Optimal Sampling Times for Bayesian Estimation of the Pharmacokinetic Parameters of Nortriptyline During Therapeutic Drug Monitoring

Abstract

Sampling times for Bayesian estimation of the pharmacokinetic parameters of an antidepressant drug, nortriptyline, during its therapeutic drug monitoring were optimized. Our attention was focused on designs including a limited number of measurements: one, two, and three sample designs in which sampling times had to be chosen between 0 and 24 hr after the last intake of a test-dose study. The optimization was conducted in four groups of patients defined by their gender and the administration or not of concomitant drugs inhibiting the metabolism of nortriptyline. The Bayesian design criterion was defined as the expected information provided by an experiment. A stochastic approximation algorithm, the Kiefer–Wolfowitz algorithm, was used for the criterion maximization under experimental constraints. Results showed that optimal Bayesian sampling times differ between patients in monotherapy and polytherapy. For one-sample designs the measurements have to be performed either at the lower (0 hr) or at the upper (24 hr) bound of the admissible interval. Replications were often found for 2- and 3-point designs. Other sampling designs can lead to criterion close to the optimum and can therefore be performed without great loss of information. In contrast, we found that several designs lead to low values of the information criterion, which justifies the approach.