Bioequivalence and Bioavailability Forum

Dear Atish,

to puzzle is an art and to read needs glasses .

❝ FA(1,1) and FA(2,1) are the inter-subject 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 G-matrix contains the inter-individual variabilities (diagonal elements).
This matrix can be parameterized in different ways.
Using the FA0(2) parameterization you get:
  sig_BR2=G(1,1)=FA(1,1)2
  sig_BT2=G(2,2)=FA(2,1)2+FA(2,2)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 SAS-output names of the covariance parameters):
  sig_BR2=G(1,1)=Var(1)
  sig_BT2=G(2,2)=Var(2)

❝ 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 log-transformed 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 subject-by-formulation 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_D2=FA(1,1)2+FA(2,1)2+FA(2,2)2-2*FA(1,1)*FA(2,1)
      =(FA(1,1)-FA(2,1))2+FA(2,2)2
and in the CSH model sig_D2=Var(1)+Var(2)-2*CSH*sqrt(Var(1))*sqrt(Var(2))
      =sig_BR2+sig_BT2-rho*sig_BR*sig_BT
(in SAS the correlation rho is named CSH).

Again my question: What is your intention in calculating the subject-by-formulation 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,
"Subject-by-Formulation Interaction in Determinations of Individual Bioequivalence: Bias and Prevalence",
Pharmaceutical Research, Volume 16, Number 2, p186-190 (1999)
A short resume can be found at
www.dkfz.de/biostatistics/iscb-gmds-99/abstracts/20062.pdf