Asthma Free Forever
Nicholas H.G. Holford
University of Auckland, Auckland, New Zealand Mats O. Karlsson
University of Uppsala, Uppsala, Sweden
11.1 INTRODUCTION
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 observations might arise but did not use models for the underlying pharmacological processes. Maxwell (2) produced a game for learning the principles of clinical trial design. The use of a computer program to simulate patient outcomes was a by-product of the actual game process. The application of sequential analysis to adaptive clinical trials (3), the influence of dropouts (4) and premature termination of trials (5) were all explored using simulation.
The application of pharmacokinetic and pharmacodynamic models as the basis for simulation of clinical trial observations took off in the middle of the 1980s. Important precursors were the growing knowledge linking drug concentration to effect (6, 7) and the application of mixed effect models in pharmacology (8, 9). Simulation of the physiological response to circulating tissue-type plasminogen activator (t-PA) was used to show that fibrinogenolysis was not sensitive to a variety of concentration profiles arising from alternative dosing patterns. (10,11). The properties of the randomized concentration-controlled trial were explored by simulation and define the kinds of clinical trials which might benefit most from prospective adjustment of doses based on drug concentrations. (12, 13).
In 1993 the European Course in Pharmaceutical Medicine (now the European Center for Pharmaceutical Medicine) received a grant from the COMETT program of the European Union to develop a computer-based multimedia CD-ROM teaching tool. The goal was to teach the principles of clinical pharmacology with a particular emphasis on their application to clinical drug development. This project was called RIDO (RIght DOse first time) (14).
Simulations of concentration time profiles were included in an interactive clinical pharmacology trainer to illustrate properties of the basic input-output model. Because the goal was to teach about drug development, a more advanced simulation system was developed to teach clinical trial design and analysis.
The RIDO clinical trial simulator includes covariate distribution, input-output, and execution model features. The output of each simulated clinical trial can be analyzed using a set of prebuilt NONMEM models. Students can use RIDO to explore alternative clinical trial designs by changing the number of subjects, type, and number of observations, and varying subject drop out rates. Each design can then be analyzed using NONMEM to see if it is capable of answering specific PK/PD model-based hypotheses. A simple pharmacoeco-nomic model is also incorporated so that the cost consequence of different clinical trial choices can be appreciated. The RIDO clinical trial simulation engine was licensed to Pharsight Corporation and used as the basis for their Trial Designer clinical trial simulation product.
Around the same time that the Pharsight Trial Designer was released, another product, ACSL Biomed, based on the advanced continuous simulation language (ASCL), was developed. Pharsight subsequently bought ACSL Biomed and produced a new product (Trial Simulator) with features taken from Trial Designer and ACSL Biomed Trial Simulator, with other extensions, was released in 1999.
Simulation can be used to teach basic principles of pharmacological experimental design and data analysis. These ideas are typically presented in basic statistics courses but often lack direct relevance to students studying clinical pharmacology. A 2 hour workshop has been used at the University of Auckland to introduce students to pharmacometric principles in their last year of a 3 year BSc degree course. The students use a Microsoft Excel workbook to simulate and analyse data.
Interpretation of pharmacological observations most commonly involves an experiment that is designed to show that a particular intervention has a detectable effect; e.g., does blood pressure fall when a new drug is given compared with giving a placebo?
The population input-output (IO) model is simple (see Chapter 2). The blood pressure (BP) fall with active drug (drug) is predicted from the population parameter for active drug. Ej^. The placebo blood pressure fall is similarly predicted from the population parameter for placebo, Eplacebo.
The group IO model is also defined in Eq. (1) for the treatment assignment to active drug (TRT = 1) or placebo (TRT = 0) as a group covariate.
The individual IO model predicts the BP fall in each subject, BP;:
where n is the individual difference in blood pressure response predicted by a random effects model based on a normal distribution with variability defined by the parameter SD. This can be simulated using Microsoft Excel using the NORMINV () function:
Equation (3) includes the observation IO model with random effects arising both from individual differences in response to treatment and to blood pressure measurement error. The execution model is implicit and assumes that all treatments are taken as assigned and that there are no missing observations.
The only experimental design property is the number of subjects in each treatment group. The number of subjects can be varied to test how it influences the statistical
Parameter |
True |
Experiment |
Property |
Subjects |
Placebo |
Drug |
Eplacebo |
-5 |
N |
10 |
1 |
15.6 |
-11.6 |
Edrug |
-10 |
2 |
10.2 |
-3.4 | ||
SD |
10 |
3 |
-11.4 |
2.2 | ||
4 |
15.7 |
-8.2 | ||||
Placebo |
Estimate |
Drug |
Estimate |
5 |
-21.2 |
-17.4 |
AVGplacebo |
-1.31 |
AVGdrug |
-11.91 |
6 |
-5.4 |
-14.0 |
SDplacebo |
12.76 |
SDdrug |
9.34 |
7 |
5.1 |
-8.5 |
Nplacebo |
10 |
Ndrug |
10 |
8 |
0.6 |
-9.2 |
SEplacebo |
4.03 |
SEdrug |
2.95 |
9 |
-9.9 |
-32.5 |
10 |
-12.4 |
-16.5 |
Hypothesis Testing Alpha 0.05
Reject Null Yes!
Hypothesis Testing Alpha 0.05
Reject Null Yes!
aThe student has chosen to have 10 subjects in each group. In this particular case the i-test has a P value exactly equal to the alpha critical value for rejecting the null hypothesis.
analysis (see Table 1). The worksheet automatic recalculation feature has been turned off so that the student must press the F9 key to generate a new set of simulated observations based on the number of subjects.
The average blood pressure can be calculated after giving each treatment and there will inevitably be some difference in the averages. A hypothesis test is used to determine how likely the observed difference arose by chance (the null hypothesis). If the probability is low enough (less than or equal to a) that the observed difference arose by chance, then the null hypothesis is rejected.
11.3.3.1 Student's f-test
The average and standard deviation of the observed responses in each group is computed and Student's i-test used to compute a P value for comparison with a nominal a value to test the null hypothesis.
Each time the worksheet is recalculated, it is equivalent to performing a new clinical trial. Different designs based on the number of subjects can be examined.
Assumptions about the size of the active drug and placebo response and its variability can be included by varying these simulation parameters.
Students are asked to count whether the null hypothesis has been rejected after each time they press the F9 key. After 100 key presses they use the count to estimate the power of the design.
The concepts of more complex IO models and the ability to estimate their parameters from typical data is taught by graphical and numerical methods. Graphical display of the true model predictions, simulated observations, and the predictions from a set of parameter estimates are used to demonstrate how a model can be fitted to data by guesses at parameter values and evaluating visually how close the estimation model predictions resemble both the true model predictions and the simulated observations.
A numerical approach to evaluating goodness of fit is demonstrated by computing an objective function value based on the current set of parameter estimates. Students are asked to try to minimize the objective function by changing the parameter estimates. They are then asked to use the Microsoft Excel Solver add-in. The Solver is set to minimize the same objective function by varying model parameters. The lowest objective function value obtained by the student can be compared with the value obtained by the Solver. The residual unknown variability (RUV) for the objective function and for the observation model is a mixed proportional and additive model (see Chapter 2). Details of the RUV are not discussed with students at this stage.
11.4.1.1 The Straight Line
The first model examined is a linear model with slope and intercept parameters.
Students can often guess parameters that are very close to the true model parameters. They see that their simulated line and the true model line match but their objective function is worse than that obtained by the Solver. This introduces them to the idea that the objective function is based on the actual observations which have error and that the true model cannot be known by the Solver.
Estimate |
Pest X |
Y |
Ytrue |
Yobs |
OLSi |
Virlsi |
IRLSi Velsi |
ELSi | ||||
0 100.0 |
100.0 |
101.3 |
1.74 |
10000.00 |
0.00 |
1Ö00Ö.ÖÖ |
9.21 | |||||
v |
1Ö.QÖ |
0.3 |
86.1 |
91.4 |
38.7 |
2246.02 |
7408.18 |
0.30 |
7408.18 |
9.21 | ||
cl |
5.00 |
0.5 |
77.9 |
86.1 |
55.5 |
503.01 |
6065.31 |
0.08 |
6065.31 |
8.79 | ||
pwr |
2.00 |
1 |
60.7 |
74.1 |
55.7 |
24.60 |
3678.79 |
0.01 |
3678.79 |
8.22 | ||
- lOOO.O |
. .._ .— |
— -- |
54.9 |
49.2 |
153.98 |
1353.35 |
0.11 |
1353.35 |
7.32 | |||
_y—; |
40.7 |
49.5 |
737.61 |
497.87 |
1.48 |
497.87 |
7.69 | |||||
lOO.U^ |
30.1 |
348 |
450.69 |
183.16 |
2,45 |
183.16 |
7.57 | |||||
Yobs . |
16.5 |
10.8 |
34.21 |
24.79 |
1.38 |
24.79 |
4.59 | |||||
9.1 |
12.2 |
106.83 |
3.35 |
31.85. |
3.35 |
33.06 | ||||||
1D 0 |
5.0 |
3.5 |
8.03 |
0.45 |
17.70 |
0.45 |
16.91 | |||||
2.7 |
2.3 |
4.15 |
0.06 |
67.47- |
0.06 |
64.68 | ||||||
1.0 |
1.5 |
0.6 |
0.22 |
0Ö1 |
26.47- |
0.01 |
21.68 | |||||
\ \ |
\a |
o.a |
O.S |
0.30 |
0.00 |
267.25 |
0.00 |
260.46 | ||||
- 0.1 |
0.5 |
0.61 |
0.31 |
_ 0.00^ |
1998.94: |
0.00 |
1990.15 | |||||
0.1 |
0.2 |
0.04 |
0.00 |
30993.98; |
0.00 |
30980.48 | ||||||
- 0.0 |
\ | |||||||||||
4271.75 4271,75 |
33409.48: 33409.48; |
33430.14 3 3430." 14 | ||||||||||
0.0 |
10 |
\ |
1 |
1: |
1 | |||||||
20 |
30 |
100 |
100: |
100 | ||||||||
00 | ||||||||||||
33395.703! | ||||||||||||
33415.36 | ||||||||||||
Figure 1 One-compartment model objective function calculations.
Figure 1 One-compartment model objective function calculations.
The second example is nonlinear and uses clearance and volume as parameters of a one-compartment disposition, bolus input pharmacokinetic model (see Figure 2).
The students quickly appreciate how much harder it is to guess values of clearance and volume and learn that the Solver is a general-purpose technique for estimating parameters of arbitrary functions.
A more advanced group of students taking graduate level courses use the same kind of Excel-based simulation models to learn about the properties of RUV models and different forms of least-squares objective function. Excel is used to calculate and display the contribution to the objective function from each observation so that the student can appreciate the consequences of different RUV model assumptions.
11.4.2.1 Ordinary Least Squares
The ordinary least squares objective function assumes a constant RUV for all observations. In the example in Eq. (6) the RUV is 1.
11.4.2.2 Weighted Least Squares
The weighted-least-squares objective function relies on a fixed function of either the observed value (WLS) or the model predicted value (IRLS) to compute a weight which is inversely proportional to the RUV for that observation (Var2).
i=Nobs 2
11.4.2.3 Extended Least Squares
The extended least squares objective function uses a parametric model for RUV (Var;) which is a function of the IO model prediction and parameters of the RUV model such as SD.
11.5 MODEL BUILDING
The graduate class is taught how to build models for simulation and parameter estimation using a range of software representative of the tools currently used in contemporary drug development (http://www.health.auckland.ac.nz/courses/ Pharmacol716).
11.5.1 Excel
Microsoft Excel (http://www.microsoft.com) is the first simulation tool that is taught. Most students are familiar with basic spreadsheet operations and are quickly able to simulate IO models and display them as graphs. They are taught how to name cells and ranges so that formulas can be written in symbolic form rather than rely on cell references.
Observation IO models are simulated using the NORMINV() function. A proportional RUV model with a coefficient of variation approximately equal to the parameter CV is shown in Eq. (9).
Poptools is an Excel add-in that includes (among many other statistical and modeling features) the ability to specify models as differential equations (http:// sunsite.univie.ac.at/Spreadsite/poptools/).
The ModelMaker program developed by Cherwell Scientific (http://www.model-kinetix.com) provides a simple graphical interface for building simulation models expressed as differential equations or closed-form solutions. It is particularly useful for demonstrating how to build complex models from simpler components, e.g., linking pharmacokinetic models to pharmacodynamic models.
11.5.3 WinNonLin
Parameter estimation and model building ideas are introduced using WinNonLin (http://www.pharsight.com). Although WinNonLin has an extensive library of common pharmacokinetic and pharmacodynamic models, students are taught to write their own user-defined models. They use observations simulated with Excel as the source of data and try different models to describe the observations. By learning how to write a model as an Excel formula, as a ModelMaker equation and a WinNonLin function they learn the general properties of a model, and are exposed to different dialects of expressing mathematical expressions.
11.5.4 NONMEM
Population approaches to parameter estimation and model building are taught using NONMEM (http://c255.ucsf.edu/nonmem0.html) and Wings for NON-MEM (http://wfn.sourceforge.net). Students are shown how to construct a simple pharmacodynamic model and to discover influential covariates using a real set of concentration and effect data collected from a concentration-controlled trial of theophylline (15,16). The main features of using NONMEM are learned after a 2 h workshop coupled with an assignment which students complete unsupervised taking an additional 6 h.
11.5.5 Trial Simulator
A brief introduction to a full clinical trial simulation project is taught by using Trial Simulator (http://www.pharsight.com). Students are asked to work through the Quick Tour introduction and then try to simulate a clinical trial based on the theophylline concentration-controlled trial they analyzed using NONMEM.
The teaching materials described so far have all relied upon computer based simulation methods. One of the most rewarding and insightful clinical trial simulations that is undertaken by undergraduate and graduate classes involves an analogue simulation of a compartmental pharmacokinetic model.
The one compartment model involves a single glass beaker with water flowing through it at constant rate. A red dye is added to the beaker and samples of water flowing out of the beaker used to measure the dye concentration. Dye concentration is measured by spectrophotometry. Graduate students use an extension to
the system with a bucket connected to the beaker by a recirculating pump system. The beaker and bucket system simulates a two-compartment pharmacokinetic model
The input of dye to the beaker can mimic a bolus or a zero-order constant rate infusion or a combination of both. The time course of resulting concentrations is used to understand the relationship between the volume of water in the beaker (volume of distribution) and the flow rate of water out of the beaker (clearance). For the two-compartment model the bucket represents the tissue compartment and the recirculating pump flow is intercompartmental clearance (Figure 3).
The calibration and measurement of dye samples using the spectrophotometer is used to teach the concepts of using a standard curve and to describe assay performance in terms of the bias and precision of replicate measurements of standard concentrations.
The time course of dye concentration in both the beaker and bucket can be observed and a pharmacokinetic model for central and tissue compartments used to fit the data. By combining a bolus dose of dye with a constant rate input from a standard hospital drip set the difficulty of maintaining a constant target concentration is demonstrated. It is then possible to show how the same apparatus can be use to administer an additional first-order input in order to achieve a constant concentration.
A 4-5 day workshop using clinical trial simulation is used at Uppsala University to teach PK, PK/PD, and aspects of clinical drug development to student groups with varying backgrounds. In the following, the principal components of the workshop are presented, thereafter some variations depending on the level of the student group, and finally some general comments about the intentions and experiences with the workshop.
In the workshop, the students design and analyze clinical studies within a fictional drug development program. The aim is to bring the investigational drug from the first-in-human study until the end of phase III. The drug selected for this exercise is a thrombin inhibitor, where the students are provided with two articles (17, 18) describing the preclinical characteristics of the thrombin inhibitor in-ogatran, which was previously under development by AstraZeneca. The intended indication is prevention of thrombosis in patients with acute myocardial infarction. A full PK/PD model has been created for the drug and main metabolite pharmacokinetics in plasma and urine, a biomarker (activated partial thrombo-plastin time—APTT) and clinical endpoints, both the primary clinical endpoint (presence/absence of thrombosis during the first week following hospitaliza-tion) and the primary toxicity endpoint (presence/absence of bleeding incidents). In the model, APTT increases nonlinearly with drug plasma concentration, thrombosis hazard decreases with increasing APTT, whereas bleeding hazard increases with increasing APTT values. The model is loosely based on the clinical profile of inogatran and other thrombin inhibitors. It describes the typical subject behavior and variability components, including covariate relations, both for healthy volunteers and patients. The model is not disclosed to the students, but is used to generate study results based on the designs decided upon by the students. Initially, the model was implemented with NONMEM, later with the Pharsight Trial Designer, and presently the Pharsight Trial Simulator is used.
In addition to the preclinical information, the students are initially provided with a fictional project team discussion, where the team members (project leader, clinician, bioanalytical chemist, pharmaceutic pharmacist, etc.) are outlining the expectations with respect to benefit and toxicity, the relative seriousness of thrombosis versus bleeding, competitor profile with respect to thrombosis and bleeding frequencies, desired dosing schedule (24 h infusion followed by daily intramuscular doses), formulation characteristics (intramuscular release rate in vitro and in animals), bioassay characteristics, etc. The first task for each of the students is to summarize all the preclinical information relevant to the design of the firstin-human studies (one for the intravenous and one for the intramuscular formulation) in an abstract. Thereafter all work is carried out in groups of 6-8 students, starting with the design of the first-in-human studies. The students are expected to specify the design with respect to study population (sex, age range, etc.), number of subjects, doses, escalation aspects including stopping rules, what to measure (drug and/or metabolite concentration in plasma, plasma water, urine and/ or faeces, and APTT), number and timing of samples, etc. They outline what information is sought and how the data will be analyzed to obtain this information. The design is finalized during a consensus discussion among the groups. The discussion is led by one of the groups, which provides the teacher with all the aspects necessary to generate the study data, based on the population PK/ PD model. The teacher then uses the consensus design to simulate the outcome of a clinical trial. The following day each group analyzes the generated data using Excel, and the estimated PK (noncompartmental, standard two-stage analyses) and PD (various regression models using pooled data) characteristics are summarized after yet another consensus discussion.
The work then progresses sequentially in a similar manner with the design and analysis of a phase II dose finding study (active control optional) and the design and analysis of two phase III studies (active control necessary). The information generated should result in a suggested dosing regimen (individualized by, e.g., weight or renal function, or not) and knowledge about strengths and weaknesses relative to the active control (heparin). Based on the information generated, each group is finally assigned to make a presentation. Examples of presentations are: a suggested text for the PK and PD part of the product label, a summary of the PK characteristics for regulatory pharmacokineticists, or a summary of the pharmacodynamic characteristics for a group of clinicians working in the therapeutic area.
During the workshop a lecture is given on regulatory considerations when reviewing pharmacokinetic documentation. A lecture is also given by a pharma-cokineticist with experience from the clinical development of thrombin inhibitors. In association with these lectures, the role of other clinical studies (e.g., drug interaction and bioequivalence studies) that could not be incorporated in this very condensed development is discussed. (Course material is available from [email protected])
11.7.2 Workshop Variations Depending on Students' Previous Knowledge
The workshop was initially created as the PK/PD part of a 20 week full-time course in clinical drug development for students with a previous academic degree (usually in medicine, pharmacy, toxicology, biomedicine, or nursing). As these students, with exception of the pharmacists, have no or little previous training in PK and PK/PD, short lectures on these topics were included in the course. To make group discussions productive, teacher involvement in this course needs to be at a relatively high level, with approximately one teacher per three groups being continuously occupied.
The workshop has mainly been used for fourth-year pharmacy students who previously had a 6 week course in pharmacokinetics. In this setting, teacher involvement in group discussions is usually low. In this course, this workshop is followed by another one, where the students are trained in the principles of clinical trial simulation and the use of the Pharsight Trial Simulator. They are asked, in groups of two or three, to design a clinical PK or PK/PD study of their choice with the restriction that it has to involve real, rather than hypothetical, drugs and diseases and that the study should not have been performed and reported in the literature. Examples of studies that students have chosen to design are drug or food interaction studies, special population studies, and bioavailability/bioequivalence studies. Their choices of study and design are then presented and discussed during a seminar. Thereafter, the students collect information about PK and PK/PD characteristics that allow them to implement a best-guess PK or PK/PD model using the Pharsight Trial Simulator. The resulting data from a single simulation using the chosen design and the best-guess model are then analyzed as decided beforehand. Should the analysis indicate a severe shortcoming of the design, the students have the opportunity to improve the design. The model and result of the study is presented orally at a seminar and individually in writing. This extension to the workshop involves an additional 2 weeks of full-time studies during which students receive lectures on various aspects of clinical drug development.
The workshop has been used for civil engineering students specializing in drug industry and who have had courses in physiology, pharmacology, pharmaceutics, and pharmacokinetics. In the analysis of PK and PD data, these students have, in contrast to the pharmacy students, used nonlinear regression as can be implemented using the Solver function in Excel.
A course in clinical trial simulation and clinical drug development for postgraduate students used the workshop with the addition that the students also were trained in principles of clinical trial simulation and the use of clinical trial simulation software, where the structure of the underlying model was revealed to the students for them to implement and use in the optimization of their study designs.
11.7.3 Workshop Objectives and Experience
The workshop is designed to provide the students with training in several different aspects. These are:
1. Basic PK principles. In particular for the student groups with no or little previous training in this area, the concepts of clearance, volume of distribution, half-life, bioavailability, and absorption rate and how these are calculated and used are the main topics. For students at higher levels, this workshop serves as an update on these issues.
2. Basic PD principles. For all student groups, the concept and potential use of a biomarker, as well as basic pharmacological models, are discussed. The search for the appropriate balance between beneficial effect and toxicity, the utility, in drug development is illustrated.
3. Study design. The students are trained in designing informative studies and consider practical, economical, and ethical aspects in their designs. The necessity for them to prespecify how the data are to be analyzed provide insight in the interaction between design and method of analysis. The specific characteristics of first-in-human dose finding and phase III studies are covered.
4. Clinical drug development principles. Although the development program is rudimentary, it provides an appreciation of the sequential nature of a program and the nature of the PK and PD information sought in each phase and for what purpose. The students are required to contemplate how to use preclinical information in the design of clinical studies.
5. Statistics. Apart from basic descriptive statistics, the students are trained in sample size calculation in the design of patient studies and in exploratory data analysis. The latter in particular from the dose finding study where the relations between outcomes and covariates, including concentration and biomarker, are explored. Also, relations between clearance and covariates are investigated. Various techniques of performing exploratory data analysis are discussed.
6. Clinical trial simulation. Although in the main workshop students are not asked to optimize their design through the use of clinical trial simulation, discussions around the weaknesses of their selected designs and how they can be detected provide an insight into the usefulness of clinical trial simulation. A short presentation on the principles of clinical trial simulation is also provided to all students. For fourth-year pharmacy students, a more comprehensive course in clinical trial simulation is given.
7. General skills. The students get experience applying their PK and PD knowledge in discussions and decision making. Also, the consensus discussions allow them training in leading a discussion. The final presentations make them familiar with presenting PK and PD information in a manner that suits the audience.
Teacher involvement in study design discussions is to make sure, if necessary, that unethical, entirely uninformative, or unpractical designs are avoided. Designs are generally suboptimal in one or several aspects, but allow sufficient information to be collected to proceed to the next phase. For the development to be considered successful, it is required that the investigational drug in phase III is significantly (p < 0.05) superior to heparin in either beneficial effect or toxicity, while not being inferior in either aspect. The drug characteristics in the simulation model are selected such that in a narrow dose range, the investigational drug is superior to heparin in both aspects. Thus, if the students have managed to find a dose within this range and perform phase III studies with sufficient sample sizes, superiority in both aspects may result. However, more commonly, significant superiority in only one of the aspects is found.
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