The estimation of population pharmacokinetic parameters using an EM algorithm

An EM algorithm was used to analyse data arising from non-linear mixed-effects models. The fixed parameters were determined by maximum likelihood using simplex minimization, and the random effects were estimated using the EM algorithm after linearization with respect to the random effects. Applications to a simple linear model and population pharmacokinetics are described. The use of posterior parameter estimates to investigate covariate relationships is briefly described. The implementation of the estimation-maximization (EM) algorithm described here has proved in practice to be robust but slow. We intend to use a Newton-Raphson minimization routine in place of the simplex method to hasten convergence. The alternative linearization of the non-linear mixed effects model suggested by Lindstrom and Bates (Biometrics 46 (1990) 673-687) is much more unstable than the usual linearization, especially during the initial iterations. In the case of indomethacin the two linearizations produced very similar results. The individual posterior parameter estimates provided by the program are very useful for the detection of covariate relationships in population pharmacokinetic studies. In addition, the posterior means can be used in the estimation of pharmacokinetic-pharmacodynamic relationships from sparse pharmacokinetic data where individual modelling is impossible.