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