Pharmacokinetic-Pharmacodynamic Modeling and Simulation

Abstract

At present, population pharmacokinetics has taken off with an exponential increase in published papers in the last decade. It is fair to say that population pharmacokinetics has revolutionized how data from clinical studies is analyzed. Population pharmacokinetics methods are used almost exclusively for phase II and III studies and to summarize data across a drug development program. Advances in pharmacokinetic and pharmacodynamic modeling will allow fewer, more focused and informative clinical trials, and lead to significant cost savings. Surprisingly, however, despite these advances, population methods are not routinely taught at the graduate level, and pharmaceutical companies still have difficulty recruiting individuals with population pharmacokinetics experience. A major hindrance to implementing population methods is that it is mathematically and statistically complex, and compared to the number of pharmacokineticists in general there are few modelers who specialize in the methodology. A newcomer can read the literature as a source to learn about population pharmacokinetics. But even this task can be difficult because few papers and books published on pharmacokinetics cover the principles of nonlinear mixed effects models. Some books (mainly written by statisticians) have been written on the relevant topics, but these books are not geared toward reading at the outset of learning the material. The purpose of Pharmacokinetic-Pharmacodynamic Modeling and Simulation is to provide pharmacokineticists and pharmacy graduate students with the statistical and modeling background necessary to perform population pharmacokinetics analyses. As the author says, “Models that are reported in the literature are not picked out of thin air. Useful models take time and effort and what is rarely shown is the process that went in to developing that model.” The focus of this book is primarily on the development of pharmacokinetic and pharmacokinetic-pharmacodynamic models, especially the modeling in drug development since that is the author's own area of expertise. Also, ultimately all pharmacokinetic-pharmacodynamic modeling is applied to the therapeutic use of drugs in clinical practice. A key feature of the book is the process of modeling. All theories, practice-related issues and case studies are presented in an evolutionary manner. We think it is a must read for every pharmacokineticist and pharmacy graduate student who is concerned about pharmacokinetic-pharmacodynamic modeling, especially population pharmacokinetics. This book is divided into 9 chapters. It begins with a broad overview of the modeling, which the author calls “The Art of Modeling.” Some of the broad topics associated with modeling are introduced here, such as model selection criterion, model validation, the importance of good communication, and ethics. These concepts are used throughout the book. Chapter 2 involves the basics of linear regression, which is the groundwork for most parametric modeling. Later chapters will expand on these concepts and present new ones with an eye towards developing a unified exposition of pharmacostatistical modeling. From there, nonlinear regression is covered. Nonlinear regression is a standard topic taught in graduate level pharmacokinetics since it is required for almost every pharmacokinetic problem encountered. With nonlinear regression, the user makes choices, such as algorithm, convergence criteria, weights, parameter bounds, etc. The choices the user makes will have an impact on the final estimates for the model parameters. Chapter 4 emphasizes the importance of variance models, weighting, and transformations. Residual variance models offer greater flexibility to regression models by relaxing the assumption of constant variance and provide greater insight into the data generating mechanism by explaining the variability in the data. Chapter 5 presents many case studies in the applications of linear and nonlinear modeling to real-life data sets to illustrate the theory that was discussed in the previous chapters. Some of the examples were relatively simple, whereas some were quite complex. In the material presented to this point, a key assumption is that each subject contributes a single observation to the data set. Subsequent chapters move to mixed effects models, which allow for multiple observations to be measured on the same individual. Chapter 6 is devoted to linear mixed effects models, which form the foundation for population pharmacokinetic-pharmacodynamic modeling. The purpose of this chapter is to introduce fixed and random effects, explain how they relate to linear mixed effects models, and illustrate the use of these models in practice. Chapter 7 may be the most important section of this book. This chapter focus on the theory behind population pharmacokinetics models. Nonlinear mixed effects models are similar to linear mixed effects models with the difference being that the function under consideration f(x, θ) is nonlinear in the model parameters θ. This is followed by Chapter 8 on a wide range of special practical issues in nonlinear mixed effects modeling, such as how weight, genetic, or racial information is incorporated into a model. The last chapter provides 2 examples that will be used to explain and illustrate the principles in developing population pharmacokinetic models and nonlinear mixed effects models in general. This book has several key strengths. First, and most important, is the inter-relatedness between the text's materials. This book develops in that manner, ie, each chapter builds upon previous chapters by first presenting the theory and then illustrating the theory using published data sets and actual data sets that were used in the development of new chemical entities collected by the author during his years in the industry. The reader will be able to see the interconnections between nonlinear mixed effects models and linear mixed effects modeling, nonlinear modeling, and linear modeling. For instance, nonlinear mixed effects models are simply extensions of linear mixed effects models, which are themselves extensions of linear models, etc. The second major strength is that the book provides some important theories that are not covered in most pharmacokinetic texts, such as linear regression and linear mixed effects models. Their application is increasing, and they form a special case of nonlinear models and nonlinear mixed effect modeling, respectively. A working understanding of these models is especially useful in pharmacokineticists. Another important strength is that the author wrote this book to be as reader friendly as possible. The non-technical parts of this book are written in an almost conversational tone with anecdotes and interesting quotes interspersed throughout. Each chapter begins with a quote that the author thought especially poignant about the forthcoming material in the chapter. This book is also well organized and easy to read. The use of lots of case examples helps illustrate essential principles. Before reading this book, the reader is expected to have a basic knowledge of simple pharmacokinetic-pharmacodynamic models, as well as matrix algebra and statistics that covers basics of probability, regression, and analysis of variance, etc. However, the reader does not need to worry about it too much. Just as the quote says (Chapter 3, page 93), “Do not worry about your difficulties in mathematics, I can assure you mine are still greater – Albert Einstein (1879-1955)”. Pharmacokinetic-Pharmacodynamic Modeling and Simulation provides a great choice to those seeking a textbook for mathematical modeling in pharmacokinetics/pharmacodynamics, especially nonlinear mixed effects models. While this book is targeted toward the pharmacokineticsts who perform pharmacokinetic-pharmacodynamic modeling, it will also be extremely useful to graduate students in pharmacokinetic or statistical modeling and professionals in pharmaceutical sciences. We highly recommend Pharmacokinetic-Pharmacodynamic Modeling and Simulation for inclusion in any pharmacy pharmacokinetics class. We believe that, after reading this book, the reader will begin to appreciate the power of modeling in being able to answer “real-world” questions. Just like the author, Professor P.L. Bonate states, “Modeling is both an art and a science.”