Dr Andrew Leary
★

Ireland,
2007-11-20 15:50
(6138 d 16:18 ago)

Posting: # 1312
Views: 18,665

## Calculation of intra-subject CVs in replicate design [General Sta­tis­tics]

Dear Helmut

I hope that Berlin went well. I contacted you directly earlier this year with a question about the replicate design. You will be glad to see that this time I've used the Forum as requested!

My statistician has the following question:
My question is how to calculate intrasubject CV's for a 4-period 2-treatment replicate bioequivalence trial which I intend to analyze using proc mixed (SAS). I have analysed crossover bioequivalence trials before and used the formula 100%(e^MSE-1)^0.5 to calculate itrasubject CV where MSE is the mean square error. MSE was claculated using proc glm. How should I calculate MSE this time? Do I calculate two separate ANOVA models for each treatment and use the different MSE's from each analysis to give separate intra-subject CV's or do I take a completly different approach?

I hope that you can help.

Kind regards

Dr Andrew Leary
[Shandon Clinic, Cork, IRELAND]
Helmut
★★★

Vienna, Austria,
2007-11-20 17:27
(6138 d 14:41 ago)

@ Dr Andrew Leary
Posting: # 1313
Views: 16,147

## Calculation of intra-subject CVs in replicate design

Dear Andrew!

❝ I hope that Berlin went well.

Actually right now I'm sitting in the conference hall and will be chairing the meeting tomorrow; so please be a little patient - maybe another member of the forum can fill in the gap in the meantime...

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
Dr Andrew Leary
★

Ireland,
2007-11-20 17:46
(6138 d 14:21 ago)

@ Helmut
Posting: # 1314
Views: 16,140

## Calculation of intra-subject CVs in replicate design

We'll be patient. Data is not due back for another 2-3 weeks!

--
Edit: Full quote removed. [HS]
Dr Andrew Leary
★

Ireland,
2007-12-05 17:35
(6123 d 14:32 ago)

@ Dr Andrew Leary
Posting: # 1356
Views: 16,070

## Calculation of intra-subject CVs in replicate design

Hello Helmut

Any word on the query (in red) below?

Kind regards

Andrew Leary

My question is how to calculate intrasubject CV's for a 4-period 2-treatment replicate bioequivalence trial which I intend to analyze using proc mixed (SAS). I have analysed crossover bioequivalence trials before and used the formula 100%(e^MSE-1)^0.5 to calculate itrasubject CV where MSE is the mean square error. MSE was claculated using proc glm. How should I calculate MSE this time? Do I calculate two separate ANOVA models for each treatment and use the different MSE's from each analysis to give separate intra-subject CV's or do I take a completly different approach?

ddubins
☆

Toronto,
2008-03-01 20:28
(6036 d 11:39 ago)

@ Dr Andrew Leary
Posting: # 1652
Views: 17,146

## Calculation of intra-subject CVs in replicate design

Hi Andrew,

It's a bit late for this reply, but I found the answer to your question. You don't need to run proc GLM. The replicate SAS output gives all of the information you need to calculate intra- and inter-CV, where it outputs the covariate matrix ("Covariate Parameter Estimates"). The SAS output might look like this:

Covariate Parameter Estimates
Cov Parm Subject Group Estimate
FA(1,1) Subject 0.5928 <---- (sig_BT, the between-subject standard deviation for the Test product)
FA(2,1) Subject 0.4968 <---- (sig_BR, the between-subject standard deviation for the Reference product)
FA(2,2) Subject 2E-17 <---- (sig_D, the subject-by-formulation interaction term)
Residual Subject Treatment A 0.124 <---- (sig_WT^2, the within-subject standard deviation for the Test product)
Residual Subject Treatment B 0.242 <---- (sig_WR^2, the within-subject standard deviation for the Reference product)

The intra-subject variabilities are still calculated from the residuals as in a 2-way crossover, using:
IntraCV_T = 100%*sqrt(exp(sig_WT^2)-1) (in this case, = 100*sqrt(exp(0.124)-1) = 36.3%
IntraCV_R = 100%*sqrt(exp(sig_WR^2)-1) (in this case, = 100*sqrt(exp(0.242)-1) = 52.3%

FA(1,1) and FA(2,1) are the inter-subject standard deviations for Test and Reference products, respectively:
InterCV_T = 100%*sqrt(exp(sig_BT^2)-1) = 100*sqrt(exp(0.5928^2)-1) = 64.9%
IntraCV_R = 100%*sqrt(exp(sig_BR^2)-1) = 100*sqrt(exp(0.4968^2)-1) = 52.9%

Hope this helps,
Dave

David Dubins, Ph.D., B.A.Sc.
Associate Professor, Teaching Stream
Director, Pharmaceutical Chemistry Specialist Program
Leslie Dan Faculty of Pharmacy
University of Toronto

144 College Street (room PB802), Toronto, ON M5S 3M2
Tel. +1 416-946-5303; FAX: +1 416 978-8511
Helmut
★★★

Vienna, Austria,
2008-03-02 14:01
(6035 d 18:07 ago)

@ ddubins
Posting: # 1653
Views: 15,913

## Data set?

Hi Dave,

I guess you are referring to one of FDA's example data sets? If yes, which one?

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,
2008-03-03 13:05
(6034 d 19:02 ago)

@ ddubins
Posting: # 1654
Views: 16,608

## Calculation of intra-subject CVs in replicate design

Hello David,

i agree with your assignment of the intraindividual error terms.

❝ Covariate Parameter Estimates

❝ Cov Parm Subject Group Estimate

❝ FA(1,1) Subject 0.5928 <---- (sig_BT, the between-subject standard

❝ deviation for the Test product)

❝ FA(2,1) Subject 0.4968 <---- (sig_BR, the between-subject standard

❝ deviation for the Reference product)

❝ FA(2,2) Subject 2E-17 <---- (sig_D, the subject-by-formulation

❝ interaction term)

But your assignment of the FA(i,i) terms to the interindividual (co)variances is not correct i think.
Think of the G matrix (using your notation):
    G(1,1) = sig_BT2    G(2,2) = sig_BR2    G(1,2) = rho*sig_BT*sig_BR

Futher it is defined (subject-by-formulation interaction variance)
    sig_D2=G(1,1)+G(2,2)-2*G(1,2)          =sig_BT2+sig_BR2-2*rho*sig_BT*sig_BR 
The FA0(2) parameterization of the G-Matrix reads
    G(1,1)=FA(1,1)2    G(2,2)=FA(2,1)2+FA(2,2)2    G(1,2)=FA(1,1)*FA(2,1)

Confer to the SAS documentation for this.
By the way: G(1,1) = sig_BT2 is only valid, if your coding of test treatment preceedes that of the reference.

Thus with some algebra you obtain
    FA(1,1)=sig_BT    FA(2,1)=rho*sig_BR    FA(2,2)=sqrt(1-rho2)*sig_BR 

Thus your assignment of FA(2,1) is only valid if rho=1 which implies FA(2,2)=0.
In that case the subject-by-formulation interaction variance is
   sig_D2=FA(1,1)2+FA(2,1)2-2*FA(1,1)*FA(2,1) 

Regards,

Detlew
Sathya
☆

India,
2008-09-20 10:17
(5833 d 22:51 ago)

@ d_labes
Posting: # 2380
Views: 15,572

## Calculation of intra-subject CVs in replicate design

Hello d_labes,

This is Sathya Again.

Now I am trying to precede 4 period, 2 treatment, and 4 sequence studies
(by using the dataset from the link given by you)

SAS Code – Proc Mixed : forum_entry.php?id=1589
Intra_CV Calculation : forum_entry.php?id=1652
Inter_Cv Calculation : forum_entry.php?id=1654

The above links are my major reference for this study.

Further it is defined (subject-by-formulation interaction variance)

sig_D2=G (1, 1) +G (2, 2)-2*G (1, 2)       =sig_BT2+sig_BR2-2*rho*sig_BT*sig_BR

How can I find rho by using SAS?
And how can I get G matrix in SAS? I tried with G and Gcorr. But I am unable to get
G (1, 1), G (2, 2) and G (1, 2).

I got the following result for G and G CORR

Estimated G Correlation Matrix Row     Effect  subj    trt     Col1    Col2 1       trt     1       1       1.0000  1.0000 2       trt     1       2       1.0000  1.0000

Labes,

What are things I have to submit to the client company generally if BA/BE studies was given to us?

What are the calculations or parameter must be in SAS report for BA/BE?

If once replicate design will give to us for BA/BE study Whether We has to do PBE/ IBE or it depends upon the client requirement? What else the document I have to submit?

Sathya
d_labes
★★★

Berlin, Germany,
2008-09-22 13:35
(5831 d 19:32 ago)

@ Sathya
Posting: # 2381
Views: 15,679

## G matrix in SAS Proc Mixed

Dear Sathya,

❝ How can I find rho by using SAS?

❝ And how can I get G matrix in SAS? I tried with G and Gcorr. But I am

❝ unable to get G (1, 1), G (2, 2) and G (1, 2).

Look at your SAS output of Proc MIXED again. If you use the G option you will have a piece of output named "Estimated G Matrix". G(i,j) is the element with row i and column j.
For instance:
  Row    Effect       treat.    Subject        Col1       Col2    1    treatment    R           1          0.1181     0.1058    2    treatment    T           1          0.1058     0.09486 
Here G(1,1) is 0.1181, G(1,2) is 0.1058 and so on.
Yes, its that easy with matrices. Try to remember your math courses on that! They are not the same thing as Matratzen (German word, in english mattresses).

Why do you need rho?
If you are interested in, take the formulas above in this thread, a little puzzled math and you have a formula for rho from the elements of the G matrix. I left this for your excercise.
The option GCORR gives you a value of rho in the off-diagonal element of the "Estimated G Correlation Matrix".
Or parameterize with the CSH structure instead of FA0(2) (look at your SAS/Stat manual) and you will get directly an estimate of rho under "Covariance Parameter Estimates". Its name is CSH in the SAS output.

For the rest of your questions:
They look like the question "How can I earn a lot of money?". How shall I answer this?
Have a look at the Guidance of the country you will submit to. There are in most cases enough hints what you have to submit (up to such very special and detailed wishes of the regulators in the new EMEA draft 'The presentation of the findings of a bioequivalence trial should include a 2x2-table that presents for each sequence (in rows) and each period (in columns) means, standard deviations and number of observations for the observations in the respective period of a sequence.').

Concerning PBE/IBE search the forum and look again into Guidances.
You will find that usually no regulatory body will request this.

Regards,

Detlew
Helmut
★★★

Vienna, Austria,
2008-09-22 13:47
(5831 d 19:21 ago)

@ d_labes
Posting: # 2382
Views: 15,432

## Wordplay :-)

Matritzen # Matratzen

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
Sathya
☆

India,
2008-09-24 13:02
(5829 d 20:05 ago)

@ d_labes
Posting: # 2392
Views: 15,483

## G matrix in SAS Proc Mixed

Dear d_labes,

Thank you very much for your responses.

I didnot ask you that "How can I earn a lot of money?" . i just asked "will you give me your live experience on earning money?". It will prevent me from the disasters and guide me in right way.

If my questions disturb you then forgive me.

But your help is much worth. Thanks a lot.

Now i am concentrate on the guidelines.

And i find out the value of rho in the off-diagonal element of the "Estimated G Correlation Matrix".

once again Thank you.

Sathya
d_labes
★★★

Berlin, Germany,
2008-09-24 14:46
(5829 d 18:21 ago)

@ Sathya
Posting: # 2393
Views: 15,379

## G matrix in SAS Proc Mixed

Dear Sathya,

my intention was not to bother you.
It was the sort of question I meant, so generic, that prevent a reasonable answer.

Regards,

Detlew
Sathya
☆

India,
2008-09-25 08:02
(5829 d 01:05 ago)

@ d_labes
Posting: # 2398
Views: 15,375

Dear d_labes,

Thank you.

Sathya