d_labes ★★★ Berlin, Germany, 20100305 11:51 (5028 d 23:31 ago) Posting: # 4864 Views: 26,458 

Dear all, after reading the tons of answers to the comments regarding the DRAFT of the new EMA Guidance I am more and more confused. As Helmut has already noted they insists on using ANOVA, ANOVA, ANOVA ... and nothing else in the statistical evaluation of bioequivalence (in SAS speak Proc GLM or for Rusers function lm()). And more over all effects in the ANOVA as fixed! Beside their joke "It is out of the scope of the guideline to give details on how to analyse the data of a replicate design, since it is standard statistical analysis " in the comments I would ask the community:
So how to react? How to proceed with replicate studies practically, technically ... to be EMA conform? — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20100305 15:17 (5028 d 20:05 ago) @ d_labes Posting: # 4866 Views: 23,848 

Dear D Labes! ❝ • From where do we get the intraindividual variabilities within Test or ❝ ❝ In a 2×2 design that's a main assumption. In replicate designs I'm not sure. ❝ • Can we have an evaluation that is not only EMA accepted? I don't think so. ❝ […] mixed model […] obsolete in the light of the new EMA guidance! ❝ So how to react? How to proceed with replicate studies practically, technically ... to be EMA conform? To be honest: not the slightest idea. I'm still trying to track down where the ANOVA comes from. Tóthfalusi et al. (2009) wrote in Section 6.1 (p 737):
Note the last two sentences! But as a statistical amateur I don't get the point looking at the referred paper: Hsuan FC, Reeve R. Assessing individual bioequivalence with highorder crossover designs: a unified procedure. Stat Med. 2003;22:2847–60. From the summary:The U.S. FDA's newly issued guidance on bioequivalence recommends the use of individual bioequivalence (IBE) for highly variable drugs and possibly for modified release dosage forms. The recommended approach to the analysis is to follow the methodology of Hyslop, Hsuan and Holder (HHH), based on a linear mixed model. A limitation of the HHH method is that it works only for uniform designs, such as RTRT/TRTR. In this paper, we present an alternative approach based on a multivariate model. The multivariate model is shown to be a strict superset of the linear mixed model and can successfully model data where the mixed model fails. Our multivariate approach coincides with the HHH method where the HHH method applies, but generalizes to any highorder crossover design, such as the Balaam design, RTR/TRT, and TRSS/RSTT/STRR. My emphasis. And on page 2858:
Too bad that WinNonlin's output states on top of each page
LINEAR MIXED EFFECTS MODELING ' by 'MULTIVARIATE ANOVA '; save file."— Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20100309 10:33 (5025 d 00:49 ago) @ Helmut Posting: # 4882 Views: 23,312 

Dear Helmut! Oh, oh the orouboros has beaten again! ❝ ... But as a statistical amateur I don't get the point looking at the referred paper: ❝ Hsuan FC, Reeve R. Assessing individual bioequivalence with highorder crossover designs: a unified procedure. Stat Med. 2003;22:2847–60. I must confess that I had not understand this paper at all, thus being less than an amateur ("Blutiger Laie" = raw recruit ). ❝ The method we proposed here has been implemented in a Pharsight™ product, WinNonlin^{®} (version 3.2 or later). Too bad I do not own WinNonlin. Can you eventually show some output of this method? What do you think about an adaption of J.P. Liu Use of the repeated crossover design in assessing bioequivalence Statist. Med. 14, 10671078 (1995) It has ANOVA tables but Liu term his model underlying the analysis "Mixed"! Mixed effects for subject and subject*formulation interaction. Without mixed effects the corresponding FTests would be others, I think. — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20100309 15:55 (5024 d 19:27 ago) @ d_labes Posting: # 4885 Views: 23,319 

Dear D Labes! ❝ Too bad I do not own WinNonlin. ❝ Can you eventually show some output of this method? Well, we had a comparison following this post. ❝ What do you think about an adaption of ❝ ❝ J.P. Liu ❝ Use of the repeated crossover design in assessing bioequivalence ❝ Statist. Med. 14, 10671078 (1995) Hhm, I don’t have it in my files yet. ❝ It has ANOVA tables but Liu term his model underlying the analysis "Mixed"! ❝ Mixed effects for subject and subject*formulation interaction. ❝ Without mixed effects the corresponding FTests would be others, I think. Mixed is the tabooword! Edit: Got the paper. It’s definitely a mixed effectsmodel. — Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20100311 12:07 (5022 d 23:15 ago) @ Helmut Posting: # 4894 Views: 23,820 

Dear Helmut, dear All, Meanwhile I have experimented a little bit with the ANOVA described in the Liu paper. I have taken Example 4.4 from the book Patterson, Jones "BIOEQUIVALENCE and STATISTICS in CLINICAL PHARMACOLOGY" Chapman & Hall / CRC 2006 a 4period study with the sequences TRTR and RTRT as the dataset (to be found here). [edit: /CRC WEB PAGE/chapter4/exam44.dat (Helmut)] The subjects with missing data were left out from the analyses. It took me some headache (and some beer ) to figure out how to formulate a Proc GLM ANOVA with the effects sequence, subject (within sequence), formulation, period and subjectbyformulation interaction. "Simple" attempts catched me often in the Type III sumofsquares trap. Here comes the code that worked without curiosities:
Proc GLM data=four; The random statement is only for letting SAS figure out the "appropriate" Ftests for the effects, because we all know meanwhile that Proc GLM is fitting the model as if all effects are fixed and the random statement only affects the Ftests, which in an allfixed model always have MS(error) as denominator. Results: ... Some points to consider:
BTW: Excuse this very long post, but I had no idea how to shorten. BTW2: The fixed effects story gets more and more curious for me. BTW3: If this ANOVA would be sufficient for the EMA we had also in SAS to follow Helmut's SOP with the adaption "delete Mixed model" . — Regards, Detlew 
d_labes ★★★ Berlin, Germany, 20100326 15:01 (5007 d 20:21 ago) @ Helmut Posting: # 4977 Views: 23,167 

Dear All! This should read in connection with my previous post in this thread. Helmut, I have posted to you because I otherwise had to post to myself. After touting the anticonservatism of the allfixedeffectsapproach of the Liu ANOVA and noticing the fact that omitting SxF results in the classical model, hopefully with SxF incorporated in the error term. I was interested in going the Bear way for replicate designs because meanwhile I hazard a guess that EMA is expecting this from us. Some little evidence:
S.A. Willavize, E.A. Morgenthin Comparison of models for average bioequivalence in replicate crossover designs Pharm. Stat. Volume 5 Issue 3, Pages 201  211 (2006) Published Online: 24 May 2006 The authors have simulated data of a TRTR/RTRT design distributed exactly according to the models underlying the evaluation methods, namely according to the classical model without any SxF interaction and some variants of including such an interaction. Various values of the involved variabilities were employed. For each setting 1500 datasets were simulated with 24 subjects. These data were then evaluated with each evaluation method. Here is a part of the results of evaluations with the classical model, also Proc Mixed was employed instead of Proc GLM (the Bear way): Probability of concluding BE at T/R = 0.8 (=alpha) model1=classical model model2=FDA model with SxF model3=EkbohmMelander (very similar to the Liu ANOVA) Although not mentioned exactly in the paper I suppose that the greatest anticonservatism / alphainflation occurred with drastic values of the SxF interaction. Seems the SxF component can not always incorporated into the error term of the simple classical evaluation. Of course the impact of these results depend on the belief if the SxF is a real phenomenon in bioequivalence studies. For instance in Endrenyi, Tothfalusi Subjectbyformulation interaction in determination of individual bioequivalence: Bias and prevalence Pharm. Res. 16 (1999), 186190 and others it is strongly argued against it in showing that the datasets used by FDA during evaluation of IBE are compatible with a SxF=0. — Regards, Detlew 
d_labes ★★★ Berlin, Germany, 20100329 18:17 (5004 d 18:06 ago) @ d_labes Posting: # 4986 Views: 23,078 

Dear All! Talking a little bit with myself for psychohygiene. After walking a while on the bear way, sun was shining , all was good, suddenly I came into a dark wood, to a big dark hole in which the threeheaded hydra resides. She was horrible looking, totally out of balance and equipped with dreadful mixed (un)expected means and (non)integer degrees of freedom . Quick I employed the famous bogus RANDOM statement of Proc GLM, which I was preventively armed with during this adventure, to inspect the expected mean squares of the data and to perform the 'appropriate' Ftests for banishing that beast arosen from the depth of moria . (Unfortunately the mightier Proc Mixed was prohibited to me by the custodians of the bearway on EMA territory.) Here the result: evaluation of example 4.2 from Patterson/Jones, a dataset from a 3period2sequence replicate crossover design with the sequences RTT (39 subjects) and TRR (35 subjects), without missing data. Classical Proc GLM, Cmax After I had survived this beastly monster due to my extrapowertoknow I had questions:
— Regards, Detlew 
ElMaestro ★★★ Denmark, 20100329 19:26 (5004 d 16:56 ago) @ d_labes Posting: # 4987 Views: 22,946 

Dear d_labes ❝ She was horrible looking, totally out of balance and equipped with dreadful mixed (un)expected means and (non)integer degrees of freedom . Hmmm, have you been smoking Schuetzomycin? ❝ Here the result: evaluation of example 4.2 from Patterson/Jones, a dataset from a 3period2sequence replicate crossover design with the sequences RTT (39 subjects) and TRR (35 subjects), without missing data. (...) I am completely lost, simply not at your level of insight. I don't know how to understand all this. Could you explain to a novice like me in slowmotion what you investigated and what you conclude and why? Many thanks for your thoughts, Best regards, EM. 
Helmut ★★★ Vienna, Austria, 20100329 20:41 (5004 d 15:41 ago) @ ElMaestro Posting: # 4988 Views: 23,299 

Ahoy! ❝ Hmmm, have you been smoking Schuetzomycin? What?! Schützomycin is an esoteric (aka undocumented) ingredient of modern preparations of _{Flying} Oint^{ment}. You don't smoke it, honey – its use is topical & delicate; believe me. ❝ ❝ Here the result: evaluation of example 4.2 from Patterson/Jones, a dataset from a 3period2sequence replicate crossover design (...) ❝ ❝ I am completely lost Well, Detlew is referring to a dataset we played with in the past. Since I’m not equipped with I’m lost in the details as well. Rumors are going that he’s on the track of evaluating a replicate study without a mixed model and all effects fixed. — Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20100330 11:20 (5004 d 01:02 ago) @ Helmut Posting: # 4992 Views: 23,141 

Gents! ❝ ... Schützomycin is an esoteric (aka undocumented) ingredient of modern preparations of _{Flying} Oint^{ment}. You don’t smoke it, honey – its use is topical & delicate; believe me. Ok, on my next leg along the Bear way I will take some dose of Schützomycin with me. Hopefully this will escape me from some more serious situations. ❝ ... Rumors are going that he’s on the track of evaluating a replicate study without a mixed model and all effects fixed. Yessss Sir, this is the Bear way, without lme() but rather lm() also known to SAS'lers as Proc GLM . And what I have observed in this adventure along the Bear way was to evaluate my original question Q2 above in this thread: How can we get the 'appropriate' tests (new BE guidance, page 16 "The ANOVA tables, including the appropriate statistical tests of all effects in the model, should be submitted.") within an ANOVA style evaluation. And I was very surprised with that finding as a statistical raw recruit. If it is real, and the right answer to a false question, it prevents us from using a test by hand of the sequence effect using simply the subject(sequence) MS as the error term because the mixture observed above depends on the degree of imbalance. Just to cite ElMaestro above, ooouch ..., below: "You still can get the effects right ... by considering all effects fixed. but you will have to do some manual brainwork still." I employed the RANDOM statement to save my small brain. I suppose a big amount of serious headache! For every new study, if using 3periodwhateversequence replicate design, if not totally balanced! Schützomycin to the rescue? BTW: In a bizarre twist, it's not allfixed but rather mixed as usual, but ANOVA, ANOVA, ANOVA ... BTW2: The Bear model is also used in Chow/Liu, Chapter 9 but evaluated with GLM (see for instance page 274). Also the various formula given there (casually also for the withinsubject variabilities!) then heavily rely on withinsubject contrasts. — Regards, Detlew 
ElMaestro ★★★ Denmark, 20100330 18:01 (5003 d 18:21 ago) @ d_labes Posting: # 4993 Views: 22,998 

Ahoy, ❝ I suppose a big amount of serious headache! For every new study, if using 3periodwhateversequence replicate design, if not totally balanced! Section 6.2.3.1.2.5.7.2: Statistical handling of volunteers Each subject will be stratified into one of three sequences. Section 8.4.9.8.3.5.1.5: Statistics The full analysis set consists of the 14 volunteers that first complete sequence ABB, plus the 14 volunteers that first complete sequence BAB, plus plus the 14 volunteers that first complete sequence BBA. ❝ Schützomycin to the rescue? Not sure. It has recently come to my attention that Schützomycin, although it's a wonderful drug, also has a few shortcomings. On board my boat I usually give my men a large dose before we make port as a preventive measure. This is because I know that once they get on land after 3 months at sea the first thing they do is [DELETED BY THE FORUM ADMINISTRATOR] after which they [DELETED BY THE FORUM ADMINISTRATOR] and frequently they will even [DELETED BY THE FORUM ADMINISTRATOR]. After such events a brief visit to the local police authority (with a stack of cash in a suitcase) and/or the consulate is now and then called for. Best regards EM. 
d_labes ★★★ Berlin, Germany, 20100401 17:20 (5001 d 19:02 ago) @ ElMaestro Posting: # 4995 Views: 22,936 

Ahoy Old Sailor, ❝ Section 6.2.3.1.2.5.7.2: Statistical handling of volunteers ❝ Each subject will be stratified into one of three sequences. ❝ ❝ Section 8.4.9.8.3.5.1.5: Statistics ❝ The full analysis set consists of the 14 volunteers that first complete sequence ABB, plus the 14 volunteers that first complete sequence BAB, plus plus the 14 volunteers that first complete sequence BBA. Nice idea, as always: ElMaestro to the rescue! Meanwhile I have inspected the Extrareference threeheaded hydra, captured on my last journey on the Bear way using some Schützomycin for immobilizing (a paradox effect, which occurs only for hydras). Whatever imbalance I put on it, the expected mean squares always show that the error term for the sequence effect is simply subject(sequence), as my bogus little RANDOM friend tells me. BTW: Played with the data set Le Roux et.al "Use of repeated crossover design in assessing bioequivalence: (within and between subjects variability  Schuirmann confidence intervals estimation)" Eur. J. Drug Metab. Pharmacokin. 23(2), 339345 (1998) Have a nice Easter. — Regards, Detlew 
ElMaestro ★★★ Denmark, 20100306 00:02 (5028 d 11:20 ago) @ d_labes Posting: # 4869 Views: 23,568 

Dear d_labes, ❝ • How do we formulate an ANOVA for replicate designs (or partial ❝ ❝ Go to church, pray, and hope for a miracle. Or go to the EMA at their upcoming event for people interested in this guideline and ask the question. ❝ • How do we get the right ("appropriate") tests for the effects in the ❝ ❝ Disagree. You still can get the effects right (in particular we talk sequence, right?) by considering all effects fixed. but you will have to do some manual brainwork still. By the way, there is even in this case a nontrivial issue with that effect. One can rightfully claim it must be null for a type III SS, because type III SS for Seq reflects a model with Per Trt and Subj, and since Subj is nested in Seq, one does not achieve anything by this single term deletion. Compare R's "drop1" with Proc GLM and see the difference. ❝ • From where do we get the intraindividual variabilities within Test or ❝ ❝ Mixed models or nothing. Church or EMA. I am not competent to tell if there is a potential gain in the Method of Moments, but I have not seen it working in bioequivalence. ❝ • Can we have an evaluation that is not only EMA accepted? FDA suggests ❝ FDA got it right. It's standard. ❝ I had used the FDA code for replicate designs up to now. But it relies definitely on mixed model (i.e. assuming subject as a random effect, factor) and thus on more elaborate and sophistic statistical method, but lacking anything that looks like ANOVA table. But this now obsolete in the light of the new EMA guidance! ❝ So how to react? How to proceed with replicate studies practically, technically ... to be EMA conform? Church or EMA. When you figure out the answers, please inform us all. I completely agree with your disorientation and I think this is a lapse in the guidance that merits a correction (better sooner than later). EM. 
d_labes ★★★ Berlin, Germany, 20100309 10:02 (5025 d 01:20 ago) @ ElMaestro Posting: # 4881 Views: 23,296 

Dear Großer Meister, ❝ Go to church, pray, and hope for a miracle. I know that the world is full of miracles. But I don't believe in . Moreover the Oracle has answered already: "It is out of the scope of the guideline to give details on how to analyse the data of a replicate design, since it is standard statistical analysis". (emphases by me) So once again: Any idea how to do that? The Bear way, i.e same model as for 2x2? Helmuts suggestion? Any other? — Regards, Detlew 
ElMaestro ★★★ Denmark, 20100309 20:02 (5024 d 15:20 ago) @ d_labes Posting: # 4886 Views: 23,326 

Dear d_labes, ❝ So once again: Any idea how to do that? The Bear way, i.e same model as for 2x2? Helmuts suggestion? Any other? Neither. If I had to do something with a dossier based on a replicated study it would be the following:
So if the product is referred to CMD, there will be limited scientific discussion there because CMD is mainly a regulatory comittee. They are highly skilled in all procedural problems, but they are not statisticians or pharmacokinetophystians or what it's called (they can bring experts, but there is a limitation to that, too). So either approval or referral to the CHMP. This would be a great chance for you. Because you can openly address it and ask them to show you how one can analyse replicated studies without a mixed model and still get unbiased separate withins for T and R. Gotcha! I have the greatest respect for the PKsubgroup, the CMD, the CHMP and EU regulators in general for all the work they undertake. But in this specific case I think the PKsubgroup has produced a document that is selfcontradictory and not on par with current standards and which may result in rejection of equivalent products if the word of the guideline is followed. For that reason, I think that medicine consumers in Europe would have a potential benefit if someone like you engages the regulators in a game of chicken. It is only one sentence that needs to be changed in the guidance in order for everything to be ok. Best regards EM. 
yjlee168 ★★★ Kaohsiung, Taiwan, 20100308 04:23 (5026 d 06:59 ago) @ d_labes Posting: # 4874 Views: 23,394 

Dear d_labes, ❝ the community: ❝ • How do we formulate an ANOVA for replicate designs (or partial ❝ ❝ With R codes, I don't know if this method is applicable to a replicate BE? Scroll down the webpage to browse "Mixed (between and Within) designs". However, it's not lm() function. Thanks. — All the best,  Yungjin Lee bear v2.9.1: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan https://www.pkpd168.com/bear Download link (updated) > here 
d_labes ★★★ Berlin, Germany, 20100309 09:52 (5025 d 01:30 ago) @ yjlee168 Posting: # 4880 Views: 23,960 

Dear Yungjin, Thanks for pointing me to this WEB site. But my R speak is not good enough to figure out what the difference between aov() and lm() is. Moreover I don't understand their data. Eventually there is someone out to enlighten me? — Regards, Detlew 