Re: Nagaraja

Date: Fri, 11 Jun 1999 12:33:04 +0200 From: Mats Karlsson <Mats.Karlsson@biof.uu.se> Subject: Re: Nagaraja Dear Nagaraja, In addition to Lewis reply, I think an idea of Taright et al (abstract below) may be important. In short, variability between individual in a covariate may be differently related to the PK parameter than variability within a subject. E.g. hematocrit may vary between subjects but not be particularly related to the parameter in question, whereas changes in hematocrit within a subject can be a surrogate for a progressing disease that may be important for the clearance of the drug. One way of handling such differences are to make 2 covariates from the hematocrit (HEM), namely baseline hematocrit (BHEM), which is the starting (or average) value and delta-hematocrit (DHEM), the difference from the individuals starting (or average) value. Hope it was clear, I can't follow up on this discussion as I'll be away for two weeks. Best regards, Mats Presented at PAGE -97 http://userpage.fu-berlin.de/~page/index.cgi NON-STATIONARITY OF KINETIC PARAMETERS IN MULTI-OCCASION DESIGNS Namik Taright, France Mentré and Alain Mallet, INSERM U436, Mathematical and Statistical Modelling in Biology and Medicine 91 boulevard de l'Hôpital, 75013 Paris, France Several studies in pharmacokinetic literature reveal variations in time of individual kinetic parameters. An interesting one is that of Tornatore et al. (1995) about methylprednisolone pharmacokinetics during chronic immunosuppression in renal transplant. They showed variations in individual parameters between visits. They also showed an alteration in population characteristics of clearance and volume. These results indicate a non-stationarity of the parameters and also suggest individual trajectories that need to be modelled in view of therapeutic drug monitoring. We extend the work of Harrison and Stevens (1976) about non-constancy of parameters in simple linear regression to the context of population pharmacokinetics. Our work follows that of Karlsson and Sheiner (1993) who prompt the use of an inter-occasions variability model. We propose second-stage models accounting for the non-stationarity of individual parameters. These models relate pharmacokinetic parameters to covariates and comprise two effects. First, a so-called cross-sectional effect relating parameters to covariates at the first occasion, which accounts for the usual interindividual variability. Second, a longitudinal random effect accounting for the impact of time-varying covariates on the pharmacokinetic parameters across occasions. Estimation is done with conditional maximum likelihood after first-order expansion of the nonlinear regression model around Bayesian estimates of random effects using a pseudo-EM algorithm. Illustrations on simulated data sets are shown. Results based on several experimental designs with various number of subjects and occasions are given, including bias and precision of the estimates. Graphical techniques are used for model building. Based on Bayesian estimates of parameters and residuals of the second-stage model, these techniques might help for detecting the inadequacy of simpler models. Nested models are compared with adequate likelihood ratio tests. Usefulness of such models will be discussed. Tornatore, Reed and Venuto (1995) Ann. Pharmacother 29, 120 -124. Harrison and Stevens (1976) J. R. Statist. Soc. B. 38, 205 - 247. Karlsson and Sheiner (1993) J. Pharmacokinet. Biopharm. 21, 735 - 750 ________________________________________________________ Mats Karlsson, PhD Uppsala University Div. of Biopharmaceutics and Pharmacokinetics Dept. of Pharmacy/ Box 580, SE-751 23 Uppsala, Sweden Internet: mats.karlsson@biof.uu.se Phone: +46 18 471 41 05 Fax: +46 18 471 40 03