Mutasim ☆ Jordan, 20190807 13:16 Posting: # 20484 Views: 4,032 

Dear Members, What is the explanation for and the impact of having a significant group by sequence interaction in a study with 4 groups and 2 sequences and 4 periods (HVD). 
Helmut ★★★ Vienna, Austria, 20190807 14:35 @ Mutasim Posting: # 20485 Views: 3,100 

Salam Mutasim, » What is the explanation for … Chance. » … and the impact of having a significant group by sequence interaction in a study with 4 groups and 2 sequences and 4 periods (HVD). If you are dealing with ABEL (the EMA’s method) chances than any (!) European agency will ask for a groupterm in the analysis are close to nil. When I gave my first presentation about it in Budapest 2017 in front of European regulatory (!) statisticians they were asking in disbelieve “What the hell are you talking about?” See what the BEGL states: The study should be designed in such a way that the formulation effect can be distinguished from other effects. This is in line what is stated in the Q&A document about TwoStage Designs: A model which also includes a term for a formulation*stage interaction would give equal weight to the two stages, even if the number of subjects in each stage is very different. The results can be very misleading hence such a model is not considered acceptable. […] this model assumes that the formulation effect is truly different in each stage. If such an assumption were true there is no single formulation effect that can be applied to the general population, and the estimate from the study has no real meaning. Replace formulation*stage by formulation*group and you get the idea.But all of this is about a groupbytreatment interaction. Sometimes in conventional 2×2×2 crossovers we see a significant sequence (better unequal carryover) effect. Since it can only be avoided by design (sufficiently long washout) any test for it is futile. Check for eventual residual concentrations in higher period(s) and exclude subjects with predose concentrations >5% of their C_{max}values. In analogy the same can be said about the groupbysequence interaction. Occasionally you will see a significant result. Ignore it. Only if you prefer braces plus suspenders: Go with the FDA’s model II. But no pretest and no interaction! The loss in power as compared to the pooled analysis is negligible. Degrees of freedom in a 2×2×2 design: Model III: n_{1} + n_{2} – 2 Model III: 3(n_{1} + n_{2}) – 4 What you never ever should do: Evaluate groups separately. Power will be terrible. Even if you are extremely lucky and one of them passes, what will you do? Submit only this one? Any agency will ask for the others as well. Guess the outcome. If you are thinking about the FDA’s group models I–III: There were very few deficiency letters (all with the same text) issued to US and Canadian companies. On the other hand, many European CROs have such letters collecting dust in archives. Politics? Even if you follow this track, model III (pooling) is justified since the conditions are practically always fulfilled. The sequential procedure (test for a groupbytreatment interaction at the 10% level) as any pretest might inflate the type I error. I even have a statement from the EMA that such a procedure is not acceptable. Groupbysequence interaction? Forget it.
— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
ElMaestro ★★★ Belgium?, 20190808 10:06 @ Helmut Posting: # 20486 Views: 3,020 

Hi Hötzi, » The precise model to be used for the analysis should be prespecified in the protocol. The statistical analysis should take into account sources of variation that can be reasonably assumed to have an effect on the response variable. » Is it reasonable to assume that groups or sequences have an effect on the PK response? Heck, no way! Same inclusion/exclusioncriteria and hence, similar demographics, same clinical site, same bioanalytical method. Hundreds (thousands?) of studies performed in multiple groups and accepted by European agencies based on pooled data. But on the other hand: Why then then include e.g. period? Let us for a moment disregard the actual wording. I don't think this is about assuming that some factor has or hasn't an effect (and not about significance in the statistical sense either). As I see it I want to construct a CI which is as wide as my real uncertainty dictates. I start out with a whole bunch of ugly variation and in the fashion of Michelangelo working on his crude blocks of marble I chip parts and bits away from my bulk of variation by applying my model. What I have left of my variation is a chunk of pristine, genuine, holy, magnificent, beautiful variation. What a sight to behold , and whose origin my experimental setup cannot account for, which I therefore use for my CI. My confidence interval now is as wide as just exactly that uncertainty merits. For a crossover this is of little practical importance since subjects are in groups. For a parallel trial I think I want group in the model. If regulators don't like this, they can ask me to take it away. I happily do so without protesting. I am a sheep at that point. But not until then. — I could be wrong, but... Best regards, ElMaestro "Pass or fail" (D. Potvin et al., 2008) 
Helmut ★★★ Vienna, Austria, 20190808 10:31 @ ElMaestro Posting: # 20487 Views: 3,021 

Ahoy, my Capt’n, » » The precise model [] » » But on the other hand: Why then then include e.g. period? Cause otherwise eventual period effects would not mean out. Given, sometimes one has to assume lacking period effects and everybody is happy with that. If an originator explores whether the drug follows linear PK, we have a paired design (SD → saturation → steady state) and compare AUC_{0–τ} with AUC_{0–∞}. A crossover would be a logistic nightmare. » Let us for a moment disregard the actual wording. [ Exactly. » […] For a parallel trial I think I want group in the model. If regulators don't like this, they can ask me to take it away. I happily do so without protesting. I am a sheep at that point. But not until then. Agree again. — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
Astea ★ Russia, 20191221 14:12 @ Helmut Posting: # 21011 Views: 2,353 

Dear Friends! Recently I've known that Belorussian experts referring to EAEC rules require to recalculate the results of large studies using FDA's Model II, that is: Group, Sequence, Treatment, Period(Group), Group×Sequence as fixed and Subject(Group×Sequence) as Random though it was not stated in protocol beforehand. I don't think it is a good idea. Moreover it could be contagious! What do you think about it? Critical points: as standard model requires Sequence, Treatment, Period and Subject(Sequence) as fixed terms, the results of the random effect model obviously will be different. What if they will change the overall result of BE? What if the Group×Sequence effect would be significant by chance? How to deal with excluded subjects? For example, if we have a subject with only one period the fixedeffect model would automatically neglect it while the randomeffect model would use it. As I understand currently it is impossible to calculate it via R, isn't it? May be Julia will help? So only people with commercial software could deal with it. — "Being in minority, even a minority of one, did not make you mad" 
PharmCat ★ Russia, 20191222 01:37 @ Astea Posting: # 21014 Views: 2,341 

Hello Astea! » As I understand currently it is impossible to calculate it via R, isn't it? May be Julia will help? So only people with commercial software could deal with it. I think any mixed model without replication (repeated factor) can be fitted in R and in Julia without problems. If variance components include repeated factor (structured R matrix) only special cases available in free software. 
Helmut ★★★ Vienna, Austria, 20191222 10:30 @ Astea Posting: # 21015 Views: 2,331 

Hi Nastia, » Recently I've known that Belorussian experts referring to EAEC rules require to recalculate the results of large studies using FDA's Model II, that is: Group, Sequence, Treatment, Period(Group), Group×Sequence as fixed and Subject(Group×Sequence) as Random though it was not stated in protocol beforehand. Regulators are always right. » I don't think it is a good idea. Moreover it could be contagious! What do you think about it? Recalculating a study is never a good idea. Entire α already spent, right? » Critical points: as standard model requires Sequence, Treatment, Period and Subject(Sequence) as fixed terms, the results of the random effect model obviously will be different. Possible but only to a (very) small degree. » What if they will change the overall result of BE? You mean that the fixed model passes and the mixed model fails? Cannot imagine to happen (see below). » What if the Group×Sequence effect would be significant by chance? Not even the FDA asks for testing Group×Sequence in Model II. » How to deal with excluded subjects? For example, if we have a subject with only one period the fixedeffect model would automatically neglect it while the randomeffect model would use it. Yep. On the other hand, the residual variance in the mixed model should not be larger than the one of fixed model. I had a few cases in the past where European regulators asked for recalculation according to the new GL (the mixed model was my standard before). The CI was sometimes narrower but differed only in the second decimal place… » As I understand currently it is impossible to calculate it via R, isn't it? I agree with PharmCat. Doable in R. — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
Astea ★ Russia, 20191222 21:23 @ Helmut Posting: # 21018 Views: 2,329 

Dear Breathtakingly Smart People! » I agree with PharmCat. Doable in R. Please check my solution... Below is my Rcode:
library(readxl) In order to check whether it works properly I used Data set 1 from Q&A and added groupfactor: first 30 subjects  group #1, and the last  group #2. To compare the results I used the following SAScode:
proc mixed data=SASuser.Dataset; Cause I wasn't sure that my code works well I used the stepbystep approach and compared different models (they all may be meaningless by nature but whatever): 1). Sequence Formulation Period as Fixed, Subject(Sequence) as Random 2). Sequence Formulation Period Group as Fixed, Subject(Sequence) as Random 3). Sequence Formulation Period(Group) Group as Fixed, Subject(Sequence) as Random 4). Sequence Formulation Period(Group) Group Sequence*Group as Fixed, Subject(Sequence) as Random 5). Sequence Formulation Period(Group) Group Sequence*Group as Fixed, Subject(Sequence*Group) as Random The results are as follows: SAS SAS SAS R R R And now, attention, the questions: 1). Looking the same is not proving to be the same, isn't it? 2). By the way, this is exactly an example where the design changes the decision of BE (of course if scaling was not stated in protocol). BE or not BE? 3). When I try to use Subject(Sequence*Group) as Random in R, it throws an error: "couldn't evaluate grouping factor (Sequence * Group):Subject within model frame: try adding grouping factor to data frame explicitly if possible". Is it right that we can simply neglect the structure of this term as we can do in standard models with Subject instead of Subject(Sequence)? — "Being in minority, even a minority of one, did not make you mad" 
PharmCat ★ Russia, 20191222 22:52 (edited by PharmCat on 20191223 17:04) @ Astea Posting: # 21019 Views: 2,325 

Hi! » Is it right that we can simply neglect the structure of this term as we can do in standard models with Subject instead of Subject(Sequence)? Edited. You can use just "Subject" in random statement in SAS. I think if you try to do this, you should get the same results. Of course, if your subject numbers not repeated. Data: DATA data; Code 1 PROC MIXED data=data; Fixed effect without denoted nested factors: problem with results, but coefficient calculated correctly. Code 2
PROC MIXED data=data; Fixed effect with nested factor: no problems, but Subjects in Dimensions = 1. Look at horrible V matrix. In this case it does not matter, but it not corresponds with reality. Code 3 PROC MIXED data=data; Good fit. Subjects in Dimensions = 8. We have individual V matrices and ready for structuring. Code 4
PROC MIXED data=data; Nested random part  no effect. I can't find any difference between subject and subject(room). As I understand nested factors affect on fixed part. I don't know how nested statment can affect on random part, but I think  in this case there is no effect. 
mittyri ★★ Russia, 20191223 14:30 (edited by mittyri on 20191223 15:05) @ Astea Posting: # 21020 Views: 2,218 

Dear Nastya, whenever possible use simple solutions, at least till the moment you must dive into mixed models galaxy And more: interaction terms are not the same in SAS and R take a look at method.B implementation inside replicateBE package I just modified it a bit library(replicateBE) — Kind regards, Mittyri 
Astea ★ Russia, 20191223 17:26 @ mittyri Posting: # 21022 Views: 2,201 

Dear mittyri! Thanks a lot for your elegant solution! Didn't you think that replicateBE was the first thing that I've thought of, but I couldn't dig up the code for get.data in order to modify it for my needs. The question that I could not solve was extremely stupid: namely, what is the difference between Dataset<rds01 and Dataset<read_excel("rds01.xlsx", sheet = 1)? The initial dataset is the same, but the results of the algo are different. So before using we should somehow prepare the data, but how to do it? "I faced the wall...and did it my way" — "Being in minority, even a minority of one, did not make you mad" 
mittyri ★★ Russia, 20191224 10:53 @ Astea Posting: # 21023 Views: 2,146 

Dear Nastya, » what is the difference between Dataset<rds01 and Dataset<read_excel("rds01.xlsx", sheet = 1)? there could be a problem with column types. check Dataset1<read_excel("rds01.xlsx", sheet = 1) — Kind regards, Mittyri 
Helmut ★★★ Vienna, Austria, 20191224 11:03 @ Astea Posting: # 21024 Views: 2,139 

Hi Nastia, » […] replicateBE was the first thing that I've thought of, but I couldn't dig up the code for get.data in order to modify it for my needs. I would not try to use this function. It calls others which are not exported. Not worth the efforts to modify it. » […] what is the difference between Dataset<rds01 and Dataset<read_excel("rds01.xlsx", sheet = 1)? The initial dataset is the same, but the results of the algo are different. So before using we should somehow prepare the data, but how to do it? Duno how you accessed the datasets. Try this one:
Edit: Hey Mittyri, you were faster! — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
Astea ★ Russia, 20191224 19:18 @ Helmut Posting: # 21029 Views: 2,140 

Dear Friends! Thanks a lot for your inestimable help! I finally found. The key point was just adding the string: Dataset$period<factor(Dataset$period). Now all works the same. I still struggle to understand what is the difference between lmer and lme in this case... — "Being in minority, even a minority of one, did not make you mad" 
Helmut ★★★ Vienna, Austria, 20191225 19:12 @ Astea Posting: # 21030 Views: 2,128 

Hi Nastia, » I still struggle to understand what is the difference between lmer and lme in this case... The syntax of the formula for random effects is different.
lme() you have to use na.action = na.omit because the default na.action = na.fail would stop and throw an error.The method to extract the PE and calculate the CI is also different. Hint: Lines 53–56 and 80–84 of the sourcecode of method.B.R .— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
Beholder ★ Russia, 20191227 13:44 @ Astea Posting: # 21031 Views: 1,955 

Dear Astea! » large studies Saying "large studies" do you mean the multicentral BE studies or large amount of subjects, e.g. 70 subjects in one clinic divided into two groups? — Best regards Beholder 
Astea ★ Russia, 20191229 21:59 @ Beholder Posting: # 21035 Views: 1,895 

Dear Beholder! » Saying "large studies" do you mean the multicentral BE studies or large amount of subjects, e.g. 70 subjects in one clinic divided into two groups? I'm sorry for the wrong terminology used. I meant studies in which volunteers were divided by two groups for the capacity reasons. (Formally this can be true even for studies with 12 subjects if the clinical site is tiny.) Multicentral studies is the other case. 
Helmut ★★★ Vienna, Austria, 20191230 12:32 @ Astea Posting: # 21036 Views: 1,881 

Hi Nastia, » I meant studies in which volunteers were divided by two groups for the capacity reasons. (Formally this can be true even for studies with 12 subjects if the clinical site is tiny.) Might also happen in midrange CROs with drugs which require continuous cardiac monitoring. 12–16 beds is not unusual. Nevertheless, I don’t understand why Belorussian experts ask for a mixed model because the guideline recommends ANOVA: 88. Сравнение исследуемых фармакокинетических параметров проводят с помощью дисперсионного анализа (ANOVA). Fixed effects are specifically recommended (taking into account effects which can affect the response):89. Статистический анализ должен принимать во внимание источники вариабельности, способные повлиять на изучаемую переменную. В такой модели дисперсионного анализа принято использовать такие факторы, как последовательность, субъект последовательности, период и лекарственный препарат. В отношении всех этих факторов следует использовать фиксированные, а не случайные эффекты. We discussed that ad nauseam. At least in the EU no regulatory statistician assumes that groups have an impact and expects a groupmodel. Pooled analysis rulez (see above). However, why all that fuzz? Let’s simulate 100,000 studies:
But you are right that in rare borderline cases a study passing with the pooled analysis might fail with the group model due to the lower degrees of freedom. \(df\text{(pooled model)}=N2\) \(df\text{(group model)}=\sum_{i=1}^{i=groups}n_i(groups1)2\) Of course, the larger the sample size and the smaller the number of groups the impact will be decrease.
» Multicentral studies is the other case. Correct. I would always recommend to include siteterms in the model. — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 