## Third opinion [RSABE / ABEL]

Hi John,

» Detlew, need help!

Here I am! But don't know if I can help anyway. The whole story "Use Proc MIXED code for Partial replicate design" is mysterious to me.

» Here is the covariance output from SAS on ln AUCt
»
» Covariance Parameter Estimates
» Cov Parm  Subject       Group         Estimate
» FA(1,1)   subject                     0.4427
» FA(2,1)   subject                     0.4236
» FA(2,2)   subject                     0.2481
» Residual  subject   formulation Ref   0.05301
» Residual  subject   formulation Test  0.02648
»
» Question, what does the residual "formulation Test" represent? Is it the residual attributed to both test and ref

No.
As Helmut already pointed out: an ambiguous attempt of the REML algo to obtain the within-subject variance of the Test formulation. But IMHO the model is over-specified (s2D + s2wT not separable, see below) and therefore there is no guarantee that the value obtained is reasonable.

» while residual "formulation ref" is attributed to the ref (since it was given 2x)?

Correct. Unambiguously identifiable.

» which one would one use to compute the 90% geometric CI then?

Not clear to me what a 90% geometric CI is .

The difference µT-µR has as standard error associated with it for the partial replicate design

sd = sqrt((s2D + s2wT + s2wR/2)*sum(1/ni)/seq^2)
where s2D is the variance of the subject-by-formulation interaction, ni are the number of subjects in the sequence groups, seq is the number of sequences.

s2D can be obtained from the G-matrix according to
s2D = g11+g22-2*g12
(see for more details this post).

Since the model seems over-specified try to use a simple model, f.i. neglect s2D which in turn results in a CS variance-covariance structure for the random part. Sometimes this helps.

BTW: @Helmut, asking the FDA seems a very good idea!

Regards,

Detlew

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