Mats O Karlsson and E Niclas Jonsson
Div of Pharmacokinetics and Biopharmaceutics, Dept of Pharmacy, Uppsala University, Sweden
Model building techniques for identifying covariate relationships that have been used include: screening each covariate on each parameter, residual plots inspection, graphical exploration of empirical Bayes (posthoc) parameter values versus covariate values (1), stepwise multiple linear regression of posthoc parameter values versus covariate values (2) and stepwise generalised additive modelling, GAM (3). These methods only identify candidate covariate relationships. In all cases, the final covariate model has to be built based on the raw data, rather than residuals or parameter estimates. Of the mentioned screening methods, we have found the GAM most useful although it is associated with several drawbacks: (i) the covariate model is built for one parameter at a time, ignoring potential covariate relationships for other parameters, (ii) it cannot appropriately handle covariates that vary over time, and (iii) it is dependent on the quality of the empirical Bayes estimates.
We suggest a model building scheme that avoids the main disadvantages of the GAM and in addition is implemented directly into NONMEM, condensing the steps of finding candidate covariates and assessing their importance on the raw data to a single procedure. The principle for it is simple: (i) a basic model without any covariate relationship is established, (ii) for this model each covariate is tested on each covariate using a linear relationship, (iii) the most important covariate-parameter relationship, provided it is significant, is included to form a new basic model, (iv) steps ii and iii are repeated and for linear relationships found, non-linear relationships are also tested, (v) when no more significant relationships can be included, a full model has been developed, (vi) the full model is stepwise challenged (backwards deletion) using a stricter criteria than the one used during the forward model building, (vii) a final model is declared when all covariate components are significant at the set significance level.
The implementation of the proposed model building scheme has two major obstacles, the complexity to set up the sequence of runs necessary and the potentially long run-times of the entire scheme. The former can be overcome by automation and for the situations where total run-time may pose a problem, we suggest a linearization of the covariate effect on the non-linear mixed effects model. The linearization which, makes use of the derivatives of the predictions with respect to the parameters from the model without covariates, turn the estimation problem from non- linear to linear mixed effects modelling.
The model building scheme, with and without the linearization, was evaluated on simulated data sets. The evaluation was performed with respect to covariates included – identification of both true and false covariate relationships – and with respect to predictive performance. The procedures identify covariate models that are close to the model supported by the data set. Also, the models generated by the model building scheme have a predictive capability close to those based on the components of the true model that are supported by the data.
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2 P.O. Maitre, M. Burer, D. Thomson, D.R. Stanski. A three-step approach combining bayesian regression and NONMEM population analysis: application to midazolam. J. Pharmacokinet. Biopharm. 19(4):377-384, 1991.
3 J.W. Mandema, D. Verotta, L.B. Sheiner. Building population pharmacokinetic/pharmacodynamic models. I. Models for covariate effects. J. Pharmacokinet. Biopharm. 20(5):511-528, 1992.
Reference: PAGE 7 (1998) Abstr 678 [www.page-meeting.org/?abstract=678]
Poster: oral presentation