Uncertainty and Variability in Physiologically Based


EPA/600/R-08/090
August 2008
Uncertainty and Variability in Physiologically Based
Pharmacokinetic Models: Key Issues and Case Studies
National Center for Environmental Assessment
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC 20460

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Uncertainty and Variability in Physiologically Based
Pharmacokinetic Models: Key Issues and Case Studies
Disclaimer: This document has been reviewed in accordance with U.S. Environmental
Protection Agency policy and approved for publication. Mention of trade names or
commercial products does not constitute endorsement or recommendation for use.
Introduction
U.S. EPA increasingly utilizes physiologically based pharmacokinetic (PBPK)
models in the development of its risk assessments. As reviewed in U.S. EPA's
Approaches for the Application of Physiologically Based Pharmacokinetic (PBPK)
Models and Supporting Data in Risk Assessment (U.S. EPA, 2006), these models are
designed to determine the relationship between external exposure and biologically-
relevant (usually internal) dose, and their predictions can be used for extrapolating across
routes, levels, or patterns of exposure, and for quantitatively characterizing differences in
susceptibility across species, populations, and life-stages. However, characterizing
uncertainty and variability in PBPK models and their predictions has been an ongoing
challenge, and this report summarizes some of the recent progress in this area that has
been conducted or funded by the National Center for Environmental Assessment
(NCEA). Specifically, the elements of this work are:
•	Identification of (i) the key issues in characterizing uncertainty and variability in
PBPK modeling; (ii) the state of the science on addressing those issues; and (iii)
the key areas in need of improvement though research or enhanced
implementation. These issues were discussed as a part of the International
Workshop on Uncertainty and Variability in PBPK Models,1 held on October 31 -
November 2, 2006. The outcome of this workshop has been summarized by
Barton et al. (2007).
•	Case examples of chemical-specific applications that demonstrate the methods
and issues associated with characterizing uncertainty and variability in PBPK
modeling. Specifically, the following case examples were completed: (i)
uncertainty and variability in the human pharmacokinetics of tetrachloroethylene
(Chiu and Bois, 2006; Chiu, 2006); (ii) uncertainty in the route-to-route
extrapolation of vinyl chloride pharmacokinetics (Chiu, 2006); (iii) the
development of a method to characterize inter-individual variability when only
pooled data (mean and standard deviation) are available, using data on 1,3-
butadiene (Chiu and Bois, 2007); and (iv) evaluation of uncertainty in human
dose metrics for methyl tertiary-butyl ether (MTBE) exposures (Blancato et al.,
2007).
Each of the topics is discussed in greater detail below.
1 Co-sponsored by NCEA, NCCT, NHEERL, and NIEHS, with additional support from CUT Centers for
Health Research (now The Hamner Institutes for Health Sciences), L'Institut National de l'environnement
industriel et des risques (INERIS), Miami University, Summit Toxicology, and the U.K. Health and Safety
Executive, Health and Safety Laboratory (HSL).

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Key Issues
The key issues in characterizing uncertainty and variability in PBPK modeling are
summarized in Table 1, reproduced from Barton et al. (2007). Here, "model
specification" refers to the process of determining the structure of the PBPK model,
"model calibration" refers to the process of determining the appropriate values for the
PBPK model parameters given the available data, and "model prediction" refers to the
use of the model to make quantitative inferences of interest to risk assessment.
The current state of the science in addressing these issues was summarized in the
background white papers and presentations that were prepared as part of the Workshop,
and listed in Tables 2 and 3.
Table 1: Key Issues in Characterizing Uncertainty and Variability in PBPK Models
Model Specification
•	Integration of deterministic3 and non-deterministic4 model development
•	Specification of alternative models
•	Commonality of model structures across species
Model Calibration
•	Use of data for estimating parameters versus "validating" the model
•	Level of depth/rigor necessary in the non-deterministic model and parameter
calibration methods
•	Implementation of non-deterministic models (data inclusion/exclusion criteria,
sources of variance/covariance, combined analysis of data with very different
experimental designs)
•	Evaluation of alternative models
Model Prediction
•	Changes to the models and parameters for risk assessment predictions
•	Characterizing uncertainty from alternative models
•	Providing feedback to data needs and experimental design	
2	URL: http://toxsci.oxfordjournals.Org/cgi/content/full/99/2/395
3	The "deterministic" model is the mathematical representation of the biological/chemical system (e.g.,
PBPK model and metabolic pathways).
4	The "non-deterministic" model is the mathematical/statistical representation of the uncertainty,
variability, and covariance of the data and parameters of the deterministic model (e.g., statistical model for
measurement errors and population variability).

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Table 2: Background White Papers on Uncertainty and Variability in PBPK
Models
Background White Paper and URL
Model Specification5
http://www.epa.gov/NCCT/uvpkm/files/Specification_PreMeeting_Draft.pdf
Author
Harvey J. Clewell,
III
CUT
Introduction to Statistical Population Modeling and Analysis for
Pharmacokinetic Data
http://www.epa.gov/NCCT/uvpkm/files/Calibration_PreMeeting_Draft.pdf
Marie Davidian
Dept. Statistics,
North Carolina
State University
State of the Art in Issues of Uncertainty and Variability for PBPK Model
Applications
http://www.epa.gov/NCCT/uvpkm/files/Prediction_PreMeeting_Draft.pdf
Frederic Bois
INERIS (Institut
National de
L'Environnement
Industriel et des
Risques).
Table 3: Background Presentations on Uncertainty and Variability in PBPK
Models
Presentation Title and URL	Presenter
! Overview of PBPK Modeling and Its Value in Risk Assessment	Harvey J. Clewell, III
http://www.epa.gov/NCCT/uvpkm/files/UVPKM 2006 HCIewell.pdf CUT
Experimental Data Used with PBPK Models
http://www.epa.gov/NCCT/uvpkm/files/UVPKM_2006_HBarton.pdf
Mediating the Meeting between Model and Data: Statistical Issues for
PBPK Modeling
http://www.epa.gov/NCCT/uvpkm/files/UVPKM 2006 WSetzer.pdf
Hugh A. Barton
US EPA
R. Woodrow Setzer
US EPA
Uncertainty and Variability in PBPK models: How Do We Put It All
Together for Risk Assessment?
http://www.epa.gov/NCCT/uvpkm/files/UVPKM 2006 WChiu.pdf
Weihsueh Chiu
US EPA
Data from Controlled Human Exposure as Basis for PBPK Modeling of
Variability
http://www.epa.gov/NCCT/uvpkm/files/UVPKM 2006 6Johanson.pdf
Gunnar Johanson
Karolinska Institute
Discrepancies and Discovery: The Value of PBPK Modeling for Insuring
Humility
http://www.epa.gov/NCCT/uvpkm/files/UVPKM 2006 MAndersen.pdf
Melvin Andersen
CUT
Title: Statistical Population Modeling and Analysis of PK Data
http://www.epa.gov/NCCT/uvpkm/files/UVPKM_2006_MDavidian.pdf
Marie Davidian
Dept. Statistics, North
Carolina State
University
Accounting for Uncertainty and Variability in PBPK Modeling
Predictions: Where are We Now, Where Should We Go?
http://www.epa.gov/NCCT/uvpkm/files/UVPKM_2006_FBois.pdf
Frederic Bois
INERIS (Institut
National de
L'Environnement
Industriel et des
Risques).
5 Subsequently published in Clewell and Clewell (2008).

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Three major short-term needs were identified that participants indicated could
make immediate impacts on the characterization of uncertainty and variability in PBPK
modeling:
•	Routine formation of multi-disciplinary teams to integrate the deterministic
(biological) and non-deterministic (statistical) components of the modeling;
•	Broader use of sensitivity analysis, particularly global sensitivity analysis in
which all parameters are allowed to vary simultaneously throughout a range of
values; and
•	Improved documentation of model structure(s), parameter values, sensitivity and
other analyses, and data so as to enhance the transparency and reproducibility of
the PBPK modeling results.
Five longer-term needs were also identified that would significantly improve the ability
to routinely address uncertainty and variability in PBPK modeling in the future:
•	Better statistical models and methods, particularly given the constraints imposed
by previously published laboratory animal studies (e.g., aggregated rather than
individual data, cross-sectional rather than longitudinal data, serial correlations in
closed chamber experiments);
•	Better databases for physiological properties, and particularly their inter- and
intra-individual variability;
•	Data, models, and analyses for a wider range of chemical classes (i.e., beyond the
volatile organic compounds typically studied); and
•	Training, documentation, and software to disseminate the available data, methods
and best practices.
Case Studies
The first case study involved the characterization of uncertainty and variability in
the human pharmacokinetics of tetrachloroethylene, in particular the amount of inhaled
tetrachloroethylene that is metabolized. The first part of this case study attempted a
replication of Bayesian analysis of uncertainty and variability performed by Bois et al.
(1996). Using updated software and greater computational resources, Chiu and Bois
(2006)6 found that the uncertainty in the results was greater than previously reported,
particularly for the extrapolation to environmentally-relevant exposures (0.001 ppm
exposure - as opposed to exposures of 70 ppm and higher). In particular, the 95%
confidence interval for the amount of tetrachloroethylene metabolized was estimated to
be 2.0%-61%, in contrast to the original Bois et al. (1996) estimate of 15%—58%. In
addition, they performed an analysis that separated uncertainty from population
variability, and found that in this case, the predicted population variability was greater
than the inferred uncertainty. Finally, it was noted that the 95% confidence interval for
the predictions at low dose encompassed predictions from all six previously published
analyses (which varied by 10-fold). A subsequent analysis (Chiu, 2006) expanded on this
comparison and examined the uncertainty in the values of Vmax and Km, the critical
determinants of the amount metabolized. As shown in Figure 1, adapted from Chiu
(2006), the point estimates from seven previously published analyses are within the
envelope of the uncertainty derived by Chiu and Bois (2006). Furthermore, all these
6 http://www. springerlink.com/content/x6khl8q47jl860m4/

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10000 =
1000 - r
100 ::

- Prior Bounds
Chiu and Bois (2006)
~	Chen and Blancato (1987)
A	Ward etal. (1988)
O	Bois et al. (1990)
Hi	Rao and Brown (1993)
A	Reitz et al. (1996)
#	Clewell et al. (2005)
©	Loizou(2001)
0.0001
0.001
0.01
0.1
10
Vmax [mg/(min LBM )]
Figure 1. Vmax and Km values from eight published analyses of tetrachloroethylene
pharmacokinetics. All parameters were converted to the same units as those in Chiu
and Bois [note in particular that the unit for Km (mg in liver) used by Chiu and Bois
(2006) is not the same as that typically used in PBPK models (mg/l in venous blood
leaving liver)]. All analyses are point estimates except for Chiu and Bois (2006), which
included a Bayesian analysis of uncertainty and variability. Points shown for Chiu and
Bois (2006) are 300 random samples of the population means for Vmax and Km (i.e.,
reflecting uncertainty in the population means); the scatter would be greater if population
variability were also included. Also included are the bounds on the prior distributions
used in that analysis.
analyses give similar fits to the available in vivo data. Therefore, this is a case in which
the available data are insufficient to highly constrain the predictions of interest, and the
Bayesian methodology was able to quantify these uncertainties in a transparent and
reproducible manner.
The second case study examined the uncertainty in route-to-route extrapolation
using vinyl chloride as the example chemical. In particular, Chiu and White (2006)7
showed that for a prototypical PBPK model, there is a simple relationship, depending on
only four parameters, between oral dose and inhalation exposure concentrations that give
the same internal dose. Chiu (2006) subsequently used Monte Carlo simulation to
examine the uncertainty in this relationship due to uncertainty in the four key parameters
(alveolar ventilation, cardiac output, hepatic blood flow, and the blood-air partition
7 http://www3.interscience.wiley.eom/journal/l 18562900/abstract?CRETRY=l&SRETRY=0

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coefficient). The results showed that because all four of these parameters are fairly well
measured, the route-to-route relationship has a coefficient of variation (standard deviation
divided by the mean) of only 21%. Thus, this case study shows an example in which
only a few model parameters determine the result, and they are all well constrained by the
available data; therefore, the predictions are estimated with relatively high confidence.
The third case study addressed the critical issue of whether it is possible to
characterize pharmacokinetic variability when only aggregated data in the form of mean
o
and standard deviations, and not individual data, are available. Chiu and Bois (2007)
used human pharmacokinetic data on 1,3-butadiene to show that using a hierarchical
Bayesian approach and several conceptually simple approximations, inter-individual
variability could still be obtained from aggregated data. A comparison was made
between population analysis in which individual data were available and the proposed
approach using only aggregated data. It was found that the uncertainty distributions for
all the pharmacokinetic parameters substantially overlapped between the two analyses,
although the uncertainty from the aggregated analyses tended to be slightly larger.
Importantly, the uncertainty in the model prediction of interest (i.e., the amount
metabolized, as per tetrachloroethylene, above), was also quite similar, though again with
somewhat higher uncertainty in the aggregated analyses. Therefore, this case study
shows that aggregated data may still be informative as to population variability and is an
important consideration given that individual data are often inaccessible for risk
assessments.
The fourth case study considered dose metrics that may be applicable for MTBE
risk assessment. A PBPK model for MTBE in rats was developed and calibrated with all
known experimental data, and used to extrapolate calculations for humans to inform an
uncertainty analysis (Blancato et al., 2007). This impact analysis (quantitative analysis of
changes in predicted dose metrics after a change in model input values) was developed
for exposure levels consistent with environmental levels. The inhalation route was
examined using the following dose metrics: peak MTBE in venous blood, area under the
curve (AUC) in venous blood at 24 hours, amount of MTBE metabolized in the liver at
24 hours, and peak metabolite tert-butanol (TBA) concentration in venous blood. An
estimate for uncertainty in resulting dose metrics due to variability in MTBE metabolism
was included in the computer simulations, consistent with variability estimates available
in the literature. The impact analysis showed that TBA blood concentration varied to a
greater extent than MTBE when accounting for human metabolic variability.
Conclusions
As discussed in Barton et al. (2007), current practices in characterizing
uncertainty and variability in PBPK models have shown significant progress in the
specification of the deterministic and stochastic model structures, the estimation of
parameters using diverse data from multiple sources, and the characterization of
uncertainty and variability in model parameters and predictions of interest for risk
assessment. However, there are many areas in need of better methods or implementation,
and the characterization of uncertainty and variability in PBPK models is not yet a
sufficiently standard practice. The case studies described above demonstrate that for
8 http://www.ingentaconnect.eom/content/asa/jabes/2007/00000012/00000003/art00003

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some purposes, the Bayesian approach to calibrating model parameters and
characterizing the uncertainty and variability in model predictions is both feasible and
transparent. However, in the route-to-route extrapolation case study with vinyl chloride,
straightforward application of Monte Carlo simulation provided robust results. The
MTBE case study also illustrated the value of a systematic, mathematically
straightforward analysis in which impacts of variation of important parameters on
estimated dose metrics for risk assessment are evaluated. Thus, the more labor-intensive
Bayesian methods are not necessarily needed for all applications. While improvements
in analytical methods and implementation are still needed, important applications of
PBPK models can now be accompanied by systematic and transparent evaluation of the
impacts of model uncertainties and inter-individual variability on risk assessment results.
Another issue is the integration of more sophisticated characterizations of PBPK
model uncertainty and variability into risk assessment. For instance, Monte Carlo and
Bayesian methods would fit naturally into probabilistic dose-response analyses (e.g.,
Hattis et al., 2002; Evans et al., 2001). However, while some example applications exist,
a generally-accepted framework for such analyses has not yet been established.
Moreover, even within probabilistic analyses, questions remain as to what percentiles of
uncertainty and variability to use, as well as how to evaluate whether the estimates of
human variability are representative of the full human population taking into account
susceptible populations and life-stages. Therefore, work remains to be done on methods
and approaches to integrating estimates of pharmacokinetic (and other sources of)
uncertainty and variability into risk assessment.
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