # split CV to sratio » sp < CV2mse(CV) # pooled s² » # (1) (s²T + s²R)/2 = s² » # (2) sT/sR = ratio » # solve (1+2) for sT, sR » swt < sqrt(2)*sqrt(sp)*ratio/sqrt(ratio^2+1) » swr < sqrt(2)*sqrt(sp)/sqrt(ratio^2+1) » r < se2CV(c(swt, swr)) » r » } ... Sometimes it would be helpful to RTFM . Try library(PowerTOST) .Note that the ratio is here the ratio of variances.— Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20150702 13:03 @ d_labes Posting: # 15016 Views: 18,435 

Dear Detlew! » Sometimes it would be helpful to RTFM . Oh, I did. You will note that I hacked your code of CVp2CV() for my function sep2s() . » Note that the ratio is here the ratio of variances.Exactly. But I was interested in the ratio of standard errors instead.
Which gives:
— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
d_labes ★★★ Berlin, Germany, 20150702 14:21 @ Helmut Posting: # 15020 Views: 18,423 

Dear Helmut! Beg me pardon, seems a copypaste devil: » CV 0.07 split based on the SE ratio: 0.0886 0.0442 » variances: 0.00782 0.00196 ratio: 4 » standard errors: 0.0807 0.0571 ratio: 2 (?) What about: library(PowerTOST) Gives standard errors: [1] 0.0884356 0.0442178 — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20150702 14:33 @ d_labes Posting: # 15021 Views: 18,432 

Dear Detlew! » Beg me pardon, seems a copypaste devil: » » CV 0.07 split based on the SE ratio: 0.0886 0.0442 » » variances: 0.00782 0.00196 ratio: 4 » » standard errors: 0.0807 0.0571 ratio: 2 (?) Oops. Correct my code above from signif(se1, 3) to signif(se2, 3) which gives now:
Your solution is elegant as ever. I noticed the squaredstuff but failed to figure out how to code it. Would have saved me time (instead of solving these equations – rusty algebra). — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
zizou ★ Plzeň, Czech Republic, 20150705 19:20 @ Helmut Posting: # 15041 Views: 18,323 

Hi everybody and nobody. Firstly I have not many experiences with replicate designs, so I may be wrong. But I have doubts about the degrees of freedom in the post above. When we are calculating the withinsubject variability of the reference product (CV_{WR}). The ANOVA model is quite reduced, as EMA stated in Questions & Answers (with errors in red): The following code removes all the test data from the dataset and then fits a model where the residual variance corresponds to the within subject variance for the test product. data var; Of course there si no formulation effect. (For TRT/RTR design there is even no sequence effect because for this design R is replicated only in one sequence.) So I think, the degrees of freedom incoming to R function CVCL() should be changed (as shown in rows below with ">"): TRTRTR No questions about df of designs (namely df of MSE: 2n3 for 2x2x3, 2n3 for 2x3x3, 3n4 for 2x2x4). I'm only pointing to degrees of freedom used for function CVCL(). I don't know how much it will change the width of CI of CV_{WR}, so I am not making conclusions. But in general, TRTRTR design looks interesting, we get estimates of test and reference variability (each from half of subjects). But I am not convinced if there is right to compare (everyone can see) which variability T or R is higher, when it is comparison of CV_{WR} from the first n/2 group of subjects (one sequence) and CV_{WT} from the second n/2 group (second sequence, i.e. different subjects)  difference of T and R variability can be caused by different subjects  it looks like little bit as comparison of results from two studies performed in the same time/place/conditions with different subjects. Of course this comparison is not the goal of average BE, where we calculate GMR + 90% CI, but still many readers want to compare variabilities T versus R (maybe). For me this design looks like a "demo version" of the full replicate design TRTRRTRT with only half of subjects for expanding Cmax acceptance limits. Best regards, zizou 
d_labes ★★★ Berlin, Germany, 20150706 11:10 @ zizou Posting: # 15042 Views: 18,206 

Dear Zizou! Did you check the output from your SAS code against your degrees of freedom tables? Here an example: Scott Patterson and Byron Jones "Bioequivalence and Statistics in Clinical Pharmacology" Chapman and Hall/CRC Press: Boca Raton, London and New York, 2005 /*EXAMPLE 4.2*/ 74 subjects, 3 periods, sequences TRR/RTT, unfortunately unbalanced with 35/39 subjects PK metric Cmax without missings Your SAS code according to the EMA crippled model with Proc GLM gives: degrees of freedom The type III df=0 for sequence or the changing df for subjects effects illustrates the typical mess with the EMA model. Some differences to yours w.r.t. subject and total . Fortunately the df's for the intrasubject variability of the reference don't play a role in the EMA recommended method for scaling of the BE acceptance ranges. BTW: Your df's are correct for sequence balanced designs, if you use only the data for subjects with replicates of the Reference or if you evaluate via intrasubject contrasts like in the FDA recommended evaluation according to the progesterone guidance. — Regards, Detlew 
ElMaestro ★★★ Denmark, 20150706 11:59 @ d_labes Posting: # 15043 Views: 18,194 

Hi d_labes, » Your SAS code according to the EMA crippled model with Proc GLM gives: » degrees of freedom » source type I type III » The type III df=0 for sequence or the changing df for subjects effects illustrates the typical mess with the EMA model. I would like to offer an alternative view here: DF=0 for sequence may be correct cf. the ordinary interpretation of type III SS and the use of the bogus statement. What I absolutely do not get is that 72+1+34 is supposed to give 108? Or what am I overlooking, perhaps this is just the power to confuse. — I could be wrong, but... Best regards, ElMaestro 
d_labes ★★★ Berlin, Germany, 20150706 13:53 @ ElMaestro Posting: # 15044 Views: 18,140 

Dear ElMaestro! » What I absolutely do not get is that 72+1+34 is supposed to give 108? Approximately This is one of the deep secrets of _{} my little statistical understanding can't understand. But it must be true since SAS says so . » ... perhaps this is just the power to confuse. Absolutely correct. — Regards, Detlew 
zizou ★ Plzeň, Czech Republic, 20150706 17:25 @ d_labes Posting: # 15045 Views: 18,225 

Dear Detlew, I didn't try the code, so it was only what I expect in result (my mistake  I didn't write that for 2x2x3 replicate design I thought to filter data to only those used in GLM). For 3period 2sequence replicate design with R replicated only in one sequence I would use code: data var; (Instead of the code which I copied from EMA Q&A in my previous post. I think there is no reason to have sequence in the GLModel for this case. And I am used to see degrees of freedom in ANOVA table which are giving us with real number of cases in evaluation: (number of subjects in evaluation1) and (number of values in evaluation1) in total) In the example, due to we have 35 subjects in sequence with replicated R, I am expecting: source df However, it does not affect anything important. But if 72+1+34 results in total 108 (similar as 2+2=?, I think 5 is a very very good estimate, ... in accordance with the principles of doublethink "Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once"), I have no power to know (same as Winston Smith has). Btw. you are right about I did not include balance/unbalance option to table of dfs in my previous post (so it's true only for cases with no dropouts there). 
Helmut ★★★ Vienna, Austria, 20150723 23:54 @ Dr_Dan Posting: # 15139 Views: 17,643 

Dear Dan et alii, today the EMA published Rev. 12 of the Q&Adocument (dated 25 June). See #23 Suitability of a 3period replicate design scheme for the Given the commonly applied T/Rratio of 0.90 for HVD(P)s and ≥80% power this issue is practically not relevant. Full throttle for any study – unless you expect a lot (≥42%) of dropouts!
Parturient montes, nascetur ridiculus mus. Horace (Ars poetica, Ep.II.3, 139) — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
d_labes ★★★ Berlin, Germany, 20150724 08:23 @ Helmut Posting: # 15140 Views: 17,440 

Dear Helmut! » Parturient montes, nascetur ridiculus mus. Horace (Ars poetica, Ep.II.3, 139) Full ACK As every Pythia's saying: Mysterious! Nowhere in the scABEL method there is an term utilizing the 'uncertainty' of the variability of the reference. Contrary to the FDA RSABE which has such a term. That's the reason why both 3period designs (TRRRTRRRT or TRTRTR) require similar numbers of subjects. And deeming 12 subjects as sufficient to 'control' that 'uncertainty' is at least strange (politely spoken): library(PowerTOST) From no widening up to cap on widening! But the net effect is of course pleasing . — Regards, Detlew 