Bioequivalence and Bioavailability Forum

Ravi ★ India, 2009-04-11 10:35 (6265 d 01:21 ago) Posting: # 3507 Views: 40,405	Intra subject CV% and Inter subject CV% [General Statistics] Post reply
	Dear All, In one of the BE crossover biostudy we performed, it was observed that CV_intra > CV_inter. Now my question is how does it affects the study analysis. Do we have to use the same apporach 80-125% for establishing BE or we have to modify/change our study design. What exactly we have do in this situation? Kindly give ur valuable suggestions. — Thanks & Regards Ravi Pandey

Helmut
★★★

Vienna, Austria,
2009-04-11 15:19
(6264 d 20:36 ago)

@ Ravi
Posting: # 3511
Views: 37,109

CV%-intra > CV%-inter

Post reply

Dear Ravi!

❝ In one of the BE crossover biostudy we performed, it was observed that CV_intra > CV_inter.

Interesting!

❝ […] how does it affects the study analysis. Do we have to use the same apporach 80-125% for establishing BE […]

Yes. But you may obtain a negative variance component in the random term subject(sequence) which calls for treating this effect as fixed. An example is given in the data-set of the Canadian guideline.

❝ […] or we have to modify/change our study design.

How will you modify the design once the study is finished?

—
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

Ravi ★ India, 2009-04-14 08:01 (6262 d 03:54 ago) @ Helmut Posting: # 3518 Views: 36,806	CV%-intra > CV%-inter Post reply
	Dear HS, Thanks for your valuable comments. — Thanks & Regards Ravi Pandey

kvitamin
☆

Hungary,
2009-10-07 13:40
(6085 d 22:15 ago)

@ Helmut
Posting: # 4313
Views: 36,596

CV%-intra > CV%-inter

Post reply

Dear Helmut,

I would like to calculate intra and inter CV values of PK parameters in SAS proc mixed (a bioav. study: 2 period, 2 treatments crossover design).
I found some documents about the proc mixed, but it was not enough for me to know what is the right way to get (right) results for CVs.

First of all, I set in the proc mixed to get residuals in a data set. Then I calculate MSE from the residuals.
Then I applied the formula: CV=100*sqrt(exp(MSE)-1), where I get a result, but I do not know it is the right method to get the real CV?

Or should I use covariance parameters (from SAS output) to get the CV?

What is the way to get inter, and intra CV?

Thank you!

Kvitamin

d_labes
★★★

Berlin, Germany,
2009-10-07 15:05
(6085 d 20:50 ago)

@ kvitamin
Posting: # 4315
Views: 40,553

Proc MIXED CV%-intra, CV%-inter

Post reply

Dear Vitamin K, (what a nick name :-)

)

❝ First of all, I set in the proc mixed to get residuals in a data set. Then I calculate MSE from the residuals.

❝ Then I applied the formula: CV=100*sqrt(exp(MSE)-1), where I get a result, but I do not know it is the right method to get the real CV?

I'm not Helmut but I hope I can answer your question to some extent.
Sorry, but I do not understand what you do with Proc Mixed from your description :confused:

.

Here is the SAS code I would employ for a classical 2x2 cross over (use search in this forum to find a lot of discussions!):

Proc MIXED data=yours;

class subject treatment period sequence;



model logPK=treatment period sequence;

random subject(sequence);

Estimate 'T-R' treatment -1 1/Cl alpha=0.1;



Run;

logPK is the log-transformed parameter under analysis (AUC, Cmax or so).
The estimate statement assumes that treatment is coded with T and R.

Le's use Helmuts data with 24 subjects found here.

Among the lengthy output you will find covariance parameter estimates


                 The Mixed Procedure

[...]


           Covariance Parameter Estimates



            Cov Parm              Estimate



            Subject(Sequence)      0.1002

            Residual               0.04102



[...]

Subject(Sequence) is the inter-subject variability s²_inter and residual the within-subject (or intra-subject) variability s²_within.
Convert them to CV with the formula CV=100*sqrt(exp(s²_{inter or within})-1) with the corresponding variance. But cave! This only applies if your PK parameter under analysis is log-transformed.

BTW: Why do you use Proc MIXED here?

—
Regards,

Detlew

kvitamin
☆

Hungary,
2009-10-07 18:15
(6085 d 17:40 ago)

@ d_labes
Posting: # 4317
Views: 38,092

Proc MIXED CV%-intra, CV%-inter

Post reply

Dear D_Labes,

Thank you very much for your help.
I apply the SAS proc mixed because this procedure is assessed in FDA's guidance and I want to learn how works it (it is not simple).

If I have a study data set as Helmuts data with 52 subjects and I calculate
intra-CV and inter-CV based on your help, I will get results for all the subjects not for subjects in group T or subjects in group R, separately.

For example, if I want to calculate inter-subject CVs for T and R formulations then intra-subject CV, how can I calculate them from the covariance parameter output? There stand only two values (as it was presented by your answer) and I need three results, eg for lognormal AUC0-t:

AUC0-t A inter-CV(?)  

         intra-CV(?)

       B inter-CV(?)

Thank you!

kvitamin

Edit: Full quote removed. Please delete anything from the text of the original poster which is not necessary in understanding your answer; see also this post!
PS: Which dataset of mine with 52 subjects are you talking about? [Helmut]

d_labes
★★★

Berlin, Germany,
2009-10-07 18:48
(6085 d 17:07 ago)

@ kvitamin
Posting: # 4318
Views: 36,203

MIXED up and lost in design

Post reply

Dear KVitamin,

❝ I apply the SAS proc mixed because this procedure is assessed in FDA's guidance and I want to learn how works it (it is not simple).

The Proc MIXED named in the FDA guidance "Statistical approaches ..." is recommended for replicate cross-over studies.
Here we are talking about the classical 2x2 cross-over.
Traditionally this is evaluated with Proc GLM if you use SAS for evaluation.

❝ If I have a study data set as Helmuts data with 52 subjects and I calculate intra-CV and inter-CV based on your help, I will get results for all the subjects not for subjects in group T or subjects in group R, separately.

There are no such subjects in group T or group R! In a cross-over study each subject gets both treatments.

I strongly suggest that you study some textbooks about design and evaluation of bioequivalence studies before fiddling with a complex piece of software such as Proc MIXED.
A good starting point are Helmut's lectures. For a collection of books see here.

—
Regards,

Detlew

kvitamin
☆

Hungary,
2009-10-08 12:50
(6084 d 23:06 ago)

@ d_labes
Posting: # 4320
Views: 36,267

MIXED up and lost in design

Post reply

Dear d_labes,

Thank you for your answer.
Really, I try to analyze a 2x2 crossover study (non replicated), where each volunteers get each formulas, but each formulas only once. So, TR and RT are the sequences in periods.
I understand (?) that there is only one intra-subject CV for each PK parameters (e.g. AUC0-t), because each subjects get both formulas, so the intra-CV gives information about the variability of subjects AUC0-t in formulas point of view.
But inter-CV get information about the variability of subjects AUC0-t for formulas in separated way: one inter-subject CV for the T formula and one other for the R formula. It is right idea or not?

kvitamin

Edit: Full quote removed. Please delete anything from the text of the original poster which is not necessary in understanding your answer; see also this post! [Ohlbe]

d_labes
★★★

Berlin, Germany,
2009-10-08 15:41
(6084 d 20:14 ago)

@ kvitamin
Posting: # 4322
Views: 36,309

2x2, inter, intra, total or what

Post reply

Dear kvitamin,

❝ I understand (?) that there is only one intra-subject CV for each PK parameters (e.g. AUC0-t), because each subjects get both formulas, so the intra-CV gives information about the variability of subjects AUC0-t in formulas point of view.

I do not understand (this).
The intra-subject CV from a classical 2x2 cross-over design is a pooled intra-subject variability for both formulations under study.
A separation in formulation specific values (for Test and Reference) is not possible within the 2x2 cross-over. It needs generally replicate designs in which each formulation is applied more then once at same subject.

❝ But inter-CV get information about the variability of subjects AUC0-t for formulas in separated way: one inter-subject CV for the T formula and one other for the R formula. It is right idea or not?

Not. If you analyze f.i. AUC for Test and Reference separately you will get the total variability, a sum of within-subject and between-subject variability:
s²_T=s²_between,T+s²_within,T for Test
s²_R=s²_between,R+s²_within,R for Reference

If you are not able to separate the intra-subject variability for Test and Reference, how will you estimate formulation specific between-subject variabilities?

Within the average bioequivalence framework all these variabilities are of no especial interest because you have to show only that the means (ratios) of the PK metrics are equivalent.

—
Regards,

Detlew

kvitamin ☆ Hungary, 2009-10-09 13:05 (6083 d 22:50 ago) @ d_labes Posting: # 4330 Views: 36,318	2x2, inter, intra, total or what Post reply
	Dear D. Labes, Ok thank you very much for your help! It is already clear, in 2x2 crossover study there is only one intra CV and one inter CV. And these are calculated from covariance parameters. kvitamin

Intra subject CV% and Inter subject CV% [General Sta­tis­tics]

CV%-intra > CV%-inter

CV%-intra > CV%-inter

CV%-intra > CV%-inter

Proc MIXED CV%-intra, CV%-inter

Proc MIXED CV%-intra, CV%-inter

MIXED up and lost in design

MIXED up and lost in design

2x2, inter, intra, total or what

2x2, inter, intra, total or what

Intra subject CV% and Inter subject CV% [General Statistics]