Mark H. Milman

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

SummaryThis 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 centres, it should lead to further improvements in patient care, especially for bacterial and viral infections, cardiovascular therapy, and cancer and transplant situations.

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.

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.

Stochastic control of pharmacokinetic systems

The application of stochastic control theory to the clinical problem of designing a dosage regimen for a pharmacokinetic system is considered. This involves defining a patient-dependent pharmacokinetic model and a clinically appropriate therapeutic goal. Most investigators have attacked the dosage regimen problem by first estimating the values of the patients unknown model parameters and then controlling the system as if those parameter estimates were in fact the true values. We have developed an alternative approach utilizing stochastic control theory in which the estimation and control phases of the problem are not separated. Mathematical results are given which show that this approach yields significant potential improvement in attaining, for example, therapeutic serum level goals over methods In which estimation and control are separated. Finally, a computer simulation is given for the optimal stochastic control of an aminoglycoside regimen which shows that this approach is feasible for practical applications.

Multiple model (MM) dosage design: achieving target goals with maximal precision

Dosage regimens based on parametric population models use single values to describe each parameter distribution. When a target goal is selected, the regimen to achieve it assumes that it does so exactly. In contrast, multiple-model (MM) dosage design is based on nonparametric (NP) population models which have up to one set of parameter values for each subject studied in the population. With this more likely model, multiple predictions are possible. Using these NP models, one can compute the MM dosage regimen which specifically minimizes the predicted weighted squared error with which a target goal can be achieved. With feedback from blood serum concentrations, each set of parameter values in the NP prior has its probability recomputed. Using that revised model, the new regimen to achieve the target with maximum precision is again computed. A new interacting MM sequential Bayesian method then estimates posterior densities when parameter values have been changing during the analysis. A new clinical software package is under development.

“Maximum Entropy” (ME) Discrete Population PK Parameter Distributions for Use with “Multiple Model” (MM) Dosage

Clinical Pharmacology & Therapeutics (1996) 59, 207–207; doi: 10.1038/sj.clpt.1996.326