LS ● 20080205 19:53 (6090 d 13:08 ago) Posting: # 1589 Views: 19,188 

Hi, For average BE analysis of replicated crossover studies, the following SAS code is from Guidance for Industry 'Statistical Approaches to Establishing Bioequivalence', January 2001, Appendix E PROC MIXED; CLASSES SEQ SUBJ PER TRT; MODEL Y=SEQ PER TRT/DDFM=SATTERTH; RANDOM TRT/TYPE=FA0(2) SUB=SUBJ G; REPEATED/GRP=TRT SUB=SUBJ; ESTIMATE 'T vs. R' TRT 11/CL ALPHA=0.1; Does anybody know which why TRT is written in random effect and also in fixed effect. Why TRT is random effect? What description is correct to address statistical method from the above code Thanks LS 
d_labes ★★★ Berlin, Germany, 20080206 14:34 (6089 d 18:26 ago) @ LS Posting: # 1590 Views: 15,000 

Hallo LS, ❝ Does anybody know which why TRT is written in random effect and also in fixed effect. Why TRT is random effect? What description is correct to address statistical method from the above code Only SAS knows (The power to know) . This is an example of the silly and somewhat counterintuitive syntax of PROC MIXED. The key is the /Sub=subj part in the random statement. This defines a random subject effect within each TRT, i.e. the random subject effects are assumed different for treatment groups in the study. So you can have different variabilities for test and reference products. If you need some deeper and more elaborate text about models and evaluation of replicate crossover designs have a look at Scott D Patterson and Byron Jones REPLICATE DESIGNS AND AVERAGE, INDIVIDUAL, AND POPULATION BIOEQUIVALENCE GSK BDS Technical Report 2002 – 01 Can be found in the net of nets http://biometrics.com/wpcontent/uploads/2009/06/tr200201.pdf  Edit: Updated URL. [Helmut] — Regards, Detlew 
LS ● 20080206 18:58 (6089 d 14:02 ago) @ d_labes Posting: # 1591 Views: 14,841 

Hi Thank your reply. So the TRT here is not a real random effect but a group factor, is it? If this kind of statement will be OK to describe the analysis method: SEC PER TRT as fixed effect and Subject within TRT as random effect LS 
d_labes ★★★ Berlin, Germany, 20080207 11:14 (6088 d 21:46 ago) @ LS Posting: # 1597 Views: 14,871 

Hello LS, nearly correct i think. Random effect is subject. The rest of Proc MIXED code in the RANDOM statement is the specification that this random effect is bivariate normal distributed with mean=0 and variancecovariance matrix s^{2}_{T} cov_{TR} i.e. has different variabilities for test and reference as you see, and a covariance term to account for the fact that observations at the same subject are correlated. The type= option defines the variancecovariance matrix and its parametrization. But again see my reference cited above for a deeper insight. — Regards, Detlew 
SKR ☆ 20080306 11:54 (6060 d 21:06 ago) @ d_labes Posting: # 1662 Views: 14,766 

Dear LS and DLabes, Thanks for your information sharing. My question is can we manually calculate MIXED ANOVA results? One more thing is, what DDFM=SATTERTH; indicates? Waiting for your Infomative reply.  Edit: Full quote removed. [Helmut] 
Helmut ★★★ Vienna, Austria, 20080306 14:57 (6060 d 18:03 ago) @ SKR Posting: # 1663 Views: 15,232 

Dear SKR! ❝ My question is can we manually calculate MIXED ANOVA results? Theoretically yes, practically no. The solution of a linear mixed effect model (this is not an ANOVA!) is based on a numeric iterative procedure – so if you have truly a lot of spare time, you should be able to do it… ❝ One more thing is, what DDFM=SATTERTH; indicates? DDFM: D (?) Degrees of Freedom SATTERTH: WelchSatterthwaite approximation for unequal variances / sample sizes (i.e., unbalanced data)$$\nu \approx \frac{\left (\frac{s_{1}^{2}}{n_1}+\frac{s_{2}^{2}}{n_2}\right )^2}{\frac{s_{1}^{4}}{n_1(n_11)}+\frac{s_{2}^{4}}{n_2(n_21)}}$$ — 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, 20080310 10:59 (6056 d 22:01 ago) @ Helmut Posting: # 1666 Views: 14,758 

Hello HS, ❝ DDFM: D (?) Degrees of Freedom ^ Denominator degrees of freedom, i.e. DF for the denominator of the FTest. — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20080310 13:24 (6056 d 19:37 ago) @ d_labes Posting: # 1670 Views: 14,865 

Dear DLabes, thanks; being not an SASuser, I did not want to speculate about it's abbreviations... — 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, 20080310 15:50 (6056 d 17:10 ago) @ Helmut Posting: # 1671 Views: 14,649 

Dear HS, ❝ thanks; being not an SASuser, I did not want to speculate about it's abbreviations... regarding SAS abbreviations it is most time needed to have a head like a pot whale (Physeter macrocephalus). Therefore it needs many years of struggling with "The power to know". — Regards, Detlew 
mathews ● 20080311 08:12 (6056 d 00:49 ago) @ d_labes Posting: # 1675 Views: 14,830 

Dear All, One doubt regarding the above mentioned FDA recommended SAS code. How can I include a SUB(SEQ) term in the above SAS code? Why the covariance structure FA0(2) is used in this code? Why not the other covariance structures? Is there any method to choose the covariance structure? Why DDFM=satterth? Why not DDFM=kenwardroger? Regards Matz 
d_labes ★★★ Berlin, Germany, 20080311 10:43 (6055 d 22:18 ago) @ mathews Posting: # 1678 Views: 14,955 

Dear Matz, ❝ One doubt ... the deeper the thoughts, the numerously the questions . ❝ How can I include a SUB(SEQ) term in the above SAS code?. SUB(SEQ) is the random subject term in the syntax of PROC GLM in case of a 2x2 cross over. It is included in the PROC MIXED code but by different syntax. If you need comparable code you can go with:
PROC MIXED data=yours; But with that you loose the disparate variance terms (between and within) for the formulations under study. ❝ Why the covariance structure FA0(2) is used in this code?.Why not the other covariance structures? The FA0(2) structure is chosen to ensure a positive definite covariance matrix, what ever this means to us as runofthemill statisticians (in german: FeldWaldundWiesen) . Roughly spoken it ensures variance terms in the model that are >0, a very reasonable assumption for such terms I think . Type=CSH (heterogenous compound symmetry) is mentioned in the FDA guidance also. Both parameterizations should be theoretically the same. Even type UN (unstructured) may be used, but suffer from sometimes negative estimates of variance components and is therefore not recommended in the FDA guidance. ❝ Is there any method to choose the covariance structure? This is too wide a subject and goes beyond the themes discussed here. Keywords are 'likelihood ratio test' and 'information criteria'. Ask the great mahatma Goooooogle. ❝ Why DDFM=satterth ? Why not DDFM=kenwardroger?. Seems the personal view of the author(s?) of the FDA guidance. The book B Jones and MG Kenward Design and Analysis of Crossover Trials Chapman & Hall/CRC, Boca Raton (2nd ed. 2003) uses DDFM=KR (abbreviations, abbreviations, abbreviations ...) most time. Not so astonishing in looking at the second author . So if you need deeper insight, I recommend this book and once again (see above) the papers by Patterson and Jones GSK BDS Technical Report 2002 – 01 (part I) http://biometrics.com/wpcontent/uploads/2009/06/tr200201.pdf GSK BDS Technical Report 2002 – 05 (part II) http://biometrics.com/wpcontent/uploads/2002/12/tr2002051.pdf  Edit: Updated URLs. [Helmut] — Regards, Detlew 
Sathya ☆ India, 20080917 09:21 (5866 d 00:40 ago) @ d_labes Posting: # 2363 Views: 16,219 

Dear d_labes/All, I am a beginner of bioequivalence study. I did only one Bioequivalence project in (2x2 Crossover study) with all your help. Now I want to develop my capability on Bioequivalence studies. So I tried to learn the Bioequivalence Study  Replicate Cross over. Because of less basic knowledge unable to move forward. I read the following post of yours. mix_entry.php?id=2292 mix_entry.php?id=1714 mix_entry.php?id=1665 mix_entry.php?id=1589#p1678 http://www.biometrics.com/downloads/tr200201.pdf I came to know lot of things. But I am unable to get flow of statistics involved in replicate cross over. So please give me complete flow of one replicate design (like the below link by Jaime_R Barcelona, 20070404 15:14 for Parallel) mix_entry.php?id=616 Please help. waiting for reply — Sathya 
d_labes ★★★ Berlin, Germany, 20080917 12:49 (5865 d 21:11 ago) @ Sathya Posting: # 2366 Views: 14,508 

Dear Sathya, ❝ I did only one Bioequivalence project in (2x2 Crossover study) with all your help. ❝ Now I want to develop my capability on Bioequivalence studies. So I tried to learn the Bioequivalence Study  Replicate Cross over. Congratulation! The russian revolutionist LENIN has already stated "Learn, learn and once again, learn!" . ❝ ... So please give me complete flow of one replicate design (like ... by Jaime_R, Barcelona ... for Parallel) Things are not so easy in evaluation of BE for replicate crossover designs (and not the second learn in Lenin's quotation, after experience with one evaluation of a conventional 2x2 crossover IMHO). The evaluation method usually involved (REML = restricted maximum likelihood) is a complicate iterative numeric procedure which cannot practically done by hand (See Helmut's post above in this thread). Thus the only flow (cook book for chef cooks ) I can give you is: 1. Evaluate your concentrationtime curves to get your desired pharmacokinetic parameters (like AUC, Cmax and so on) as usual for each subject in each period. 1.a logtransform the parameters believed to be distributed as lognormal (or are regulated to have been logtransformed). 2. Fire up your software capable of doing mixed effects analysis (SAS, Winnonlin or whatever you have and is convenient to you). 2.a Define your model (fixed, random effects, structure of variancecovariance terms) within that software. 2.b Require 90% confidence intervals for the treatment effect. 3. Look at the results and interpret them with your knowledge acquired up to now. If this is not enough see a statistician (seek for a competent one! ). If you are dealing with average BE the only essential piece of the software output is the 90% confidence interval, which is used as usual in BE studies, replicate or not. If you need some data to play with have a look at the FDA site Edit: Link corrected for new FDA’s website. [Helmut] — Regards, Detlew 
Sathya ☆ India, 20080918 08:43 (5865 d 01:17 ago) @ d_labes Posting: # 2376 Views: 14,432 

Dear d_labes, Thank you very much. I will get back to you with sufficient knowledge in Replicate Design. Once Again thank you. — Sathya 