Roger W. Jelliffe1 and David S. Bayard2
1) Laboratory of Applied Pharmacokinetics, University of Southern California, School of Medicine, Los Angeles CA, 90033; 2) Senior Research Scientist, Jet Propulsion Laboratory, Pasadena CA, 91109
This report considers updating Bayesian posterior densities for pharmacokinetic models having changing parameter values. The prior probability is assumed to be a discrete joint density. Parameter changes are modeled as “jumps” from one model support point to another within the same discrete density. Given such discrete priors, the multiple model (MM) estimation approach provides an exact analytical solution for updating the Bayesian posteriors. Our laboratory’s earlier studies showed that the MM estimator works well in pharmacokinetic applications where the patient’s parameters are unknown but constant.
Unfortunately, the MM estimator works less well where the patient’s parameter values vary. The IMM algorithm has emerged as an effective method in the literature for tracking changing parameter values, and is used by the aerospace community for tracking maneuvering targets. We implemented the IMM sequential Bayesian algorithm in pharmacokinetic software. Its performance was compared with the MM and MAP sequential Bayesian estimation methods, which are used in pharmacokinetic applications where parameter values do not change, using both simulated and real clinical data for the drug Tobramycin.
In a simulated therapeutic scenario of changing parameter values taking place at a stated time, the IMM approach tracked the behavior of the simulated patient with about half the integrated total error found with the MM and MAP methods. Further, in examining a real patient’s data, in which parameter values appeared to change significantly during therapy, the IMM approach tracked the patient’s data quite acceptably, and much better than the MAP Bayesian approach.
While the present paper focuses on estimation, the authors’ main motivation for studying this problem is to eventually develop better controllers, i.e., to extend the present Multiple Model active control approach to designing dosage regimens for unstable patients with varying parameter values.
Supported in part by NIH grants LM 05401 and RR 11526
Reference: PAGE 9 (2000) Abstr 117 [www.page-meeting.org/?abstract=117]
Poster: poster