atish_azad ☆ 20080320 12:33 (5990 d 17:20 ago) Posting: # 1714 Views: 13,455 

Dear HS/all, Please suggest wheather we can calculate intersubject variation in replicated four period, two sequence, two formulation bioequivalence study using WinNonlin or SAS software as per the model given in Guidance for Industry Statistical Approaches to Establishing Bioequivalence or any other method to calculate the same. If yes kindly suggest the method to calculate intersubject variation. Regards, Atish 
d_labes ★★★ Berlin, Germany, 20080326 14:34 (5984 d 15:20 ago) @ atish_azad Posting: # 1722 Views: 11,183 

Dear Atish, ❝ ... wheather we can calculate intersubject variation in ❝ replicated four period, two sequence, two formulation bioequivalence study ❝ .... SAS software as per the model given in Guidance for ❝ Industry Statistical Approaches to Establishing Bioequivalence ... The answer lies in your question. The intersubject variation (separated for Test and Reference) is part of the model of the FDA and therefore part of the output of the SAS code given in Appendix E of the guidance. Look for Gmatrix. See the threads forum_entry.php?id=1589 or forum_entry.php?id=1312 here in the forum and puzzle things together . Regarding WINNONLIN I am not an initiate. By the way: Why do you need the intersubject variation? — Regards, Detlew 
atish_azad ☆ 20080331 17:02 (5979 d 13:52 ago) @ d_labes Posting: # 1731 Views: 11,261 

Dear d_labes, Thank you for the reply, I need intersubject variation because it is written in the protocol. After refering to the mail given to Andrew by Dave and GSK BDS Technical Report 2002  01, I found the answer to the question. ❝ The replicate SAS output gives all of the information needed to calculate ❝ intra and interCV, in it outputs of covariate matrix ("Covariate ❝ Parameter Estimates"). The SAS output look like this: ❝ ❝ Covariate Parameter Estimates ❝ Cov Parm Subject Group Estimate ❝ FA(1,1) Subject 0.4289 < (sig_BR, the betweensubject standard ❝ deviation for the Reference product) ❝ FA(2,1) Subject 0.3131 < (sig_BT, the betweensubject standard ❝ deviation for the Test product) ❝ FA(2,2) Subject < (sig_D, the subjectbyformulation interaction ❝ term) ❝ Residual Subject Formulation R 0.1479 < (sig_WR^2, the withinsubject ❝ standard deviation for the Reference product) ❝ Residual Subject Formulation T 0.2539 < (sig_WT^2, the withinsubject ❝ standard deviation for the Test product) ❝ The intrasubject variabilities are still calculated from the residuals as ❝ in a 2way crossover, using: ❝ IntraCV_R = 100%*sqrt(exp(sig_WT^2)1) (in this case, = ❝ 100*sqrt(exp(0.1479)1) = 39.92% ❝ IntraCV_T = 100%*sqrt(exp(sig_WR^2)1) (in this case, = ❝ 100*sqrt(exp(0.2539)1) = 53.76% ❝ FA(1,1) and FA(2,1) are the intersubject standard deviations for Reference ❝ and Test products, respectively: ❝ InterCV_R = 100%*sqrt(exp(sig_BT^2)1) = 100*sqrt(exp(0.4289^2)1) = 44.94% ❝ InterCV_T = 100%*sqrt(exp(sig_BR^2)1) = 100*sqrt(exp(0.3131^2)1) = 32.09% Kindly let me know whether the above calculate inter and intra subject variability are correct. In SAS code the Random statement, TYPE=FA0(2) if replaced by TYPE=CSH we could directly get inter and intra subject variance, isn't it? Regards, Atish 
Jaime_R ★★ Barcelona, 20080331 17:09 (5979 d 13:44 ago) @ atish_azad Posting: # 1733 Views: 11,065 

Dear Atish! ❝ [...] I need intersubject variation because it is written in the protocol. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ That's a reason! (sorry, but I could not resist) — Regards, Jaime 
atish_azad ☆ 20080401 08:15 (5978 d 22:39 ago) @ Jaime_R Posting: # 1734 Views: 11,440 

Dear d_labes/all, subjectbyformulation interaction variance is sig_D^2=FA(1,1)^2+FA(2,1)^22*FA(1,1)*FA(2,1) As far as WinNonlin is concerned Under 'Final Variance Parameters' values of lambda(1,1)_11, lambda(1,2)_11 and lambda(2,2)_11 corresponds to SAS output of FA(1,1), FA(2,1) and FA(2,2) respectively. Based on above mentioned parameters we can calculate inter and intra subject variation. Regards, Atish 
d_labes ★★★ Berlin, Germany, 20080401 12:01 (5978 d 18:52 ago) @ atish_azad Posting: # 1737 Views: 11,300 

Dear Atish, to puzzle is an art and to read needs glasses . ❝ FA(1,1) and FA(2,1) are the intersubject standard deviations for ❝ Reference and Test products, respectively ... This is not correct in my opinion. See my last comment in the thread here. To state it once more: Apart from the specific model used the Gmatrix contains the interindividual variabilities (diagonal elements). This matrix can be parameterized in different ways. Using the FA0(2) parameterization you get: sig_BR^{2}=G(1,1)=FA(1,1)^{2} By the way: Be shure your coding of R preceeds T, else change indices. Check it in comparing to the CSH parameterization in which case you have (with the SASoutput names of the covariance parameters): sig_BR^{2}=G(1,1)=Var(1) ❝ InterCV_R = 100%*sqrt(exp(sig_BT^2)1 .... ❝ InterCV_T = 100%*sqrt(exp(sig_BR^2)1) ... Correct only if you use sig_BR in the first formula and sig_BT in the second. Correct only if you analyze logtransformed PK parameters. ❝ In SAS code the Random statement, TYPE=FA0(2) if replaced by TYPE=CSH we ❝ could directly get inter and intra subject variance, isn't it? That's correct to me. See above. Your formula regarding subjectbyformulation interaction later on in this thread (after Jaime's spontaneous outcry ) is not correct to me. It is only valid, if the correlation (thinking in the CSH model) amounts to 1. In general it reads in the FA0(2) model sig_D^{2}=FA(1,1)^{2}+FA(2,1)^{2}+FA(2,2)^{2}2*FA(1,1)*FA(2,1) and in the CSH model
sig_D^{2}=Var(1)+Var(2)2*CSH*sqrt(Var(1))*sqrt(Var(2)) (in SAS the correlation rho is named CSH). Again my question: What is your intention in calculating the subjectbyformulation interaction? Are you going for individual bioequivalence? If it is only for descriptive purposes within average BE take care in interpretation of the value for that. See for instance L. Endrenyi and L. Tothfalusi, "SubjectbyFormulation Interaction in Determinations of Individual Bioequivalence: Bias and Prevalence", Pharmaceutical Research, Volume 16, Number 2, p186190 (1999) A short resume can be found at www.dkfz.de/biostatistics/iscbgmds99/abstracts/20062.pdf — Regards, Detlew 
atish_azad ☆ 20080402 17:27 (5977 d 13:27 ago) @ d_labes Posting: # 1752 Views: 11,138 

Dear d_labes Thank you for solving the puzzle. I checked it in comparing to the CSH parameterization in which we had Var(1) and Var(2) as sig_BR2=G(1,1)=Var(1) sig_BT2=G(2,2)=Var(2). I referred Design and Anaysis of BA and BE Studies Second Edition by CHOW & LIU (Page 405) for Subject by formulation interaction which confirmed CSH model for sig_D2=Var(1)+Var(2)2*CSH*sqrt(Var(1))*sqrt(Var(2)). We are not going for individual bioequivalence is was only for the sake of my understanding. I would like to study in detail about Average, Population and Individual bioequivalence. Kindly send some reference for the same. Regards, Atish 