Model-based, goal-oriented, individualised drug therapy. Linkage of population modelling, new 'multiple model' dosage design, bayesian feedback and individualised target goals.

This article examines the use of population pharmacokinetic models to store experiences about drugs in patients and to apply that experience to the care of new patients. Population models are the Bayesian prior. For truly individualised therapy, it is necessary first to select a specific target goal, such as a desired serum or peripheral compartment concentration, and then to develop the dosage regimen individualised to best hit that target in that patient. One must monitor the behaviour of the drug by measuring serum concentrations or other responses, hopefully obtained at optimally chosen times, not only to see the raw results, but to also make an individualised (Bayesian posterior) model of how the drug is behaving in that patient. Only then can one see the relationship between the dose and the absorption, distribution, effect and elimination of the drug, and the patient's clinical sensitivity to it; one must always look at the patient. Only by looking at both the patient and the model can it be judged whether the target goal was correct or needs to be changed. The adjusted dosage regimen is again developed to hit that target most precisely starting with the very next dose, not just for some future steady state. Nonparametric population models have discrete, not continuous, parameter distributions. These lead naturally into the multiple model method of dosage design, specifically to hit a desired target with the greatest possible precision for whatever past experience and present data are available on that drug--a new feature for this goal-oriented, model-based, individualised drug therapy. As clinical versions of this new approach become available from several centers, it should lead to further improvements in patient care, especially for bacterial and viral infections, cardiovascular therapy, and cancer and transplant situations.

SAAM II: Simulation, Analysis, and Modeling Software for tracer and pharmacokinetic studies.

Kinetic analysis and integrated systems modeling have contributed substantially to our understanding of the physiology and pathophysiology of metabolic systems and the distribution and clearance of drugs in humans and animals. In recent years, many researchers have become aware of the usefulness of these techniques in the experimental design. With this has come the recognition that the discipline of kinetic analysis requires its own expertise. The expertise can impact experimental design in many ways, from the collaborative and service activities in which individuals interact in formal ways to the development of software tools to aid in kinetic analysis. The purpose of this report is to describe one such software tool, Simulation, Analysis, and Modeling Software II (SAAM II). In the first part, we describe in general how the user can take advantage of the capabilities of the software system, and in the second part, we give three specific examples using multicompartmental models found in lipoprotein (apolipoprotein B [apoB] kinetics) and diabetes (glucose minimal model) research.

Approaches to population kinetic analysis with application to metabolic studies.

Population kinetic analysis is the methodology traditionally used to quantify inter-subject variability in pharmacokinetic studies. In the statistics literature, it is also called analysis of repeated measurement data or analysis of longitudinal data. In this work, we will state the population kinetics problem and give some historical background to its significance. Then we will describe and apply to case studies in intermediary metabolism various two-stage and other parametric methods for nonlinear mixed effects models. We will then briefly review the software available for population kinetic analysis.

Simulation of linear compartment models with application to nuclear medicine kinetic modeling.

Several techniques are evaluated for solving the linear ordinary differential equations arising from compartment models. The methods involve approximating the matrix exponential of the state matrix (i.e. the transition matrix). The computational efficiencies of these techniques, together with that of a general purpose differential equation solver, are compared for several models arising from radiopharmacokinetic studies. The matrix exponential calculations are performed using both Ward's Padé approximation method and an eigenvalue-eigenvector decomposition (QR factorization) of the matrix A. These two algorithms have been incorporated as simulation options into the programs of the ADAPT package. ADAPT consists of a set of high-level programs for simulation, parameter estimation and experiment design, developed primarily for basic and clinical research modeling and data analysis applications involving pharmacokinetic and pharmacodynamic processes. The advantages and disadvantages of these simulation strategies for solving linear kinetic models within a parameter estimation setting are illustrated and discussed.

A program package for simulation and parameter estimation in pharmacokinetic systems.

A set of programs is presented which has been developed for parameter estimation and simulation of models arising from pharmacokinetic applications. The programs can accommodate linear and nonlinear models with multiple inputs and multiple outputs. When the model is defined by differential equations, non-uniform repetitive dosage regimens can be handled. The model may also be entered in integrated form when single dose studies or uniform multiple dose studies are being considered. The programs employ a variable-step, variable-order integration routine to solve the model differential equations, and the Nelder-Mead simplex procedure to determine the parameter values which minimize a weighted least squares criterion. The programs have been written for an interactive time-sharing environment with the experimental data and model equations stored in files for future use.

Modeling, adaptive control, and optimal drug therapy.

Drug therapy, its clearly development, and the advent of pharmacokinetic models are described, from the original work of Teorell, through that of Augsberger and Kruger-Thiemer, to the present. Adaptive control of such models, long known in engineering, began in therapeutics with methods for linear and nonlinear least-squares regression, and has progressed to the Maximum Aposteriori Probability (MAP) Bayesian method. Strategies for optimal monitoring of serum concentrations are described and their clinical results briefly evaluated. Lastly, the new method of Approximate Optimal Closed-Loop (AOCL) control is described, in which the therapeutic regimen is used at the same time to probe (learn about) the patient's model approximately optimally. The new method considers the expected values of planned future serum concentrations (or other responses), in addition to the traditional measurement of past serum concentrations. This should optimize the process of learning about a patient's model while treating him at the same time.

Design of dosage regimens: a multiple model stochastic control approach.

This paper presents a general stochastic control framework for determining drug dosage regimens where the sample times, dosing times, desired goals, etc., occur at different times and in an asynchronous fashion. In the special case of multiple models with linear dynamics and quadratic cost (MMLQ), it is shown that the optimal open-loop stochastic control with linear control/state constraints can be solved exactly and efficiently as a quadratic program. This provides a simple and flexible method for computing open-loop feedback designs of drug dosage regimens. An implementation of the MMLQ adaptive control approach is demonstrated on a Lidocaine infusion process. For this example, the resulting MMLQ regimen is more effective than the MAP Bayesian regimen at reducing interpatient variability and keeping patients in the therapeutic range.

Population pharmacokinetics/pharmacodynamics modeling: parametric and nonparametric methods.

As clinicians acquire experience with the clinical and pharmacokinetic behavior of a drug, it is usually optimal to record this experience in the form of a population pharmacokinetic model, and then to relate the behavior of the model to the clinical effects of the drug or to a linked pharmacodynamic model. The role of population modeling is thus to describe and record clinical experience with the behavior of a drug in a certain group or population of patients or subjects.

Symbolic programs for structural identification of linear pharmacokinetic systems.

Most parameter estimation techniques implicitly assume that it is possible to determine the parameters of the system uniquely if there were no noise in the output. In practice, this is not always the case. Whether or not this assumption is true for a given input-output experiment is the problem of structural identification. Two programs utilizing symbolic matrix calculus are presented which aid in solving this problem for linear systems. Pharmacokinetic examples are given.

Pharmaco-informatics: more precise drug therapy from "multiple model" (MM) stochastic adaptive control regimens: evaluation with simulated vancomycin therapy.

MM stochastic control of dosage regimens permits essentially full use of information, either in a population pharmacokinetic model or a Bayesian updated MM parameter set, to achieve and maintain selected therapeutic goals with optimal precision. The regimens are visibly more precise than those developed using mean parameter values. Bayesian MM feedback has now also been implemented.

Achieving target goals most precisely using nonparametric compartmental models and "multiple model" design of dosage regimens.

Multiple model (MM) design and stochastic control of dosage regimens permit essentially full use of all the information contained in either a Bayesian prior nonparametric EM (NPEM) population pharmacokinetic model or in an MM Bayesian posterior updated parameter set, to achieve and maintain selected therapeutic goals with optimal precision (least predicted weighted squared error). The regimens are visibly more precise in the achievement of desired target goals than are current methods using mean or median population parameter values. Bayesian feedback has now also been incorporated into the MM software. An evaluation of MM dosage design using an NPEM population model versus dosage design based on conventional mean population parameter values is presented, using a population model of vancomycin. Further feedback control was also evaluated, incorporating realistic simulated uncertainties in the clinical environment such as those in the preparation and administration of doses.

Pharmaco-informatics: more precise drug therapy from 'multiple model' (MM) adaptive control regimens: evaluation with simulated vancomycin therapy.

A multiple model (MM) stochastic control of dosage regimens permits essentially optimal use of the information contained in either a population pharmacokinetic model or in a MM Bayesian updated parameter set to achieve and maintain selected therapeutic goals with optimal precision. The regimens are visibly more precise than those achieved using mean parameter values. Feedback has now also been incorporated into the MM software. An evaluation of MM adaptive control precision versus control achieved using population mean parameter values is presented using a real population model (Vancomycin). Further feedback control was evaluated, incorporating simulated clinical errors in the preparation and administration of doses.

Individualizing drug dosage regimens: roles of population pharmacokinetic and dynamic models, Bayesian fitting, and adaptive control.

The role of population pharmacokinetic modeling is to store experience with drug behavior. The behavior of the model is then correlated with the clinical behavior of the patients studied, permitting selection of a specific serum level therapeutic goal that is based on each individual patient's need for the drug and on the risk of adverse reactions, both of which must be considered. A dosage regimen is then computed to achieve that goal with maximum precision. The patient should not run a greater risk of toxicity than is justified, and should obtain the maximum possible benefit within the acceptable risk. The regimen is given and the patient monitored.