Bioequivalence and Bioavailability Forum

LS
●

2008-02-05 19:53
(6089 d 18:26 ago)

Posting: # 1589
Views: 19,185

random effect, fix effect in the guidance Appendix E [Regulatives / Guidelines]

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 1-1/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,
2008-02-06 14:34
(6088 d 23:45 ago)

@ LS
Posting: # 1590
Views: 14,999

random effect, fix effect in the guidance Appendix E

Post reply

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) :-D

.

This is an example of the silly and somewhat counter-intuitive 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 cross-over 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/wp-content/uploads/2009/06/tr2002-01.pdf

--
Edit: Updated URL. [Helmut]

—
Regards,

Detlew

LS ● 2008-02-06 18:58 (6088 d 19:20 ago) @ d_labes Posting: # 1591 Views: 14,840	random effect, fix effect in the guidance Appendix E Post reply
	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,
2008-02-07 11:14
(6088 d 03:04 ago)

@ LS
Posting: # 1597
Views: 14,870

random effect, fix effect in the guidance Appendix E

Post reply

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 variance-covariance matrix

|s²_T     cov_TR|

|cov_TR   s²_R  |

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 variance-covariance matrix and its parametrization.

But again see my reference cited above for a deeper insight.

—
Regards,

Detlew

SKR ☆ 2008-03-06 11:54 (6060 d 02:25 ago) @ d_labes Posting: # 1662 Views: 14,765	random effect, fix effect in the guidance Appendix E Post reply
	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,
2008-03-06 14:57
(6059 d 23:21 ago)

@ SKR
Posting: # 1663
Views: 15,231

Satterthwaite degrees of freedom

Post reply

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… :lol3:

❝ One more thing is, what DDFM=SATTERTH; indicates?

DDFM: D (?) Degrees of Freedom
SATTERTH: Welch-Satterthwaite approximation for unequal variances / sample sizes (i.e., unbalanced data)$$\nu \approx \frac{\left (\frac{s_{1}^{2}}{n_1}+\frac{s_{2}^{2}}{n_2}\right )^2}{\frac{s_{1}^{4}}{n_1(n_1-1)}+\frac{s_{2}^{4}}{n_2(n_2-1)}}$$

—
Dif-tor 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, 2008-03-10 10:59 (6056 d 03:20 ago) @ Helmut Posting: # 1666 Views: 14,757	Satterthwaite degrees of freedom Post reply
	Hello HS, ❝ DDFM: D (?) Degrees of Freedom `^` Denominator degrees of freedom, i.e. DF for the denominator of the F-Test. — Regards, Detlew

Helmut ★★★ Vienna, Austria, 2008-03-10 13:24 (6056 d 00:55 ago) @ d_labes Posting: # 1670 Views: 14,863	Satterthwaite DF; SAS Post reply
	Dear DLabes, thanks; being not an SAS-user, I did not want to speculate about it's abbreviations... — Dif-tor 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, 2008-03-10 15:50 (6055 d 22:29 ago) @ Helmut Posting: # 1671 Views: 14,648	Satterthwaite DF; SAS Post reply
	Dear HS, ❝ thanks; being not an SAS-user, 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 ● 2008-03-11 08:12 (6055 d 06:07 ago) @ d_labes Posting: # 1675 Views: 14,829	Satterthwaite DF; SAS Post reply
	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,
2008-03-11 10:43
(6055 d 03:36 ago)

@ mathews
Posting: # 1678
Views: 14,954

SAS Proc Mixed coding, replicate design

Post reply

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;

  class treatment period sequence subject;

  model lnPKParam=treatment period sequence / DDFM=KR;

  random subject(sequence) subject*treatment;

run;

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 run-of-the-mill statisticians (in german: Feld-Wald-und-Wiesen-) ;-)

.
Roughly spoken it ensures variance terms in the model that are >0, a very reasonable assumption for such terms I think :-D

.
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 Cross-over 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 :yes:

.

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/wp-content/uploads/2009/06/tr2002-01.pdf
GSK BDS Technical Report 2002 – 05 (part II)
http://biometrics.com/wp-content/uploads/2002/12/tr2002-051.pdf

--
Edit: Updated URLs. [Helmut]

—
Regards,

Detlew

Sathya
☆

India,
2008-09-17 09:21
(5865 d 05:58 ago)

@ d_labes
Posting: # 2363
Views: 16,217

SAS Proc Mixed coding, replicate design

Post reply

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/tr2002-01.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,
2007-04-04 15:14 for Parallel)

mix_entry.php?id=616

Please help. waiting for reply

—
Sathya

d_labes
★★★

Berlin, Germany,
2008-09-17 12:49
(5865 d 02:30 ago)

@ Sathya
Posting: # 2366
Views: 14,507

Replicate design evaluation

Post reply

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!" :-D

❝ ... 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 cross-over designs (and not the second learn in Lenin's quotation, after experience with one evaluation of a conventional 2x2 cross-over 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 concentration-time curves to get your desired pharmacokinetic parameters (like AUC, Cmax and so on) as usual for each subject in each period.
1.a log-transform the parameters believed to be distributed as log-normal (or are regulated to have been log-transformed).

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 variance-covariance 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! :-P

).

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 ~~http://www.fda.gov/cder/bioequivdata/~~ http://www.fda.gov/Drugs/ScienceResearch/ResearchAreas/Biostatistics/ucm081434.htm

Edit: Link corrected for new FDA’s website. [Helmut]

—
Regards,

Detlew

Sathya ☆ India, 2008-09-18 08:43 (5864 d 06:36 ago) @ d_labes Posting: # 2376 Views: 14,431	Replicate design evaluation Post reply
	Dear d_labes, Thank you very much. I will get back to you with sufficient knowledge in Replicate Design. Once Again thank you. — Sathya

random effect, fix effect in the guidance Appendix E [Regulatives / Guidelines]

random effect, fix effect in the guidance Appendix E

random effect, fix effect in the guidance Appendix E

random effect, fix effect in the guidance Appendix E

random effect, fix effect in the guidance Appendix E

Satterthwaite degrees of freedom

Satterthwaite degrees of freedom

Satterthwaite DF; SAS

Satterthwaite DF; SAS

Satterthwaite DF; SAS

SAS Proc Mixed coding, replicate design

SAS Proc Mixed coding, replicate design

Replicate design evaluation

Replicate design evaluation