Pharmacometrics

The Science of Quantitative Pharmacology

Ene I. Ette, Paul J. Williams, Ene I. Ette, Paul J. Williams

• Publisher: Wiley-Interscience
• Year: 2013
• Print ISBN: 9780471677833
• eBook ISBN: 9781118679517
• Edition: 1
• Topic: Medicine
• Subtopic: Pharmacology

Pharmacometrics is the science of interpreting and describing pharmacology in a quantitative fashion. The pharmaceutical industry is integrating pharmacometrics into its drug development program, but there is a lack of and need for experienced pharmacometricians since fewer and fewer academic programs exist to train them. Pharmacometrics: The Science of Quantitative Pharmacology lays out the science of pharmacometrics and its application to drug development, evaluation, and patient pharmacotherapy, providing a comprehensive set of tools for the training and development of pharmacometricians.

Edited and written by key leaders in the field, this flagship text on pharmacometrics:

• Integrates theory and practice to let the reader apply principles and concepts.
• Provides a comprehensive set of tools for training and developing expertise in the pharmacometric field.
• Is unique in including computer code information with the examples.

This volume is an invaluable resource for all pharmacometricians, statisticians, teachers, graduate and undergraduate students in academia, industry, and regulatory agencies.

CHAPTER 1

Pharmacometrics: Impacting Drug Development and Pharmacotherapy

PAUL J. WILLIAMS and ENE I. ETTE

1.1 INTRODUCTION

Drug development continues to be expensive, time consuming, and inefficient, while pharmacotherapy is often practiced at suboptimal levels of performance (1–3). This trend has not waned despite the fact that massive amounts of drug data are obtained each year. Within these massive amounts of data, knowledge that would improve drug development and pharmacotherapy lays hidden and undiscovered. The application of pharmacometric (PM) principles and models to drug development and pharmacotherapy will significantly improve both (4,5). Furthermore, with drug utilization review, generic competition, managed care organization bidding, and therapeutic substitution, there is increasing pressure for the drug development industry to deliver high-value therapeutic agents.

The Food and Drug Administration (FDA) has expressed its concern about the rising cost and stagnation of drug development in the white paper Challenge and Opportunity on the Critical Path to New Products published in March of 2004 (3). In this document the FDA states: “Not enough applied scientific work has been done to create new tools to get fundamentally better answers about how the safety and effectiveness of new products can be demonstrated in faster time frames, with more certainty, and at lower costs…. A new product development toolkit—containing powerful new scientific and technical methods such as animal or computer-based predictive models, biomarkers for safety and effectiveness, and new clinical evaluation techniques—is urgently needed to improve predictability and efficiency along the critical path from laboratory concept to commercial product. We need superior product development science to address these challenges.” In the critical path document, the FDA states that the three main areas of the path that need to be addressed are tools for assessing safety, tools for demonstrating medical utility, and lastly tools for characterization and manufacturing. Pharmacometrics can be applied to and can impact the first two areas, thus positively impacting the critical path.

For impacting safety, the FDA has noted opportunities to better define the importance of the QT interval, for improved extrapolation of in vitro and animal data to humans, and for use of extant clinical data to help construct models to screen candidates early in drug development (e.g., liver toxicity). Pharmacometrics can have a role in developing better links for all of these models.

For demonstrating medical utility, the FDA has highlighted the importance of model-based drug development in which pharmacostatistical models of drug efficacy and safety are developed from preclinical and available clinical data. The FDA goes on to say that “Systematic application of this concept to drug development has the potential to significantly improve it. FDA scientists use and are collaborating with others in the refinement of quantitative clinical trial modeling using simulation software to improve trial design and to predict outcomes.” The pivotal role of pharmacometrics on the critical path is obvious.

Drug development could be improved by planning to develop and apply PM models along with novel pathways to approval, improved project management, and improved program development. Recent advances in computational speed, novel models, stochastic simulation methods, real-time data collection, and novel biomarkers all portend improvements in drug development.

Dosing strategy and patient selection continue to be the most easily manipulated parts of a patient’s therapy. Optimal dosing often depends on patient size, sex, and renal function or liver function. All too often, the impact of these covariates on a PM parameter is unstudied and therefore cannot be incorporated into any therapeutic strategy. PM model development and application will improve both drug development and support rational pharmacotherapy.

1.2 PHARMACOMETRICS DEFINED

Pharmacometrics is the science of developing and applying mathematical and statistical methods to characterize, understand, and predict a drug’s pharmacokinetic, pharmacodynamic, and biomarker–outcomes behavior (6). Pharmacometrics lives at the intersection of pharmacokinetic (PK) models, pharmacodynamic (PD) models, pharmacodynamic-biomarker–outcomes link models, data visualization (often by employing informative modern graphical methods), statistics, stochastic simulation, and computer programming. Through pharmacometrics one can quantify the uncertainty of information about model behavior and rationalize knowledge-driven decision making in the drug development process. Pharmacometrics is dependent on knowledge discovery, the application of informative graphics, understanding of biomarkers/surrogate endpoints, and knowledge creation (7–10). When applied to drug development, pharmacometrics often involves the development or estimation of pharmacokinetic, pharmacodynamic, pharmcodynamic-outcomes linking, and disease progression models. These models can be linked and applied to competing study designs to aid in understanding the impact of varying dosing strategies, patient selection criteria, differing statistical methods, and different study endpoints. In the realm of pharmacotherapy, pharmacometrics can be employed to customize patient drug therapy through therapeutic drug monitoring and improved population dosing strategies. To contextualize the role of pharmacometrics in drug development and pharmacotherapy, it is important to examine the history of pharmacometrics. The growth of pharmacometrics informs much on its content and utility.

1.3 HISTORY OF PHARMACOMETRICS

1.3.1 Pharmacokinetics

Pharmacometrics begins with pharmacokinetics. As far back as 1847, Buchanan understood that the brain content of anesthetics determined the depth of narcosis and depended on the arterial concentration, which in turn was related to the strength of the inhaled mixture (11). Interestingly, Buchanan pointed out that rate of recovery was related to the distribution of ether in the body. Though there was pharmacokinetic (PK) work done earlier, the term pharmacokinetics was first introduced by F. H. Dost in 1953 in his text, Der Blutspeigel-Kinetic der Knozen-trationsablaufe in der Kreislauffussigkeit (12). The first use in the English language occurred in 1961 when Nelson published his “Kinetics of Drug Absorption, Distribution, Metabolism, and Excretion” (13). The exact word pharmacokinetics was not used in this publication.

In their classic work, the German scientists Michaelis and Menton published their equation describing enzyme kinetics in 1913 (14). This equation is still used today to describe the kinetics of drugs such as phenytoin. Widmark and Tandberg (15) published the equations for the one-compartment model in 1924 and in that same year Haggard (16) published his work on the uptake, distribution, and elimination of diethyl ether. In 1934 Dominguez and Pomerene (17) introduced the concept of volume of distribution, which was defined as “the hypothetical volume of body fluid dissolving the substance at the same concentration as the plasma. In 1937 Teorrel (18) published a seminal paper that is now considered the foundation of modern pharmacokinetics. This paper was the first physiologically based PK model, which included a five-compartment model. Bioavailability was introduced as a term in 1945 by Oser and colleagues (19), while Lapp (20) in France was working on excretions kinetics.

Polyexponential curve fitting was introduced by Perl in 1960 (21). The use of analog computers for curve fitting and simulation was introduced in 1960 by two groups of researchers (22, 23).

The great growth period for pharmacokinetics was from 1961 to 1972, starting with the landmark works of Wagner and Nelson (24). In 1962 the first symposium with the title pharmacokinetics, “Pharmacokinetik und Arzniemitteldosireung,” was held.

Clinical pharmacokinetics began to be recognized in the 1970s, especially in two papers by Gibaldi and Levy, “Pharmacokinetics in Clinical Practice,” in the Journal of the American Medical Association in 1976 (25). Of further importance that same year was a paper by Koup et al. (26) on a system for the monitoring and dosing of theophylline based on pharmacokinetic principles.

Rational drug therapy is based on the assumption of a causal relationship between exposure and response. There pharmacokinetics has great utility when linked to pharmacodynamics and the examination of pharmacodynamics is of paramount importance.

1.3.2 Pharmacodynamics

In 1848 Dungilson (27) stated that pharmacodynamics was “a division of pharmacology which considers the effects and uses of medicines.” This definition has been refined and restricted over the centuries to a more useful definition, where “pharmacokinetics is what the body does to the drug; pharmacodynamics is what the drug does to the body” (28, 29). More specifically, pharmacodynamics was best defined by Derendorf et al. (28) as “a broad term that is intended to include all of the pharmacological actions, pathophysiological effects and therapeutic responses both beneficial or adverse of active drug ingredient, therapeutic moiety, and/or its metabolite(s) on various systems of the body from subcellular effects to clinical outcomes.” Pharmacodynamics most often involves mathematical models, which relate some concentration (serum, blood, urine) to a physiologic effect (blood pressure, liver function tests) and clinical outcome (survival, adverse effect). The pharmacodynamic (PD) models have been described as fixed, linear, log-linear, E_max, sigmoid E_max, and indirect PD response (29–31).

The indirect PD response model has been a particularly significant contribution to PD modeling (30, 31). It has great utility because it is more mechanistic than the other models, does not assume symmetry of the onset and offset, and incorporates the impact of time in addition to drug concentration, thus accounting for a delay in onset and offset of the effect. For these models the maximum response occurs later than the time of occurrence of the maximum plasma concentration because the drug causes incremental inhibition or stimulation as long as the concentration is “high enough.” After the response reaches the maximum, the return to baseline is a function of the dynamic model parameters and drug elimination. Thus, there is a response that lasts beyond the presence of effective drug levels because of the time needed for the system to regain equilibrium. Whenever possible, these mechanistic models should be employed for PD modeling and several dose levels should be employed for accurate determination of the PD parameters, taking into consideration the resolution in exposure between doses.

The dependent variables in these PD models are either biomarkers, surrogate endpoints, or clinical endpoints. It is important to differentiate between these and to understand their relative importance and utility.

1.3.3 Biomarkers

The importance of biomarkers has been noted in recent years and is evidenced by the formation of The Biomarkers Definitions Working Group (BDWG) (32). According to the BDWG, a biomarker is a “characteristic that is objectively measured and evaluated as an indicator of normal biological processes, pathogenic process or pharmacologic responses to a therapeutic intervention.” Biomarkers cannot serve as penultimate clinical endpoints in confirming clinical trials; however, there is usually considered to be some link between a biomarker based on prior therapeutic experience, well understood physiology or pathophysiology, along with knowledge of the drug mechanism. Biomarkers often have the advantage of changing in drug therapy prior to the clinical endpoint that will ultimately be employed to determine drug effect, thus providing evidence early in clinical drug development of potential efficacy or safety.

A surrogate endpoint is “a biomarker that is intended to substitute for a clinical endpoint. A surrogate endpoint is expected to predict clinical benefit, harm, lack of benefit, or lack of harm based on epidemiologic, therapeutic, pathophysiologic or other scientific evidence” (32). Surrogate endpoints are a subset of biomarkers such as viral load or blood pressure. All surrogate endpoints are biomarkers. However, few biomarkers will ever become surrogate endpoints. Biomarkers are reclassified as surrogate endpoints when a preponderance of evidence indicates that changes in the biomarker correlate strongly with the desired clinical endpoint.

A clinical endpoint is “a characteristic or variable that reflects how a patient feels, functions or survives. It is a distinct measurement or analysis of disease characteristics observed in a study or a clinical trial that reflect the effect of a therapeutic intervention. Clinical endpoints are the most credible characteristics used in the assessment of the benefits and risks of a therapeutic intervention in randomized clinical trials.” There can be problems with using clinical endpoints as the final measure of patient response because a large patient sample size may be needed to determine drug effect or the modification in the clinical endpoint for a drug may not be detectable for several years after the initiation of therapy.

There are several ways in which the discovery and utilization of biomarkers can provide insight into the drug development process and patient care. Biomarkers can identify patients at risk for a disease, predict patient response, predict the occurrence of toxicity, and predict exposure to the drug. Given these uses, biomarkers can also provide a basis for selecting lead compounds for development and can contribute knowledge about clinical pharmacology. Therefore, biomarkers have the potential to be one of the pivotal factors in drug development—from drug target discovery through preclinical development to clinical development to regulatory approval and labeling information, by way of pharmacokinetic/pharmacodynamic–outcomes modeling with clinical trial simulations.

1.3.4 PK/PD Link Modeling

PK/PD modeling provides the seamless integration of PK and PD models to arrive at an enlightened understanding of the dose–exposure–response relationship. PK/PD modeling can be done either sequentially or simultaneously (33, 34). Sequential models estimate the pharmacokinetics first and fix the PK parameters, generating concentrations corresponding to some PD measurement. Thus, the pharmacodynamics is conditioned on the PK data or on the estimates of the PK parameters. Simultaneous PK/PD modeling fits all the PK and PD data at once and the PK and PD parameters are considered to be jointly distributed. When simultaneous modeling is done, the flow of information is bidirectional. Both of these approaches appear to provide similar results (33, 35). However, it is important to note that PD measurements are usually less precise than PK measurements and using sequential PK and PD modeling may be the preferred approach in most instances.

PK and PD can be linked directly through a measured concentration that is directly linked to an effect site. The direct link model does not work well when there is a temporal relationship between a measured concentration and effect, as ...

Table of contents

• Cover
• Half Title page
• Title page
• Copyright page
• Dedication
• Contributors
• Preface
• Acknowledgments
• Chapter 1: Pharmacometrics: Impacting Drug Development and Pharmacotherapy
• Part I: General Principles
• Part II: Population Pharmacokinetic Basis of Pharmacometrics
• Part III: Pharmacokineticsi Pharmacodynamics Relationship: Biomarkers and Pharmacogenomics, Pk/Pd Models for Continuous Data, and Pk/Pd Models for Outcomes Data
• Part IV: Clinical Trial Designs
• Part V: Pharmacometric Knowledge Creation
• Part VI: Pharmacometric Service and Communication
• Part VII: Specific Application Examples
• Index