Re: Parameterization!!!

From: Mats Karlsson <Mats.Karlsson@farmbio.uu.se> Subject: Re: Parameterization!!! Date: Sun, 13 May 2001 12:29:30 +0200 Dear Leonid, See comments below. "Gibiansky, Leonid" skrev: > As you mentioned, the model > CL=THETA(1)*EXP(ETA(1)+ETA(3)) > V=THETA(2)*EXP(ETA(2)+ETA(3)) > imposes restrictions on the covariate matrix. For example, the models with > negative correlations > CL=THETA(1)*EXP(ETA(1)+ETA(3)) > V=THETA(2)*EXP(ETA(2)-ETA(3)) > are not covered. Yes. One could certainly try this if the correlation is negative. I just presented the positive correlation because that is the most commonly expected one for CL and V. > More general (and the most general) one would be > CL=THETA(1)*EXP(ETA(1)+ETA(3)) > V=THETA(2)*EXP(ETA(2)+THETA(3)*ETA(3)) > However, with this model one has an extra parameter, and it may cause > problems on the covariance and/or POSTHOC steps (have you tried it ? is it > really a problem ?). I would use the following instead (which I think is as general but with only three parameters): CL= THETA(1)*EXP(THETA(3) * (ETA(1) + THETA(5)*ETA(3)) V = THETA(2) *EXP(THETA(4) * (ETA(2) + SQRT(THETA(5)*THETA(5))*ETA(3)) Where omega for ETA(1), ETA(2) and ETA(3) are fixed to 1. IF THETA(5) is negative, correlation is negative, whereas if it is positive correlation is positive. > Alternatively, one can try > CL=THETA(1)*EXP(ETA(1)) > V=THETA(2)*EXP(ETA(2)+THETA(3)*ETA(1)) > In this case, ETA(1) is mainly responsible for the covariates present in CL, > THETA(3) shows the correlation, and ETA(2) is mainly responsible for the > covariates that are present only in V. Plots of ETA(1) and ETA(2) vs. > covariates then will show what to include into covariate model for each of > the parameters. Do you have any experience with similar parameterizations ? Only with the one I mention above which seems to work fine. Best regards, Mats -- Mats Karlsson, PhD Professor of Pharmacometrics Div. of Pharmacokinetics and Drug Therapy Dept. of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 SE-751 24 Uppsala Sweden phone +46 18 471 4105 fax +46 18 471 4003 mats.karlsson@farmbio.uu.se