Pascal Maire, Roger W. Jelliffe, Xavier Barbaut, Nathalie Bleyzac, Bruno Charpiat, Christine Pivot, Eliane Vermeulen, Pierre Ducrozet, Marie-Aude Confesson, Alain Laffont,
Laboratory of Applied Pharmacokinetics, University of Southern California, Los Angeles and ADCAPT, Hospices Civils de Lyon, Hospital A. Charial, 69340 Francheville
What is the clinical relevance of population modeling approaches ? We need the results of population studies as Bayesian priors for therapeutic drug monitoring and optimal individualization of drug regimens. Also, because as we are in clinical settings, we are in a good position to obtain population behavior from the truly relevant patients, by collecting the data as we care from them. In this presentation we will illustrate these two aspects from our clinical experience of applied pharmacokinetics (PK).
1. Adaptive optimal control of drug regimens
Many drugs have narrow margins of safety and need individualized dosage for each patient. For some drugs, even the concept of a therapeutic window is too wide. It is better to set an individualized target goal based on that patientÃs need for the drug (a concentration in one of the compartments of the PK model) and then to try to achieve that goal as precisely as possible. This is optimal îgoal-oriented” drug therapy.
The compartmental model will have : a central (serum) compartment, possibly an absorptive compartment ; the first one possibly also connected to various peripheral compartments. Some of them will have their parameters estimated for each individual patient. Others will have fixed parameters gathered from the literature. Still others will be parts of pathophysiologic models, such as a model of diffusion into an endocardial vegetation, with in vitro parameters. It is also possible to model the effect itself, like the bacterial killing proccess for an antibiotic.
Traditional Bayesian controllers imply a Gaussian distribution for the pharmacokinetic parameters, storing the population information only as means, standard deviations, and covariances. Even with these restrictions we are able to control some clinical cases pretty well, as in endocarditis in very old patients.
The new Multiple Model Stochastic Bayesian controller (MM), however, uses the past information from nonparametric population analysis optimally, as it is not necessary to make any assumption about the form of the distribution. The result is a complete discrete probability density function which can be regarded as consisting of many (not just one) competing versions (or îmodels”) of the patient for whom the next initial drug regimen is designed. Each population support point (version, or model) is weighted by its probability of îbeing” the patient. In this way a given dosage regimen generates many serum level trajectories. Based on this, we can then compute the regimen which minimizes the weighted squared error in the achievement of our desired goal for each individual patient at the desired time(s). This MM controller can also take into account intraindividual variability such as model misspecification, and also stated environmental errors in dosage preparation and timing.
For the MM controller, in the event that a parametric or continuous prior is initially provided, it must be converted into a discrete distribution that approximates the original distribution in some fashion. Milman has developed an approach based on replacing the given parameters and their ranges with one that shares some of the original distribution=92s caracteristics in a moment matching / maximum entropy optimization.=20
2. Exploration of a noisy clinical environment
As you develop a TDM program in a hospital, one must deal with several problems, most of them related to the above environmental sources of noise. We have made systematic explorations of the critical noise in clinical situations : serum assay errors, drug dispensing errors (in our studies approximatly 10% CV), uncertainties about sampling times, I.V. preparations, and times of drug administration. All of these lead to a decrease in therapeutic precision.
We have developed specific forms to gather useful clinical data during clinical practice. Such a precise database is a wealth of information for future population studies based on the actual clinical situations in the really relevant patient population.
3. Nonparametric population analysis
Nonparametric population analysis will become especially useful for therapeutic drug monitoring and invidualized dosage regimens when used with multiple model controllers.
By itself it also permits the study of large populations. An example is a population of 634 patients treated with amikacin, which can in fact be composed of various subpopulations such general medicine, diabetic, neutropenic, and elderly patients. More and more we must deal in clinical practice with patients who are at the same time members of several different subpopulations, i.e. : both old, diabetic, and neutropenic. This is different from using prior information from only one subgroup.
In elderly patients, nonparametric population modeling also lets one deal with the differential aging process affecting renal elimination for drugs mainly excreted via the kidneys, such as the aminoglycosides.
In the near future, larger online computation resources can help us deal with larger and nonlinear PK/PD population model parameter estimation.
Conclusions
Nonparametric population models, coupled with the new multiple model dosage design strategy, are specifically designed to achieve goals with a minimum weighted squared error, and are also able to incorporate Bayesian feedback from later serum level data, properly revising the multiple support points. Thus nonparametric population modeling, Bayesian feedback, and multiple model dosage design provide us with powerful new methods both to study drug behavior in patients, and to apply such information to optimize precise drug therapy for practical clinical patient care.
Reference: PAGE 5 (1996) Abstr 561 [www.page-meeting.org/?abstract=561]
Poster: oral presentation