FRIDAY, February 15, 2008
Time: 1:30 - 2:30 PM
Constant 1048

Title: Statistical Analysis Using Physiologically Based Pharmacokinetic Modeling

Martin D. Kline
Department of Mathematics and Statistics
University of Maryland-Baltimore County

Physiologically based pharmacokinetic (PBPK) modeling provides a mathematical means to simulate the time courses of chemicals and their metabolites throughout the body. In this talk I will first illustrate the basic principles behind this type of modeling by presenting some particular PBPK models in detail. Next I will show how one can use an appropriate PBPK model to carry out a statistical analysis of pharmacokinetic data. In this context, pharmacokinetic data describe absorption, distribution, metabolism, and/or excretion of some chemical to which a subject is exposed. In conducting a statistical analysis, the pharmacokinetic data can be modeled by means of an appropriate PBPK model.

The PBPK model itself consists of a system of (nonlinear) ordinary differential equations (ODEs) and algebraic equations. These models are physiologically based because as we will see, the model consists of several inter-related compartments corresponding to bodily tissues such as fat, liver, blood, muscle, etc. In analyzing pharmacokinetic data, typically an observed response Y is modeled as arising from an unknown mean coupled with a random noise. The mean in turn is assumed to come from the solution to the system of ODEs describing the appropriate PBPK model. The solution to this system of ODEs in general admits no closed form. Usually there are many parameters appearing in these ODEs, which either need to be estimated or can be determined from other sources. The major difficulty in dealing with such PBPK models, which distinguishes this approach from standard statistical inference problems, is that the ODEs cannot be readily solved to yield explicit expressions for the means. Hence we must solve the ODEs via complex numerical computations and algorithms. I will discuss three specific problems of data analysis using PBPK modeling. We will see that from a statistical point of view, each of these problems presents its own challenges.