## Solving Pharmacokinetic Models Analytically

Pharmacokinetic models can be fairly simple, or incredibly complex, or anything in between. It is fairly straightforward to solve simple models analytically (that is, by means of algebraic solution of the kinetic equations). In the case of a single bolus infusion with first-order elimination from a single compartment, the plasma level rises (almost) immediately to a maximum value determined by dose and volume of distribution, and then declines exponentially, with a rate constant that depends on...

## Computational Considerations in Clinical Trial Simulations

Georgetown University, Washington, D.C., U.S.A. Simulation is a standard component of the analytical arsenal of many disciplines, including engineering, physics, astronomy, and statistics. Its theoretical foundations and techniques are well developed, but the application of this technology to the field of drug development is relatively new (1). This chapter aims to explain the process underpinning simulation as it applies to clinical trial design. Simulation involves creating a mathematical...

## Covariance

It is important to retain information about the covariance of individual IO model parameters in order to obtain plausible sets of parameters. While some covariance between parameters may be included in the simulation via the group IO model, e.g., if weight is used to predict Vgip and CLgrp, there is usually further random covariance which cannot be explained by a model using a covariate such as weight to predict the group parameter value. The need to include parameter covariance in the model is...

## Protocol Deviations and Execution Models

University of Queensland, Brisbane, Australia 4.1 GOALS OF CLINICAL TRIAL SIMULATION An important goal of clinical trial simulation (CTS) is to develop well-designed protocols that will maximize the ability to address the stated aim(s) of a proposed clinical trial. The first step in this process is to identify a useful input-output model (IO), including the model structure and its parameters, which will adequately reproduce salient characteristics that clinicians wish to observe in a future...

## Why Simulate Clinical Trials

Simulation allows the evaluation of competing trial designs, e.g., comparison of dosage regimens, to be compared in terms of their efficacy to produce the desired outcomes prior to conducting the actual trial. The act of performing a simulation requires the development of a series of linked simulation models. This model development process has innate educational benefits since it allows clear identi fication of what is known about the drug in question. The corollary of this process is that...

## O2ti J

Finally, multiply the transpose of X with V and X to produce the final matrix M. This matrix M is also known as the moment matrix (hence the symbol M) and reflects changes in parameter information with time. Scalar measures derived from manipulation of M, e.g., D-optimality, can be used to reflect the overall precision of the parameter estimation procedure. D-optimality (22) is the most popular design metric used in PK PD optimization. It is defined as the det(M_1) and is useful because it...

## Optimal Design of Experiments in PKPD

In the design of PK PD experiments, it has been established that the precision of estimated parameters is correlated with the sampling design properties, i.e., the number, the range, and the spacing of sampling times (1,5,38). This statistical property-design property relationship has been used to develop design metrics, which provide an optimal design yielding the most precisely estimated parameters. An often used design metric is the D-optimality criterion (4, 22, 39, 40), which selects...

## An Industry Perspective

Timothy Goggin,* Ronald Gieschke, Goonaseelan (Colin) Pillai Barbel Fotteler, Paul Jordan, and Jean-Louis Steimert F. Hoffmann-La Roche, Basel, Switzerland Current trends within the pharmaceutical industry and within the offices of some regulatory authorities in particular the U.S. Food and Drug Administration (FDA) suggest a promising future for modeling and simulation (M& S) incorporating pharmacokinetic and pharmacodynamic (PK PD) modeling and clinical trial simulation (CTS) (1-5). The...

## Generating Normally Distributed Random Numbers

There are several ways to generate normally distributed random numbers from uniformly-distributed numbers. Some are approximate others are exact. Some methods are more efficient than others, and some are easier to program. Perhaps the simple and most convenient of the exact methods involves the inverse of the distribution function. In Excel this function is called NORMSINV (Excel also supports NORMINV which allows the user to specify the mean and SD of the distribution). This function may not...

## Simulation in PKPD and Drug Development

The increasing use of simulation in drug development (30) has led to the creation of a good practices guide (27) detailing the necessary components of a clinical trial simulation and issues to consider when organizing and performing a clinical trial simulation. The PK PD and drug development literature is full of examples where computer simulation has been used for one reason or another, but in general, three categories of simulation projects have been identified (24). Simulation is used to...

## Clinical Trial Simulation

In modeling and simulation analysis, it is important to distinguish between a system's structure or the inner constitution, and its behavior, which is the observable manifestation of that system. External behavior can also be described in terms of the relationship that the system imposes between its input and output time histories. The internal structure of the system defines the system states and transition mechanisms, and maps its states to output transitions. Knowing the system structure...

## Regulatory Clinical Pharmacology Perspective

Lesko Center for Drug Evaluation and Research, Food and Drug Administration, Rockville, Maryland, U.S.A. A number of published reports have addressed the fundamental problems that affect the pharmaceutical and biotechnology industries today (1,2). The cost of drug development continues to increase, the time from drug discovery to peak sales is thought to be too long, and the amount of data and information arising from clinical trials is increasing exponentially,...

## Simulation And Design

There are at least two ways to look at the relationship between SA and CTS& D. According to the more limited view, one can regard SA as a methodology for development and validation of the system of models used in CTS& D, including the PK PD models. The potential of SA in model building in general are undisputed and have been thoroughly analyzed (1-4, 21, 22), but still remain to be widely utilized by the PK PD modeling community. The power and capabilities of SA for model building in...

## Solving Pharmacokinetic Models Numerically

More complicated processes, such as those involving multiple compartments, may have analytical solutions, although they may be very complicated. It is possible to use mathematical software such as Mathematica or MATLAB to assist in finding analytical solutions to complex systems of differential equations, if such solutions do in fact exist. But for more complicated models it is usually necessary to resort to numerical integration of the ordinary differential equations. Here the advantages of a...

## Qualification Of Covariate Distribution Models

As with other aspects of clinical trial simulation, the analyst should attempt to show that the model used for creating the virtual patient population matrix reflects the distribution of covariates in the expected patient enrollment. Models used to generate covariate vectors should be tested and qualified with the same scientific Figure 6 Implementation of a two-stage generation of suitable covariate vectors for a simulation study. Virtual patients are generated according to either a parametric...

## Sensitivity Analysis Of Pharmacokinetic And Pharmacodynamic Models

The majority of the commonly used models in PK and PD share a similar structure. For example, the most popular whole body PK model structure used is the compartmental mammilary structure (Figure 1). This follows from the fundamental assumption that drugs are transported throughout the body by the blood circulation system. With a small modification, this structure also applies to the relatively complex whole-body PBPK models (Figure 2), which can be converted to a purely mammilary structure by...

## Modeling and Simulation as a Teaching Tool

University of Auckland, Auckland, New Zealand Mats O. Karlsson University of Uppsala, Uppsala, Sweden This chapter briefly reviews the history of clinical trial simulation and applications of how it might be used for teaching in an academic setting. 11.2 HISTORY OF CLINICAL TRIAL SIMULATION The history of clinical trial simulation and recent applications have been reviewed by Holford et al. (1). Early clinical trial simulators were based solely on predicting the stochastic aspects of how...

## Creating Multivariate Distributions of Covariates

Simulation of virtual patients with entirely new covariants provides an alternative to resampling strategies. Therefore, if no data set containing appropriate patient demographic information exists, or if the simulation team decides not to use a resampling approach to generate virtual patients, then a virtual patient data set must be created entirely through simulation. There are two methods for generating covariate vectors through a series of univariate distributions or by using a multivariate...

## Method III all data

Figure 6 Plot of weighted residuals versus subject identification number. From Williams et al. 26 . dation of a Population Model, e-mail to NONMEM Usernet Participants, Feb. 2, 1992 . For an adequate model i.e., a stable model yielding reliable parameter estimates with no severe deficiencies the mean of the WRES should be scattered evenly about zero on the WRES axis and most observations should be within 4. Figure 6 was taken from a comparison of several methods for generating predictions of...