Bioequivalence and Bioavailability Forum

Dear randombadger!

The badger [zool.] or to badger ?

Dear Helmut!

Let me snap-in.
RB's question is a wide field. It is tilled with many matrices some beyond the horizon of a normal mortal mind.

The difference of your two codes lies in the specification of the inter-subject covariances.
The FDA model specifies different variabilities of the treatment groups plus a correlation of T vs. R within a subject.
Let us write it down in the CSH notation which is another possibility in the FDA Statistical guidance:
(   s2bT     rho*sbT*sbR )
( rho*sbT*sbR   s2bR     )
This notation is easier to interpret than the FA0(2) parametrisation which is only for assuring that the G-matrix is positive definite.

From that specification the so-called subject-by-treatment interaction variance is defined as
s2D = s2bT + s2bR - 2*rho*sbT*sbR
This term is also known under the name subject-by-formulation interaction.
It had became famous in the days of IBE - individual bioequivalence.

If you are convinced that there doesn't exists such a horrible thing like subject-by-treatment-interaction set it to zero!
This is only possible under the two conditions
1: sbT = sbR = sbetween i.e. equal between-subject variabilities of T and R
2: rho = 1, i.e. perfect correlation
as you can easily verify.
Then the G-matrix above reduces to
( s2between   s2between )
( s2between   s2between )

Unfortunately there is no TYPE=blabla in the SAS Proc MIXED code to specify exactly this structure in the FDA like syntax.
But your second code with the different RANDOM statement is fitting exactly this model!

You can eventually try the TYPE=CS which specifies a matrix according to
( s2+s1   s2   )
(  s2    s2+s1 )
and start with the parameter s₁=0 and hold it at this value during the REML fit. Or cross your fingers and hope that the data are best fit with s₁=0 (called CS in the SAS output).

Hope this all makes sense to you. To me only after some beer .
The key message: Different models of the inter-subject covariance -> different intra-subject CVs.
But I'm convinced if the subject-by-treatment interaction is approximately negligible there shouldn't be great differences in the intra-subject CVs.
RB, can you eventually post your values?

BTW: Concerning carry-over in the model I fully coincide with Helmut.
Concerning the DDFM=Satterth or DDFM=KR its a matter of taste. The FDA code arose from times where the Kenward-Roger method was not implemented or experimental in SAS. But its the more modern method and commonly seen as more appropriate in case of small sample sizes.
DDFM=KR is used through out in the book B. Jones and M.G. Kenward "Design and Analysis of Cross-over Trials" Chapman & Hall/CRC, Boca Raton (2nd ed. 2003). Not so astonishing if you look at the second author .