From farkad.ezzet@chbs-msm1.chbs.mhs.ciba.com Thu Oct 12 04:19:11 1995
Subject: Negative values for ETA

Dear nonmem user,

I have the following problem, if you ave an answer I would appreciate a reply:

12 healthy volunteers provided data in an absolute bioavalability trial using a two-period cross over design. Following the iv formulation 17 blood samples were withdrawn while following the oral formulation 12 blood samples were withdrawn. The PK model is a two compartment model as can easily be seen from the iv data.

I wanted to fit this model to all data together using the following parameterization :

ALPH = THETA(1) * EXP(ETA(1))
BETA = THETA(2) * EXP(ETA(2))
K21 = THETA(3)
V = THETA(4) * EXP(ETA(3))
KA = THETA(5) * EXP(ETA(4))
FA = 0.23 * EXP(ETA(5))
LAG = 0.3 * EXP(ETA(6))
Y = F + F * EPS(1) + EPS(2),

where KA is absorption rate, FA is bioavaialbility fraction and LAG is lag time.

It looks that I have a reasonable fit (as can be checked by WRES and by other goodness of fit criteria). Values for the individual ETA's are well behaved and nicely spread around zero, except for ETA(4). ETA(4) has negative values except for one individual. Meaning ETA(4) does not distribute normally around zero. Of course this leads to overestimation of the population estimate of KA. In fact if I take the average of KA using KA= THETA(5) * EXP(ETA(4)), this gives a value of 0.77.

Now in a separate run where I fix THETA(5), that is if I define KA = 0.77 * EXP(ETA(4)), the individual ETA's are now well spread around zero.

I feel very uncomfortable at fixing KA this way, because I would like the algorithm to estimate it for me and to provide a SE. So where is the problem, and how do I fix it. Can I accept the estimate of KA as 0.77 ?

I look forward to hearing from you.

Best regards

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