cher0424 ☆ China, 20150107 06:39 (2696 d 11:07 ago) (edited by cher0424 on 20150107 10:32) Posting: # 14234 Views: 29,657 

Dear all: I have a query concerning Statistical Analysis section of partial replicate. There is a paragraph i quote from one of partial replicate design (EU scope) BE study protocol:
Thanking you advance!!!!! Edit: Category changed. [Helmut] 
d_labes ★★★ Berlin, Germany, 20150107 14:45 (2696 d 03:01 ago) @ cher0424 Posting: # 14236 Views: 27,318 

Dear Cher, » 1. The selection of subjects who complete at least two periods with at least one test and one reference treatment of the study will be included in the pharmacokinetic and statistical analysis. » 2. The Selection of subjects who completes at least two periods with at least one test and one reference treatment of the subject will be considered for Bioequivalence » 3. The subjects who complete minimum of two periods with two references in the study will be included in the statistical analysis to estimate withinsubject variability of the reference product (SWR). IMHO point 1 and point 3 are contradictory. Since according to 1. a subject with two periods, each with reference, will not be included in the pharmacokinetic analysis it can't be included in the statistical analysis (of whatever) since no PK metrics are available. — Regards, Detlew 
cher0424 ☆ China, 20150107 15:35 (2696 d 02:11 ago) (edited by Dr_Dan on 20150107 15:57) @ d_labes Posting: # 14237 Views: 27,249 

Dear Detlew Thank you for your response. So you mean in ponit 1, if subject 1 complete T and R1, subject 2 complete T and R2, since R are different, so data can't be used for PK analysis? Edit: Please delete all text which is not specific to your reply (see forum's policy). [Dr_Dan] 
cher0424 ☆ China, 20150108 06:28 (2695 d 11:19 ago) @ d_labes Posting: # 14243 Views: 27,329 

Dear Detlew » Since according to 1. a subject with two periods, each with reference, will not be included in the pharmacokinetic analysis it can't be included in the statistical analysis (of whatever) since no PK metrics are available. Thank you for your response. One more query, why a subject with two periods, each with reference, will not be included in the pharmacokinetic analysis for SWR? 
d_labes ★★★ Berlin, Germany, 20150108 09:03 (2695 d 08:44 ago) @ cher0424 Posting: # 14246 Views: 27,310 

Dear Cher, » One more query,why a subject with two periods, each with reference, will not be included in the pharmacokinetic analysis for SWR? I didn't not recommend this. I only pointed you to the problem in your cited rules. I myself would include all subjects with at least 2 periods, regardless which formulation was applied, into PK and statistical analysis. The rest is done automatically: Subjects with Reference only will not contribute to the BE decision but to the sWR estimation, subjects with Test and only one Reference will contribute to the BE decision but not to the sWR estimation. — Regards, Detlew 
cher0424 ☆ China, 20150108 09:51 (2695 d 07:56 ago) @ d_labes Posting: # 14249 Views: 27,188 

Dear Detlew Sorry to ask again, but I can't see any contradiction between point 1 and 3. And to point 1 and 2, subjects who complete at least two periods with at least one test and one reference treatment of the study will be included in the pharmacokinetic and statistical analysis,so then can be considered for Bioequivalence. Is it causal relationship between 1 and 2?? And do you know any literature about statistical analysis of partial replicate BE study? 
d_labes ★★★ Berlin, Germany, 20150108 10:27 (2695 d 07:19 ago) @ cher0424 Posting: # 14251 Views: 27,151 

Dear Cher! » Sorry to ask again, but I can't see any contradiction between point 1 and 3. Once again slowly to take notes: Suppose you have a subject with two periods absolved, in both Reference applied. According to your rules, point 1, you don't have at least one Reference and one Test applied, so you will not include such a subject in the pharmacokinetic and statistical analysis. Full stop. — Regards, Detlew 
Shuanghe ★★ Spain, 20150108 11:08 (2695 d 06:38 ago) @ d_labes Posting: # 14252 Views: 27,572 

Hi all, If I can generalise the question in original post to "Subjects to be considered in replicate BE study in EU/FDA submission" to avoid a new post. For 3period partial replicate BE I did the same thing as mentioned by Detlew. To state it briefly:
For 4period full replicate BE for FDA submission, what I did is the following and I'd appreciate any comments:
The 2nd and 3rd points are answers from FDA. In one of the original questions I suggested to modify their code to included subjects with 1T2R, 2T1R etc but they stress that only subjects with 4 periods should be included for BE but all subject with 2R, even without any T, should be used for Swr. So the code is too sacred to be changed. The last point is a recent addition (as I forgot to ask FDA years ago) from one replicate study that happened to have high dropout rate (missing 1 or 2 periods) but ISCV of one PK parameter is less than the HVDP criterion so no scaled approach for that parameter. But the protocol didn't have the point 4 so only subjects with 4 periods were included and the power is sh** due to few subjects we have! so any suggestions on this point? For EU it seems much easier as the sample data set in the PK Q/A document has some missing periods (but all have at least 1T and 1R). — All the best, Shuanghe 
cher0424 ☆ China, 20150108 13:56 (2695 d 03:50 ago) (edited by cher0424 on 20150108 14:25) @ Shuanghe Posting: # 14254 Views: 27,144 

Hi Shuanghe, First Thank you for spelling out. » For 4period full replicate BE for FDA submission, what I did is the following and I'd appreciate any comments: » – for scaled approach, only subject who complete all 4 periods will be included for BE evaluation » – if Swr is less than the criterion for scaled approach then average BE approach will be used and all subject who can provide at least 1T and 1R will be included for BE evaluation. So 3period partial replicate BE for scaled approach is the same as above? And the second point need to be writen in the protocol? otherwise can't be applied? 
Relaxation ★ Germany, 20150302 09:46 (2642 d 08:01 ago) @ Shuanghe Posting: # 14520 Views: 26,462 

Dear all. Sorry for bringing this thread back to life instead of creating a new one, but as I only think I want to point on one thing, this seemed more appropriate to me. It was here stated twice that » To state it briefly: » – samples from subjects who complete at least 2 periods will be analysed » – subjects who has 2 periods of R will be included to determine Swr » – subject who can provided at least one T and one R will be included for BE evaluation » The last 2 is "done automatically" as Detlew said but I would prefer to state it very clearly in the protocol just in case. and I am not sure, whether I miss something here. From my experience, including the sample data set of the EMAPKWP, there is no automatism for these subjects, even in case the "method A" / GLM object is used. In other words, subjects with missing data will be included in the evaluation unless we exclude them by selection. As a quick example (method A on the EMA dataset I (?, the 4 period one)) Original result: 115.66 (107.11124.97) Incomplete subjects excluded by hand: 115.46 (106.49125.19) [no 11/20/24/31/42/67/69/71] > no automatic excludion of incomplete data sets For the show, subject 100 with R twice with values of 1000 and 500 added: 112.21 (1.1610833.43) > even subjects without data for a T vs R comparison have an impact (choosing such values for ln(data) was a little bit too much but is nicely illustrating, isn't it). So also subjects with missing periods including those with Reference Data only will remain in the evaluation if we simply use the code and, if wanted, subjects have to be excluded manually beforehand (which for BE assessment seems to be acceptable with EMA only for those with Reference only). Sorry, if I missed somethin and this is a triviality . Then feel free to simply ignore the post . Just wanted to add these piece of info to the "automatic"statements. 
d_labes ★★★ Berlin, Germany, 20150302 11:38 (2642 d 06:09 ago) @ Relaxation Posting: # 14521 Views: 26,299 

Dear Relaxation. » As a quick example (method A on the EMA dataset I (?, the 4 period one)) » Original result: » 115.66 (107.11124.97) » Incomplete subjects excluded by hand: » 115.46 (106.49125.19) » [no 11/20/24/31/42/67/69/71] > no automatic excludion of incomplete data sets All the subjects with incomplete data in the EMA dataset I have at least one period with T and one with R. Thus they of course have a contribution to the evaluation of TR and you will find differences if including or excluding them. » For the show, subject 100 with R twice with values of 1000 and 500 added: » 112.21 (1.1610833.43) » > even subjects without data for a T vs R comparison have an impact (choosing such values for ln(data) was a little bit too much but is nicely illustrating, isn't it). Seems here you are totally correct . — Regards, Detlew 
mittyri ★★ Russia, 20150319 20:12 (2624 d 21:35 ago) @ Relaxation Posting: # 14581 Views: 25,263 

Dear Relaxation and all, Your suggestions seems very interesting! » even subjects without data for a T vs R comparison have an impact I'm not sure that the subjects without T vs R comparison should be included in the analysis according to the EMA GL: […] subjects in a crossover trial who do not provide evaluable data for both of the test and reference products […] should not be included. Also see this post — Kind regards, Mittyri 
Dr_Dan ★★ Germany, 20150108 08:59 (2695 d 08:48 ago) @ d_labes Posting: # 14245 Views: 27,366 

Dear Detlew I agree that the study protocol text is insufficiently verbalized. However, if a subject completes two periods, he/she can be included either in the assessment of bioequivalence (in case of one period with test and the other with reference) or in the assessment of withinsubject variability of the reference product (in case both periods with reference), right? Kind regards Dr_Dan — Kind regards and have a nice day Dr_Dan 
d_labes ★★★ Berlin, Germany, 20150108 09:04 (2695 d 08:43 ago) @ Dr_Dan Posting: # 14247 Views: 27,115 

Dear Dan, see my answer above to Cher. — Regards, Detlew 
Astea ★★ Russia, 20150301 18:12 (2642 d 23:34 ago) @ d_labes Posting: # 14518 Views: 26,185 

Dear all! Excuse me for wedging for this thread... If we must hold all subjects that completed at least two periods in the analyses how to do this? Whether is it possible to calculate NCA in BEAR for 4period crossover (2x2x4) if we have a subject with all zero concentrations in one of the periods? I tried to do this but BEAR declaimed an error... — "Being in minority, even a minority of one, did not make you mad" 
yjlee168 ★★★ Kaohsiung, Taiwan, 20150301 19:01 (2642 d 22:46 ago) @ Astea Posting: # 14519 Views: 26,352 

Dear Astea, It is not possible to analyze your data using bear when there is a subject with all zero concentration in one of period. It will fail when doing NCA. » ... Whether is it possible to calculate NCA in BEAR for 4period crossover (2x2x4) if we have a subject with all zero concentrations in one of the periods? I tried to do this but BEAR declaimed an error... — 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 
Astea ★★ Russia, 20150309 14:43 (2635 d 03:04 ago) @ yjlee168 Posting: # 14554 Views: 25,979 

Dear yjlee168! Thank you a lot for your answer! BEAR helps me greatly... Would you be so kind to answer my other silly questions? » It is not possible to analyze your data using bear when there is a subject with all zero concentration in one of period. It's a very pity... » It will fail when doing NCA. But if it is so, why can't we use NCA data received manually for the latest statistical analyses in BEAR? I tried to use NCA data contained unequal numbers of subjects in different periods and BEAR didn't show errors while doing statistics. For example, we omit one of the period from the study for the N'th subject. Will the statistics compilated by BEAR be correct in such a case? By the way, what is the reason for which BEAR couldn't calculate NCA for subjects with all zero concentrations in one of the period? In my mind, all individual pharmacokinetic parameters should be calculated independently for each period? And the last question: am I right when thinking that for calculation CI of Cmax/AUC0t I can simply change the columns AUC0INF and lnAUCOINF for Cmax/AUC0t and ln Cmax/AUC0t respectively? Looking forward for your answers... — "Being in minority, even a minority of one, did not make you mad" 
yjlee168 ★★★ Kaohsiung, Taiwan, 20150309 15:24 (2635 d 02:23 ago) @ Astea Posting: # 14555 Views: 25,985 

Dear Astea, » [...] But if it is so, why can't we use NCA data received manually for the latest statistical analyses in BEAR? » I tried to use NCA data contained unequal numbers of subjects in different periods and BEAR didn't show errors while doing statistics. » For example, we omit one of the period from the study for the N'th subject. Will the statistics compilated by BEAR be correct in such a case? Really? I have no idea right now. No error with omitting one of the periods from a subject? I am not sure about that. A very good question. » By the way, what is the reason for which BEAR couldn't calculate NCA for subjects with all zero concentrations in one of the period? In my mind, all individual pharmacokinetic parameters should be calculated independently for each period? You are right about the procedures of NCA. However, when doing NCA, it also calculates some other parameters. For example, clearance (CL) is calculated with Dose*F/AUC_{0inf}. For all zero concentrations, AUC_{0inf} is zero. So it crashes. Also to estimate the terminal phase elimination rate constants (k_{el}), it requires nonezero data from terminal phase to perform linear regression (to get a slope). It certainly stops the run at this step too. » And the last question: am I right when thinking that for calculation CI of Cmax/AUC0t I can simply change the columns AUC0INF and lnAUCOINF for Cmax/AUC0t and ln Cmax/AUC0t respectively? Smart way. It should work well. You have to remember to change the name of parameters with all output files. — 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 
mittyri ★★ Russia, 20150325 09:50 (2619 d 07:57 ago) @ yjlee168 Posting: # 14613 Views: 24,825 

Dear Yungjin, » For all zero concentrations, AUC_{0inf} is zero. So it crashes. Also to estimate the terminal phase elimination rate constants (k_{el}), it requires nonezero data from terminal phase to perform linear regression (to get a slope). It certainly stops the run at this step too. Could you implement in Bear the approaches described by Helmut and ElMaestro in this thread? As I understand, according to the EMA GL we can exclude the data of volunteers without evaluable data for both TIMP and RIMP. In case we don't exclude them and try to estimate the PK parameters, Phoenix and SAS will ignore them and take into account as missing values. So it would be great if Bear will get these options for "null" PK parameters (to exclude the volunteer from analysis or take these data as missing) — Kind regards, Mittyri 
yjlee168 ★★★ Kaohsiung, Taiwan, 20150328 21:03 (2615 d 20:43 ago) @ mittyri Posting: # 14627 Views: 24,446 

Dear mittyri, » Could you implement in Bear the approaches described by Helmut and ElMaestro in this thread? Very sorry for the delay of this message. I will think about your suggestion seriously. But if users leave the problem to bear, I first need to know the criteria to exclude the subject (i.e. when to exclude). The case with all zero concentrations should be very easy to exclude. What if the subject with only 23 evaluable data available as Helmut said in your pointed thread? It may still cause the problem too. » As I understand, according to the EMA GL we can exclude the data of volunteers without evaluable data for both TIMP and RIMP. » In case we don't exclude them and try to estimate the PK parameters, Phoenix and SAS will ignore them and take into account as missing values. I don't quite understand here: if you can exclude the subjects who do not have evaluable data point available beforehand, why not? — 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 
mittyri ★★ Russia, 20150329 19:04 (2614 d 23:42 ago) @ yjlee168 Posting: # 14631 Views: 24,318 

Dear Yungjin, » What if the subject with only 23 evaluable data available as Helmut said in your pointed thread? It may still cause the problem too. Yes, you're right, at this moment it is impossible to make a software "push a button" (BTW some subjects tried) So only pharmacokinetist can make a decision about the data (is it evaluable or not). I would not delegate the responsibility to the software. In the meantime I think Bear can report to the user some helpful comments (e.g. "please be informed that only 3 evaluable points are provided for subject# in period#"). So user can make a decision: to exclude this data or not. » I don't quite understand here: if you can exclude the subjects who do not have evaluable data point available beforehand, why not? As I understood the PK guru's in the mentioned thread: Helmut wrote: "I would exclude the subject and maybe the other subjects with only one or two concentrations as well." ElMaestro answered: "If the software throws an error for the log step without executing a default solution, then I think it is justified to introduce NA's where the software can't logarithmise and then let the chips run their course. Otherwise it is a choice between analysing something or analysing nothing (which is unethical)." Grey zone of BE... I would add a row to the options, where the user can decide what to do with this data: to exclude the subject from analysis or to mark the data of period as NA Anyway my suggestions could be wrong, I'll be glad to see the additional comments from another PK members — Kind regards, Mittyri 
yjlee168 ★★★ Kaohsiung, Taiwan, 20150330 11:28 (2614 d 07:19 ago) (edited by yjlee168 on 20150330 11:48) @ mittyri Posting: # 14633 Views: 24,389 

Dear Mittyri, So the issue is to exclude the subject who do not have enough evaluable or allzero data point manually or automatically. You suggest that the exclusion better be done automatically by specified the least data points by users (good idea!) as the the exclusion criteria. It should be doable. The only question for me is how to add this option without significantly slowing down the current performance of NCA. The best way is to screen out all subjects after loading analyzed data and then execute exclusion if there is any. Assign 'NA' to all PK parameters for excluded subjects first. Then do NCA without excluded subjects. Meanwhile, I have to remember to adjust the final sample size when doing 90% CI and other stats. Ok and thanks for your suggestions. » [...] In the meantime I think Bear can report to the user some helpful comments (e.g. "please be informed that only 3 evaluable points are provided for subject# in period#"). So user can make a decision: to exclude this data or not. How a nice idea. — 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 
ElMaestro ★★★ Denmark, 20150330 15:44 (2614 d 03:03 ago) (edited by ElMaestro on 20150330 16:04) @ yjlee168 Posting: # 14634 Views: 24,432 

Hi all, how about having a procedure that determines if a given period for a subject subject has
I am not saying it is good science, I am just saying this is practically implementable and there would be a certain low level of reason. Update: Dammit, there are studies where you not have anything like three ascending points regardless of how good you do it. Example: inhaled beta2 agonists. — Pass or fail! ElMaestro 
yjlee168 ★★★ Kaohsiung, Taiwan, 20150331 11:15 (2613 d 07:31 ago) @ ElMaestro Posting: # 14637 Views: 24,361 

Dear Elmaestro, Thanks for your comments. » how about having a procedure that determines if a given period for a subject subject has » – three (consecutive?) ascending data points » – three (consecutive?) descending data points OK but sounds more complicated... » If yes, include the period for that subject as she does have a rudimentary profile, and if no, exclude the period for that subject. only to exclude "the period for that subject" or "all periods of that subject"? Which one is more acceptable? latter one? [edit: I mean when doing 90% CI and other stats.. The rest of periods of that subject will still perform NCA. Sorry about this.] — 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 
ElMaestro ★★★ Denmark, 20150331 12:16 (2613 d 06:31 ago) @ yjlee168 Posting: # 14638 Views: 24,262 

Hi Yungjin, » only to exclude "the period for that subject" or "all periods of that subject"? Which one is more acceptable? latter one? [edit: I mean when doing 90% CI and other stats.. The rest of periods of that subject will still perform NCA. Sorry about this.] I think you don't have to worry about this. When I say it like I mean the statistics function like R's lm will take care of it.Mathematically you have a myriad of constraints on effect estimates and in a sense this is what determines degrees of freedom. For example, if I recall correctly this is only from the top of my head and I could be somewhat off when we do the linear model the average of the two "LSMeans" (booh! ) must equal the grand mean, and so forth. There are constraints like for all factors. Also means that you can express the constraints as relationships between estimates of the factor levels across different factors (and that the histogram of residuals must be symmetric in a 222BE study???). To satisfy these constraints you cannot include subjects from a 222BE study where one period is missing. I believe another way of saying this is that the model matrix cannot be inverted if we try to include such a subject. This is why the lm, PROC GLM, lmer etc take the appropriate decision for you. These functions or procedures will exclude the subjects that need to be excluded  Those that do not allow estimation of their own treatment effect for both T and R (and note that with a mixed model you can include subjects with a missing period in a 222BEstudy  but that is another discussion and has been debated on this forum a few times).— Pass or fail! ElMaestro 
yjlee168 ★★★ Kaohsiung, Taiwan, 20150331 13:13 (2613 d 05:34 ago) @ ElMaestro Posting: # 14640 Views: 24,214 

Hi ElMaestro, » I think you don't have to worry about this. When I say it like I mean the statistics function like R's lm will take care of it.I can see your points. Sounds great if it is correct. Never try this before since all periods of all subjects must be evaluable with bear of the current version. » To satisfy these constraints you cannot include subjects from a 222BE study where one period is missing. I believe another way of saying this is that the model matrix cannot be inverted if we try to include such a subject. Got it. » This is why the lm, PROC GLM, lmer etc take the appropriate decision for you. These functions or procedures will exclude the subjects that need to be excluded...Ok and thanks again. — 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 
ElMaestro ★★★ Denmark, 20150331 14:26 (2613 d 04:21 ago) @ yjlee168 Posting: # 14641 Views: 24,068 

Hi Yungjin, » » This is why the lm, PROC GLM, lmer etc take the appropriate decision for you. These functions or procedures will exclude the subjects that need to be excluded...Upon furter reflexion: I might actually be wrong about a mixed model taking care to expell subjects that do not have one T and one R at least. Probably it can be said the whole point of the mixe models is they don't and this is the direct reason why a subject with a missing period in 222BE study will still count towards the result if it is for some reason fit by a mixed model and subject as random. I need to sit down and work the general model constraints to know for sure. This quickly gets into a territory where I don't have the skills. Try and google "likelihood of a matrix" — Pass or fail! ElMaestro 
mittyri ★★ Russia, 20150401 08:25 (2612 d 10:21 ago) @ ElMaestro Posting: # 14647 Views: 23,904 

Dear ElMaestro, Could you please clarify some moments? May be I didn't catch something. What about the Relaxation's post above? He tried to add to the EMA dataset the data of subject with Reference data only. And the result wasn't the same. Should we exclude the data of such subjects manually or not? I didn't test the dataset 222 BE with some missing data in mixed model. BTW the inclusion of subjects with missing data in 1 of 2 periods in model with all effects fixed can affect the results. — Kind regards, Mittyri 
d_labes ★★★ Berlin, Germany, 20150401 09:15 (2612 d 09:32 ago) @ ElMaestro Posting: # 14651 Views: 24,136 

Dear ElMaestro! » ... » This is why the lm, PROC GLM, lmer etc take the appropriate decision for you. These functions or procedures will exclude the subjects that need to be excluded ... I thought that this often spread misunderstanding was already cleared by this post and the follower of a well known Mahatma . lmer() is another story since it's mixed muddle software.— Regards, Detlew 
ElMaestro ★★★ Denmark, 20150401 16:29 (2612 d 02:18 ago) @ d_labes Posting: # 14654 Views: 23,927 

Oh dear, thanks d_labes, I stand corrected. Thanks for the important info. I humbly apologise for my mistake. — Pass or fail! ElMaestro 