United States
Environmental Protection
Agency
Developing Relative Potency
Factors for Pesticide Mixtures:
Biostatistical Analyses of Joint
Dose-Response
-------
EPA/600/R-03/052
September 2003
Developing Relative Potency Factors
for Pesticide Mixtures: Biostatistical
Analyses of Joint Dose-Response
L* u-s- Environmental Protection Agency
Region 5, Library (PJ.-12J)
12th
National Center for Environmental Assessment
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, OH 45268
/"T'V Recycled/Recyclable
Printed with vegetable-based ink on
paper that contains a minimum of
50% post-consumer fiber content
processed chlorine free.
-------
NOTICE
The U.S. Environmental Protection Agency through its Office of Research and
Development funded and managed the research described here. It has been subjected
to the Agency's peer and administrative review and has been approved for publication
as an EPA document. Mention of trade names or commercial products does not
constitute endorsement or recommendation for use.
-------
FOREWORD
This report was developed by the U.S. Environmental Protection Agency's (EPA)
Office of Research and Development (ORD), National Center for Environmental
Assessment - Cincinnati Office (NCEA-Cin) in collaboration with EPA's Office of
Pesticide Programs. It contains information concerning biological concepts and
statistical procedures for improving the application of Relative Potency Factors (RPFs)
to pesticide mixtures. This research supports the need for chemical mixtures risk
assessment research as mandated in 1996 by both the Food Quality Protection Act
(FQPA) and the Safe Drinking Water Act Amendments. Research results are presented
regarding the theoretical basis for RPF-based risk assessments; new quantitative
methods for applying RPFs are shown. The RPF approach assumes toxicity of the
mixture components can be characterized using dose addition. Thus, the basic tenets
of dose addition, common toxic modes of action and similarly-shaped dose-response
curves among the mixture components, are investigated and discussed. This research
was undertaken to continue exploring and developing cumulative risk assessment
strategies beyond current applications and is intended to improve future applications of
RPF based risk assessments.
The statistical methods presented in this effort are based on research conducted
by Jim Chen, Yi-Ju Chen, and Ralph Kodell through an Interagency Agreement
between EPA and the Food and Drug Administration's National Center for Toxicological
Research. An external review was conducted by Drs. Christine F. Chaisson, Pavel
Muller, and Walter W. Peigorsch under EPA Contract No. 68-C-02-060/061 with Versar,
Inc.
-------
RESEARCHERS
This research was sponsored by the U.S. Environmental Protection Agency
(EPA), Office of Research and Development, National Center for Environmental
Assessment - Cincinnati Division (NCEA-Cin). NCEA-Cin researchers collaborated with
scientists from other organizations to conduct this research and to author this report. A
number of other scientists also contributed their ideas, provided discussions and
review, and wrote text toward completion of this effort. These individuals are listed
below.
Authors:
EPA's National Center for Environmental Assessment, Cincinnati, OH
Linda K. Teuschler
Glenn E. Rice
John C. Lipscomb
EPA's Homeland Security Research Center, Cincinnati, OH
Richard C. Hertzberg
EPA's Office of Pesticide Programs, Washington, DC
Karen Hamernik
Alberto Protzel
U.S. Food and Drug Administration's National Center for Toxicological Research,
Division of Biometry and Risk Assessment, Jefferson, Arkansas
James Chen
Yi-Ju Chen
Ralph L. Kodell
Contributors and Reviewers:
EPA's National Center for Environmental Assessment, Research Triangle Park, NC
Gary Foureman
EPA's National Center for Environmental Assessment, Washington, DC
Femi Adeshina
EPA's National Health and Environmental Effects Research Laboratory, Research
Triangle Park, NC
Jane Ellen Simmons
IV
-------
TABLE OF CONTENTS
Page
FOREWORD iii
RESEARCHERS iv
LIST OF ABBREVIATIONS vii
KEY DEFINITIONS viii
EXECUTIVE SUMMARY xiii
1. INTRODUCTION 1
2. DOSE ADDITION CONCEPTS 9
3. RELATIVE POTENCY FACTORS 12
3.1. JUDGMENTS OF COMMON TOXICOLOGIC ACTION 15
4. CHOICE OF DOSE METRIC IN CHARACTERIZING MIXTURE
TOXICITY BY DOSE ADDITION 20
4.1. RPF DOSE ISSUES 20
4.1.1. Administered Dose 21
4.1.2. Internal Dose 21
4.1.3. Mixtures Exposures Through Multiple Exposure Routes 21
4.1.4. Mixtures Exposures Though a Single Exposure Route in
Different Species 22
4.2. CHOICE OF DOSE MEASURES 25
5. BIOSTATISTICAL DOSE-RESPONSE MODELING FOR
CUMULATIVE RISK 26
5.1. DOSE-RESPONSE MODEL FOR COMBINED EXPOSURES 2
5.1.1. Constant Relative Potency 30
5.1.2. Nonconstant Relative Potency 31
5.1.3. Constant and Nonconstant Relative Potencies in the
Same Mixture 32
-------
TABLE OF CONTENTS cont.
Page
5.2. STATISTICAL ALGORITHMS FOR SUBCLASS GROUPS
WITHIN A MIXTURE 34
5.2.1. Top-Down Approach 36
5.2.2. Bottom-Up Approach 39
5.3. CUMULATIVE RISK ASSESSMENT 42
5.3.1. Mixtures Reference Dose 43
6. CONCLUSIONS 45
7. REFERENCES 48
APPENDIX A: Chen et al., 2001. Using Dose Addition to Estimate
Cumulative Risks from Exposures to Multiple Chemicals A-1
APPENDIX B: Chen et al., 2003 (In Press). Cumulative Risk Assessment for
Quantitative Response Data B-1
VI
-------
LIST OF ABBREVIATIONS
CRA Cumulative Risk Assessment
DBFs Disinfection By-Products
ED Effective Dose
EPA Environmental Protection Agency
FQPA Food Quality Protection Act
HI Hazard Index
ICED Index Chemical Equivalent Dose
LOAEL Lowest-Observed-Adverse-Effect Level
MF Modifying Factor
NOAEL No-Observed-Adverse-Effect Level
OP Organophosphorus Pesticide
ORD Office of Research and Development
PBPK Physiologically-Based Pharmacokinetic
RAF Risk Assessment Forum
RfD Reference Dose
RPF Relative Potency Factor
TEF Toxicity Equivalence Factor
TEQ 2,3,7,8-TCDD Toxicity Equivalents
UF Uncertainty Factor
VII
-------
KEY DEFINITIONS
Absorbed Dose - the amount of a substance crossing a specific barrier through uptake
processes.1
Additivity - When the "effect" of the combination is estimated by the sum of the
exposure levels or the effects of the individual chemicals. The terms "effect" and "sum"
must be explicitly defined. Effect may refer to the measured response or the incidence
of adversely affected animals. The sum may be a weighted sum (see "dose addition")
or a conditional sum (see "response addition").3
Bioavailability - The state of being capable of being absorbed and available to interact
with the metabolic processes of an organism. Bioavailability is typically a function of
chemical properties, physical state of the material to which an organism is exposed,
and the ability of the individual organism to physiologically take up the chemical.1
Chemical Classes - Groups of components that exhibit similar biologic activities, and
that frequently occur together in environmental samples, usually because they are
generated by the same commercial process. The composition of these mixtures is
often well controlled, so that the mixture can be treated as a single chemical. Dibenzo-
dioxins are an example.3 (Note: this is slightly modified from the original version).
Chemical Mixture - Any set of multiple chemical substances that may or may not be
identifiable, regardless of their sources, that may jointly contribute to toxicity in the
target population. May also be referred to as a "whole mixture" or as the "mixture of
concern."3
Complex Mixture - A mixture containing so many components that any estimation of its
toxicity based on its components' toxicities contains too much uncertainty and error to
be useful. The chemical composition may vary over time or with different conditions
under which the mixture is produced. Complex mixture components may be generated
simultaneously as by-products from a single source or process, intentionally produced
as a commercial product, or may coexist because of disposal practices. Risk
assessments of complex mixtures are preferably based on toxicity and exposure data
on the complete mixture. Gasoline is an example.3
Components - Single chemicals that make up a chemical mixture that may be further
classified as systemic toxicants, carcinogens, or both.3
Dose Additivity - When the effect of the combination is the effect expected from the
equivalent dose of an index chemical. The equivalent dose is the sum of component
doses scaled by their potency relative to the index chemical.3
Dose - The amount of a substance available for interaction with metabolic processes or
biologically significant receptors after crossing the outer boundary of an organism1.
VIII
-------
Dose-Response Assessment - A determination of the relationship between the
magnitude of an administered, applied, or internal dose and a specific biological
response. Response can be expressed as measured or observed incidence, percent
response in groups of subjects (or populations), or as the probability of occurrence
within a population.2
Dose-Response Relationship - The relationship between a quantified exposure
(dose), and the proportion of subjects demonstrating specific, biological changes
(response).2 U.S. EPA's draft 1996 Cancer Guidelines further state: "Whether animal
experiments or epidemiologic studies are the sources of data, questions need to be
addressed in arriving at an appropriate measure of dose for the anticipated
environmental exposure. Among these are:
whether the dose is expressed as an environmental concentration,
applied dose, or delivered dose to the target organ,
whether the dose is expressed in terms of a parent compound, one or
more metabolites, or both,
the impact of dose patterns and timing where significant,
conversion from animal to human doses, where animal data are used,
and
the conversion metric between routes of exposure where necessary and
appropriate."
Effective Dose (ED10) - The dose corresponding to a 10% increase in an adverse
effect, relative to the control response.2
Exposure - Contact made between a chemical, physical, or biological agent and the
outer boundary of an organism. Exposure is quantified as the amount of an agent
available at the exchange boundaries of the organism (e.g., skin, lungs, gut).2
Exposure Assessment - An identification and evaluation of the human population
exposed to a toxic agent, describing its composition and size, as well as the type,
magnitude, frequency, route and duration of exposure.2
Extrapolation, low dose - An estimate of the response at a point below the range of
the experimental data, generally through the use of a mathematical model.2
Human Equivalent Concentration (HEC) or Dose (HED) - The human concentration
(for inhalation exposure) or dose (for other routes of exposure) of an agent that is
believed to induce the same magnitude of toxic effect as the experimental animal
species concentration or dose. This adjustment may incorporate toxicokinetic
information on the particular agent, if available, or use a default procedure, such as
assuming that daily oral doses experienced for a lifetime are proportional to body
weight raised to the 0.75 power.2
IX
-------
Index Chemical -The chemical selected as the basis for standardization of toxicity of
components in a mixture. The index chemical must have a clearly defined
dose-response relationship.3
Index Chemical Equivalent Dose -The exposure to a chemical that is expected to
elicit the same response as that of the index chemical, when the chemicals are
administered by the same route, at the same duration and frequency. The chemical
and the index chemical must share a common mode of action.
Internal dose - A more general term denoting the amount absorbed without regard to
absorption process.1
Independence of Action - Mixture components that cause different kinds of toxicity, or
effects in different target organs; the risk assessor may then combine the probabilities
of toxic effects for the individual components.3
Mechanism of Toxicity or Mechanism of Toxic Action - The set of molecular and
cellular events leading to a toxicologic outcome. [A toxicologic outcome is considered to
be damage to the organism at any level of biological organization (i.e., molecular,
cellular, tissue,...).]4
Mode of Action - The set of biological events at the target tissue or target organ
leading to a toxicologic outcome. [A toxicologic outcome is considered to be damage to
the organism at any level of biological organization (i.e., molecular, cellular, tissue,...).]4
Model - A mathematical function with parameters that can be adjusted so the function
closely describes a set of empirical data. A mechanistic model usually reflects observed
or hypothesized biological or physical mechanisms, and has model parameters with
real world interpretation. In contrast, statistical or empirical models selected for
particular numerical properties are fitted to data; model parameters may or may not
have real world interpretation. When data quality is otherwise equivalent, extrapolation
from mechanistic models (e.g., biologically based dose-response models) often carries
higher confidence than extrapolation using empirical models (e.g., logistic model).2
Physiologically Based Pharmacokinetic (PBPK) Model - Physiologically based
compartmental model used to characterize pharmacokinetic behavior of a chemical.
Available data on blood flow rates, and metabolic and other processes which the
chemical undergoes within each compartment are used to construct a mass-balance
framework for the PBPK model.2
Point of Departure - The dose-response point that marks the beginning of a low-dose
extrapolation. This point is most often the upper bound on an observed incidence or on
an estimated incidence from a dose-response model.2
Risk - The probability of deleterious effects on health.1
-------
Relative Potency Factor Method - A mixtures risk assessment approach used to
assess risks posed by mixture components that exhibit a common mode of action. The
toxic potency of each mixture component is compared to that of an index chemical
generating a measure of potency for each component that is relative to the toxicity of
the index chemical. For application, the shapes of the individual component dose-
response functions must be similarly over the region of the mixture exposure.
Response Additivity - When the response (rate, incidence, risk, or probability) of
effects from the combination is equal to the conditional sum of component responses
as defined by the formula for the sum of independent event probabilities.3
Similar Components - Single chemicals that cause the same biologic activity or are
expected to cause a type of biologic activity based on chemical structure. Evidence of
similarity may include parallel log-probit dose-response curves and same mechanism of
action or toxic endpoint. These components are expected to have comparable
characteristics for fate, transport, physiologic processes, and toxicity.3
Similar Mixtures - Mixtures that are slightly different, but are expected to have
comparable characteristics for fate, transport, physiologic processes, and toxicity.
These mixtures may have the same components but in slightly different proportions, or
have most components in nearly the same proportions with only a few different (more
or fewer) components. Similar mixtures cause the same biologic activity or are
expected to cause the same type of biologic activity due to chemical composition.
Similar mixtures act by the same mechanism of action or affect the same toxic
endpoint. Diesel exhausts from different engines are an example.3
Simple Mixture - A mixture containing two or more identifiable components, but few
enough that the mixture toxicity can be adequately characterized by a combination of
the components' toxicities and the components' interactions.3
Target Organ - The biological organ(s) most adversely effected by exposure to a
chemical substance.2
Uptake - The process by which a substance crosses an absorption barrier and is
absorbed into the body.1
Sources
1U.S. EPA. 1992. Guidelines for Exposure Assessment; Notice. Federal Register.
57(104):22888-22938.
2U.S. EPA. 2003. Integrated Risk Information System. Office of Research and
Development, National Center for Environmental Assessment, Washington, DC.
Online- http://www.epa.gov/iris
XI
-------
3U.S. EPA. 2001. Supplementary Guidance for Conducting Health Risk Assessment of
Chemical Mixtures. Office of Research and Development, Washington, DC.
EPA/630/R-00/002. Available in PDF format at: www.epa.gov/NCEA/raf/chem mix.htm
4U.S. EPA. 2002. The Feasibility of Performing Cumulative Risk Assessments for
Mixtures of Disinfection By-Products in Drinking Water. NCEA-C-1257. Final Draft.
XII
-------
EXECUTIVE SUMMARY
Cumulative Risk Assessment (CRA) is defined in U.S. EPA's Risk Assessment
Forum (RAF) CRA Framework (U.S. EPA, 2002a) as "the combined risks from
aggregate exposures to multiple agents or stressors." CRA has become an important
research area, reflecting the interest of U.S. EPA's regional risk assessors, program
offices, Office of Environmental Justice, and Office of Children's Risk. In implementing
the requirements of the Food Quality Protection Act of 1996, U.S. EPA's Office of
Pesticide Programs has developed guidance for conducting CRA's of chemicals that
appear to act by a common mechanism of toxicity (U.S. EPA, 2002b). Because the
organophosphorus pesticides (OPs) are considered to exert some of their toxic effects
via a common toxicologic mechanism (i.e., cholinesterase inhibition), these compounds
have been the subject of a CRA (U.S. EPA, 2001 b). Additional CRA's may be
performed on additional pesticide classes (e.g., triazinines, carbamates) and other co-
occurring substances for which a common mode of action can be identified. The risk
assessment method employed in the OP cumulative risk study is the Relative Potency
Factor (RPF) approach (U.S. EPA, 2000). Dose addition is the critical methodological
assumption, requiring the mixture components to act by the same toxic mode of action
and to have similarly-shaped dose-response curves.
Assessing the cumulative toxicological effects of multiple chemicals has been
addressed from time to time (NRC, 1988; U.S. EPA, 1986, 2000). Methods and data
that can be used to estimate the risk of exposures to multiple chemicals have been
developed. Although U.S. EPA guidance exists regarding the basic theory for RPFs,
XIII
-------
the toxicological criteria for defining and determining a common mode of action among
chemicals continue to need refinement; results on this subject are presented in this
report. Further, results are presented on appropriate statistical methods for CRA,
based on research published in Chen et al. (2001, 2003). Biostatistical approaches are
shown for grouping chemicals identified as having common modes of action, proposing
two classification algorithms to cluster chemicals into subclasses within which
chemicals have similarly-shaped dose-response functions. Chemicals within subclasses
are combined using the RPF method when a constant relative potency among
chemicals exists. Additional methods are shown to calculate cumulative risks inclusive
of these subclasses (i.e., combining across subclasses for which a non-constant
relative potency exists) using either a joint dose-response approach or by integrating
the concepts of dose addition and response addition.
An important question in mixtures risk assessment research is how to assess a
mixture containing some chemicals that share a common toxic mode of action and
other chemicals that do not. Current additivity methods have evolved to handle either
the former (dose addition) or the latter (response addition). Alternatively, the risk
assessor may choose to do the assessment based on whole mixture data. The
biostatistical methods developed in this report provide alternative methods to evaluate a
mixture under three scenarios. The simple case occurs when there is certainty that a
common toxic mode of action is operating, so a dose addition approach can be applied.
The second case occurs when the mixtures can be divided into independent mode of
action subclasses; dose addition and response addition can be integrated to make the
assessment. The third case occurs when mode of action is uncertain, so a joint
XIV
-------
dose-response modeling procedure is used to create a range of risk estimates. Thus,
these approaches enrich the available library of mixture risk assessment methods
beyond what is currently published by the U.S. EPA (1986, 2000). Further, these
approaches may be useful in future assessments of pesticide mixtures to be evaluated
under FQPA. Finally, the results presented here are generalizable to assessments of
other environmental mixtures; the risk assessments that support environmental
regulations of important environmental mixtures such as dioxins, polychlorinated
biphenyls, and OPs are based on concepts of additivity (U.S. EPA, 1989b, 2000,
2001 b).
The research results in this report can be applied to reduce uncertainties in
RPF-based risk assessments of chemical mixtures. These results also show how
mixtures risk assessments can be conducted using additivity concepts. Various sources
of uncertainty exist in most mixtures risk assessments, including uncertainties
addressed in this report regarding several factors:
Common mode of action across mixture components (Sections 2, 3)
Similarly shaped dose-response curves across mixture components
(Sections 2, 5)
Value of internal vs. external dose estimates for developing RPFs
(Section 4)
Choice of dose metric (moles vs. mass) to use in a cumulative risk
assessment (Section 4)
Cross-species extrapolation of relative potency factors (Section 4)
Estimating risks for a mixture with two or more common mode of action
subclasses (Section 5).
xv
-------
Biostatistical modeling in this report presents ways to combine dose-response
information, partitioning the mixtures into common mode of action subclasses. These
models can then be used to estimate risks for specific exposure scenarios or used to
develop toxicity values, such as a reference dose for the mixture. Three RPF-based
methods are discussed, reflecting what is known or uncertain about the mixture
toxicology. These approaches can be applied using internal or external doses.
Development of approaches based on internal doses may reduce some toxicokinetic
uncertainties associated with RPFs based on administered doses. In the Chen et al.
papers (2001, 2003) in Appendices A and B, external doses were used to develop
statistical methods for grouping components into common mode of action subclasses.
The next step in this process is to use RPFs based on internal doses and compare
subclass groupings and modeling results with those developed using external doses.
Recommendations for future RPF research on pesticide mixtures are listed here.
1) Develop kinetic models for pesticide mixtures in rodents.
2) Using experimental cholinesterase inhibition measures, determine RPFs
based on both external and internal dose estimates for the rodent.
3) Determine if the RPFs based on internal dose estimates significantly differ
from RPFs developed from external doses for the rodent.
4) Apply the biostatistical methods for grouping by common dose-response
curves using RPFs based on internal and external doses and compare the
groupings that result.
5) Develop kinetic models for pesticide mixtures in humans.
6) Estimate human risks using rodent cholinesterase inhibition responses,
RPFs based on rodent internal doses, and human internal dose estimates
using the three approaches presented in Chen et al. (2001, 2003), as
appropriate.
XVI
-------
7) Compare subclass groupings and human risk estimates for all scenarios
of internal and external RPFs.
8) Ealuate the toxicity of different human exposure scenarios with the RPF
models developed.
This research was undertaken to continue exploring and developing cumulative
risk assessment strategies based on dose addition concepts beyond current
applications and is intended to improve future applications of RPF based risk
assessments.
XVII
-------
1. INTRODUCTION
The U.S. Environmental Protection Agency (U.S. EPA) and other regulatory
agencies use risk assessment to evaluate the risk posed to humans through chemical
exposures to contaminants in food, drinking water, or environmental media. Risk
assessment for toxic agents is often conducted to evaluate the potential risks from
exposure to a single toxic agent through a single route of exposure. Although it is
important to evaluate individual toxic agents, people frequently are exposed to many
chemicals simultaneously or in sequence by different exposure routes. These
exposures to multiple chemicals through various media could cause unexpected
cumulative effects. The combined risk from such exposures may be greater or less than
what would typically be predicted from data on individual chemicals. Assessing the
cumulative toxicological effects of multiple chemicals has been addressed from time to
time (NRC, 1988; U.S. EPA, 1986, 2000). However, new methods and improvements
to existing approaches are still needed to estimate risk from exposures to multiple
chemicals.
Cumulative Risk Assessment (CRA) is defined in U.S. EPA's Risk Assessment
Forum (RAF) CRA Framework (U.S. EPA, 2002a) as "the combined risks from
aggregate exposures to multiple agents or stressors." CRA can include both chemical
and non-chemical stressors, multiple-route exposures, population factors that
differentially affect exposure or toxicity, and community based assessments. CRA has
become an important research area, reflecting the interest of U.S. EPA's regional risk
assessors, program offices, Office of Environmental Justice, and Office of Children's
-------
Risk. In 2002, U.S. EPA's Office of Research and Development (ORD) jointly
sponsored a workshop with U.S. EPA's Regions to discuss current case studies,
methods and research needs regarding CRA (U.S. EPA, 2003a). Regional scientists
are confronted with conducting community-based CRA's (e.g., assessing risks from
multi-media, multi-stressor exposures to a population in a specified geographic area).
Successful completion of such assessments require development of new data,
methods, and guidance.
U.S. EPA's Program Offices generally conduct CRA's on a select group of co-
occurring chemicals, and set broad national standards. Examples of programmatic
interests include:
The Office of Water needs to conduct chemical mixtures research to support
requirements of the Safe Drinking Water Act Amendments of 1996 (U.S. EPA,
1996).
The Office of Air Quality Planning and Standards has used a CRA approach in
conducting the National Air Toxics Assessment of 33 air pollutants (a subset of
32 air toxics from the Clean Air Act's list of 188 air toxics plus diesel particulate
matter) (U.S. EPA, 2001 a).
The Office of Solid Waste and Emergency Response assesses contaminant
mixtures at Superfund Sites (U.S. EPA, 1989a) under the Comprehensive
Environmental Response, Compensation, and Liability Act (U.S. EPA, 1980).
The Office of Pesticide Programs has conducted a CRA on organophosphorus
pesticide (OP) mixtures (U.S. EPA, 2001 b), under the Food Quality Protection
Act (FQPA) of 1996 (U.S. EPA, 1997). Case studies may be performed on
additional pesticide classes (e.g., triazinines, carbamates) and other co-occurring
substances for which a common mode of action can be identified.
The FQPA is the most specific act regarding CRA, requiring EPA to consider the
potential human health risks of multiple route exposures to multiple pesticide residues
-------
and substances that have a common mechanism of toxicity (U.S. EPA, 1997).1 The
first pesticide group to be evaluated (U.S. EPA, 2002b) is the organophosphorus
pesticides (OPs), a group of closely related pesticides that affect nervous system
function. They are applied to many food crops, as well as to residential and commercial
buildings and lawns. The many uses of this class of pesticides result in frequent and
consistent human exposures. The acute and chronic effects of OPs in humans, wild
animals, and test animals are well known. OPs are neurotoxic because they bind to
and phosphorylate the enzyme acetylcholinesterase in both the central (brain) and
peripheral nervous systems, reducing the ability of the enzyme cholinesterase to
function properly in regulating acetylcholine, a neurotransmitter. Acetylcholine is a
critical factor in the transfer of nerve impulses from a nerve cell to a muscle cell or
another nerve cell. If acetylcholine levels are not properly reduced by cholinesterase,
the nerve impulses or neurons remain active longer than they should, overstimulating
the nerves and muscles and causing toxic effects at many sites, including
neuromuscular junctions and synapses of the central and autonomic nervous system.
As part of the implementation of FQPA, U.S. EPA's Office of Pesticide Programs
has developed guidance for conducting cumulative risk assessments of chemicals that
appear to act by a common mechanism of toxicity (U.S. EPA, 2002b). Because the
OPs are considered to exert some of their toxic effects via a common toxicologic
'The terms mechanism of toxicity (or mechanism of toxic action) and mode of action represent a
continuum of understanding regarding a toxicodynamic process (U.S. EPA, 2002c). A toxicologic outcome
is considered to be damage to the organism at any level of biological organization (i.e., molecular, cellular,
tissue,...). Knowledge of a chemical's mechanism of toxicity or mechanism of toxic action implies that the
molecular and cellular events leading to a toxicologic outcome are described and well-understood.
Knowledge of a chemical's mode of action implies a general understanding of the key toxicodynamic
events that occur at a tissue level, but not a detailed description of these events at the cellular or
molecular level. Mode of action is defined as the set of biological events at the target tissue or target
organ leading to a toxicologic outcome.
-------
mechanism (i.e. cholinesterase inhibition), these compounds have been the subject of a
CRA (U.S. EPA, 2001 b). The risk assessment method employed in the OP CRA and
likely to be used in future pesticide CRA's is the Relative Potency Factor (RPF)
approach (U.S. EPA, 2000). This report examines the theoretical basis for the RPF
method, providing useful information to improve and enhance such future applications.
The RPF approach is appropriate under FQPA because dose addition is the
critical RPF methodological assumption; implementation requires that the mixture
components act by the same toxic mode of action. As explained in Section 2, a
theoretical consequence of this assumption is that the components should have
similarly-shaped dose-response curves between the response threshold and the
maxima. To summarize the procedure, doses of mixture components are scaled by
their potency relative to a well-studied component of the chemical mixture (referred to
as the index chemical) using scaling factors called RPFs. The product of each mixture
component's dose and its RPF is considered to be its equivalent dose in units of the
index chemical. These dose equivalents of all the mixture components are summed to
express the total mixture dose in terms of an Index Chemical Equivalent Dose (ICED).2
The risk posed by the mixture is then quantified by comparing the mixture's ICED to the
dose-response assessment of the index chemical. To implement this approach, the
index chemical must have an adequate toxicologic dose-response data set.
U.S. EPA (2000) characterized the RPF methodology as a generalized form of
the toxicity equivalence factor (TEF) methodology that has been used to assess risks
2The ICED has the same mathematical interpretation as the dioxin toxicity equivalents (TEQ).
TEQ refers to the quantification of dioxin concentrations based on the congeners' equivalent 2,3,7,8-
TCDD toxicity (U.S. EPA, 1989b). ICED is applied to mixtures other than dioxins.
-------
posed by some dioxins (U.S. EPA, 1989b). The TEF approach uses a single TEF for
each dioxin congener, applying this same TEF to all exposure routes, health effects,
and exposure durations. The RPF methodology was developed for application to a
broad set of chemical groups whose data sets are either less complete than the dioxins
or indicate more variation in mode of action across route, effects and duration. The
significant generalizations in the RPF methodology include the following:
1. RPFs may be developed to assess risks for a subset of the health effects
caused by a mixture's components. For example, the same mixture
components may be shown to cause both hepatotoxicity and renal toxicity in
bioassays. Different RPFs may be developed to address the risk of each type of
toxicity following human exposures. Mixture Component A may exhibit greater
hepatotoxicity than Component B when compared to Index Chemical C; to reflect
this, the RPF for the hepatotoxicity of Component A should be greater than the
RPF of Component B. However, mixture Component B may exhibit greater renal
toxicity than Component A when compared to Index Chemical C and, to reflect
this, the RPF for the renal toxicity of Component A should be less than that of
Component B.
Note that some mixture components may act through multiple modes of action
on different target tissues. It is conceivable that several RPFs may need to be
developed to adequately address the risks posed by human exposures to the
mixture. Thus, the membership of component chemicals may differ across
groups of RPFs and may also overlap.
-------
2. RPFs may be developed to assess risk for a single route of exposure. For
example, the same mixture components may pose risk through inhalation and
oral exposures. Based on differences in the relative toxicity of the components
measured in inhalation and oral bioassays, different RPFs may be developed to
address the human health risks following inhalation or oral exposures.
3. RPFs may be developed to assess risks for different durations of exposure.
The toxicity of a group of mixture components may change relative to each other
depending on the duration and frequency of the exposures. Different RPFs may
be developed to address the human health risks following different exposure
frequencies or exposure durations (e.g., different RPFs may be developed for
exposures that achieve steady-state tissue concentrations of mixture
components than for those exposures that do not result in steady-state tissue
concentrations of the mixture components over the duration of the experiment).
4. RPFs may be developed to assess risks within a restricted range of dose
levels of the mixture's components. The toxicities of different chemicals
relative to each other may change with dose. For example, at higher dose levels
where significant adverse responses are observed, an assumption of additivity
may not be appropriate (i.e., observed effects may be greater than or less than
those expected under an assumption of additivity). Thus, it is appropriate to
restrict the dose range of the components in two ways: limit the range to levels
for which additivity is an appropriate assumption and, ensure the range reflects
the exposure levels of interest to the risk assessment. Different RPFs may be
developed to assess risks to humans for these different ranges.
6
-------
These generalizations of the TEF methodology allow RPF development to be limited to
specific aspects of mixture toxicity and exposure, allowing the RPF approach to be
more broadly applied.
An identified research need for the RPF methodology is continued development
of appropriate statistical methods to support the assumption of a common toxic mode of
action. One way to examine this assumption is to evaluate the similarity of the dose
response curves across the mixture's components. Components with similar dose
response curves can be grouped together into a mode of action subclass for which an
RPF-based risk assessment can be developed.
Chen et al. (2001, 2003) present biostatistical approaches for grouping
chemicals suspected to have common modes of action, proposing two classification
algorithms to cluster chemicals into subclasses within which chemicals have similarly-
shaped dose-response functions. Chemicals within subclasses are combined using the
RPF method when a constant relative potency among chemicals exists. Additional
methods are shown to calculate cumulative risks inclusive of these subclasses (i.e.,
combining across subclasses for which a non-constant relative potency exists) using
either a joint dose-response approach or by integrating the concepts of dose addition
and response addition.
Users of the RPF approach should appreciate that this model of mixtures toxicity
is actually a fairly simplistic depiction of the risk posed by the mixture. Theoretically, the
number of mixture components that can be included in an RPF-based approach is
unlimited, as long as each component is truly a toxicologic clone of the index chemical.
Pragmatically, there are a number of limitations including the availability of relevant
-------
toxicologic data upon which to base the RPFs. The Chen et al. biostatistical methods
were developed for pesticide mixtures. Pesticide mixtures are unusual among
environmental mixtures because component toxicologic data are often available due to
the laws that govern U.S. pesticides. These approaches can likely be used on as many
as 30 or so individual components. The key limitations are having data describing the
dose-response function for each component and toxicologic evidence that each
component shares a common toxic mode-of-action. A statistical issue is caused by the
toxic potency weighting of the exposure levels. If a poorly studied (high uncertainty)
chemical has high potency, its equivalent dose is high with no discounting for the
uncertainty. As the number of components increases, there may be an increased
likelihood of such a dominant uncertainty. This emphasizes the need for careful
discussion of uncertainties: their sources and impact on the final risk assessment.
This report presents research results regarding the theoretical basis for RPF
based risk assessments and presents quantitative methods for applying RPFs. The two
basic assumptions of dose addition, common toxic modes of action and similarly-
shaped dose-response curves, are investigated and discussed. Research results
produced by Chen et al. are presented, showing the integration of this research with
applications of the RPF approach. This research was undertaken to continue exploring
and developing cumulative risk assessment strategies beyond current applications and
is intended to improve future applications of RPF based risk assessments.
8
-------
2. DOSE ADDITION CONCEPTS
U.S. EPA guidance documents on chemical mixtures risk assessment (U.S.
EPA, 1986, 2000) recommend no-interaction approaches underdose addition for the
risk assessment of mixtures of toxicologically similar chemicals. Assuming the
chemicals in a mixture are noninteractive and elicit a common response through similar
actions on a biological system, the chemicals are then assumed to act as if one is a
simple dilution or concentration of the index chemical, and, by extension, each other.
The joint action of the chemicals, then, can be described by "dose addition" (Finney,
1971).
The fundamental assumption of dose addition is that the components of a
mixture exhibit a common toxic mode of action, underlying the addition of scaled doses.
Research issues include the development of meaningful toxicological criteria for
identifying a common toxic mode of action and the application of these criteria to
evaluate and identify mixture components that share a common toxic mode of action.3
A theoretical consequence of this assumption is that the dose-response
functions of the components exhibit similar shapes. Theoretically, mixture components
sharing a common mode of action act as either concentrates or dilutions of each other.
The components interact with a common toxicological target, eliciting the same
response. Because the chemicals act as concentrates or dilutions of each other, the
number of organisms within a dose group responding to the same dose of different
3There are other mixtures approaches that are based on dose additivity. The hazard index (U.S.
EPA, 2000), for example, provides a quantitative method that indicates whether a mixture may pose risk
or not. The hazard index method may be used when detailed toxicity data are not available; for example, a
hazard index can be developed from exposure estimates and Reference Doses.
9
-------
chemicals should differ in a consistent manner across doses. The consistent
differences in the responses across dose groups will yield similarly shaped response
functions, sometimes referred to as "constant relative potency." For example, if
chemical 2 is one-half as toxic as chemical 1, then, at the same dose, chemical 2
should elicit a response in half as many test organisms as that dose of chemical 1.
This pattern should persist with increases of dose until a maximum response is
achieved (e.g., 100% response). The similar shapes should also persist as doses are
diminished until a response threshold is observed or until one molecule of chemical 2
elicits an observable response. Between the toxicity threshold and the response
maximum, similar shapes of the dose-response curves should hold.
In practice, toxicological assays of chemicals having a common mode of action
may not exhibit similarly-shaped dose-response functions. Differences in the observed
dose-response function shapes between chemicals that share a common mode of
action may result from toxicokinetic differences or toxicodynamic differences. Other
factors could include differences in age or gender of the animals tested in the bioassay,
differences in animal stress status either within or across studies, and differences in
whether or not the test animals were naive to the chemical prior to testing. Random
errors of response may also explain differences in shape. These random errors
describe, from a biostatistical perspective, the distance that an individual's response
may be from the population mean response at a given dose. These differences in the
observed dose-response functions may result in different maximal responses as well as
different thresholds of response within the exposed population.
10
-------
These differences in shape of the dose-response functions may preclude
application of a dose-additive model. If the dose-response functions exhibit different
shapes and the resulting risk estimate predicted by dose addition is quite different from
the expected joint mixture response, then scaling the toxicity of one chemical by that of
the other may be an inappropriate means of estimating a mixture's risk. The RPF
mixture risk model may be rejected under these circumstances, even if the chemicals
exhibit a common toxic mode of action.
On the other hand, these differences in shape of the dose-response functions
may not preclude application of a dose-additive model. If the components exhibit
similarly shaped response functions over the relevant range of doses, as judged by the
exposure assessment, then the use of dose addition may be valid. This relevant range
includes the range of exposures to the individual components and extends to the range
of the additive dose (i.e., the total mixture dose in units of the index chemical).
Dose-response modeling research for dose addition includes assessing what is
meant statistically by a "similar shape" (see Section 5), including approaches to quantify
the amount of uncertainty potentially introduced in the risk estimate when the slopes
are dissimilar. Methods and criteria are needed to "determine" when a group of
components share a common dose-response function. To conclude, both common
mode of toxic action and similarity shaped dose-response functions are prerequisites
for valid application of dose addition to a chemical mixture.
11
-------
3. RELATIVE POTENCY FACTORS
U.S. EPA (2000) developed the RPF approach to assess risks posed by
mixtures that are comprised of chemical components exhibiting a common mode of
action for a toxic effect. The RPF approach is based on the concept of dose addition.
Mixture components are grouped using scientific judgment into subclasses called "RPF
Sets" using data on characteristics such as membership in a chemical class (relating to
observed toxicity), and commonality of toxicologic effects, exposure routes, exposure
durations, or dose ranges. To implement the approach, the exposure level of each
component of an RPF Set is scaled by a measure of the component's toxicity relative to
a selected index chemical (a toxicologically well-studied component of the RPF Set).
This scaling factor, the RPF, is based on a comparison of the component's toxicity with
a similar measure of toxicity for the index chemical (e.g., a ratio of equally effective
doses of the component to the index chemical). The product of the measured
administered dose of each mixture component and its RPF is defined as an Index
Chemical Equivalent Dose (ICED). The ICEDs of all the mixture components are
summed to express the total mixture dose in terms of an equivalent dose of the index
chemical. The risk posed by the mixture is quantified by comparing a mixture's total
ICED to the dose-response assessment of the index chemical. [The mathematical
formulas for the RPF are detailed in Text Box 3-1.]
12
-------
Appropriate application of the RPF
method requires a judgment that the
mixture components share a common
mode of toxic action and evidence that
the components have similarly shaped
dose-response curves. Evidence that a
chemical class fulfills one of these
requirements does not necessarily imply
that the second requirement is fulfilled.
For the first assumption, the term,
Common Mode of Action, implies that
chemicals in a mixture exhibit a common
toxicologic outcome when tested and that
the principal toxicodynamic events
leading to this common outcome after the
chemicals reach the target site and the
sequence of these events is understood,
but many of the details are not known.
Because detailed toxicodynamic data are
not abundant for most chemical mixtures
and their components, analysts typically
Text Box 3-1
Mathematical Representations and RPF Formulas
d, = dose of chemical 1 present in a mixture (units
not specified)
d2 = dose of chemical 2 present in a mixture (units
not specified; must be consistent with those of d,)
pot, = potency estimate (e.g., a slope factor) for
chemical 1 (risk per unit of dose specified for d,)
pot2 = potency estimate (e.g., a slope factor) for
chemical 2 (risk per unit of dose specified for d2)
ICED = index chemical equivalent dose based on
relative potency estimates (units consistent with d,
and d2)
f,(*)=dose-response function of the index chemical
for the response(s) common to chemical 1 and
chemical 2 (units consistent with d, and d2)
h(d,,d2) = mixture risk from dose d, of chemical 1
and dose dj of chemical 2
[ED10], = dose of chemical 1 that results in a 10%
response, either as a fraction of exposed test animals
that respond, or as a fractional change in a measured
physiological value.
[ED10]2 = dose of chemical 2 that also results in the
same 10% response
Then, designating chemical 1 as the index chemical
in the RPF approach,
(or equivalently = potj / pot,)
ICED = d, + (RPF2* d2)
h(d1,d2)=f1(ICED) = mixture risk from chemicals 1
and 2 evaluated at the ICED of chemical 1
must judge whether or not the mixture components exhibiting a common toxicologic
outcome also share a common mode of action. At times, the term Common Mechanism
13
-------
of Action is used. This term implies a greater degree of understanding of
toxicodynamic events, such that the chemicals in a mixture exhibit a common
toxicologic outcome when tested and that the underlying molecular and cellular
toxicodynamic events leading to this outcome are the same for each chemical, after
they reach the target site. (Toxicodynamic events include the initial interaction of a
toxicant with its molecular or cellular target and subsequent responses to the toxic
insult.) These two terms represent a continuum of toxicodynamic understanding; they
are degrees of scientific resolution. For RPFs, there must be a judgment that chemicals
exhibiting a common mode of action either do or do not share a common mechanism of
action. If judged that they do, then subclasses are not needed. If judged that they do
not, then subclasses should be developed and a second set of assumptions should be
identified and used to combine (or not combine) the toxicities that the subclasses
exhibit.
The second prerequisite for applying an assumption of dose-addition is that the
chemicals have similarly shaped dose-response functions at least within the region of
exposure of interest for the risk assessment. An evaluation will often be needed of the
expected shapes of the dose-response functions in the low dose region including the
region that may lie below the lowest dose tested in the relevant toxicological bioassay.
In Section 5 of this report, we describe procedures that can be used to evaluate
similarity among the observable regions of dose-response functions. If there is an
evaluation of shape below the experimental response region, it may include an
assessment of the mechanism/mode of action.
14
-------
RPFs are based on comparisons with an index chemical, and the mixture risk is
estimated using the dose-response function of the index chemical. Criteria pertaining to
the inclusion of compounds in an RPF Set apply to the index chemical. The index
chemical should be a well-studied member of the RPF Set; studies on the index
chemical need to provide exposure data for routes of interest and health assessment
data for health endpoints of interest. To estimate relative potency, toxicity studies of
compounds in the RPF Set need to be comparable to studies conducted on the index
chemical.
3.1. JUDGMENTS OF COMMON TOXICOLOGIC ACTION
"Pesticides are determined to have a "common mechanism of toxicity" if they act
the same way in the body; that is, if scientifically reliable data demonstrate that upon
exposure to these chemicals, the same toxic effect occurs in or at the same organ or
tissue by essentially the same sequence of major biochemical events" (U.S. EPA,
2002b). The issue of a common mechanism of toxicity has been addressed by a
working group of experts convened by the International Life Sciences Institute Risk
Science Institute (Mileson et al., 1998).4 The working group presented three criteria to
describe a common mechanism of toxicity: (1) cause the same critical toxic effect; (2)
act on the same molecular target at the same target tissue; and (3) act by the same
biochemical mechanism of action or share a common toxic intermediate. The working
group agreed that all three points are useful to apply to chemicals that may act by a
common mechanism of toxicity, but did not state whether all three points must be met
Subsequent to the International Life Sciences Institute expert panel, U.S. EPA issued a guidance
document for identifying pesticides with a common mechanism of toxicity (U.S. EPA, 2002b) and a CRA
case study for the organophosphorus pesticides (U.S. EPA, 2001 b).
15
-------
before a firm common mechanism of toxicity determination can be reached. It is
recognized, however, that precise mechanistic information on animal or human effects
for pesticides and most environmental chemicals is scant. Common mechanism
determinations will therefore be difficult to establish with these three points because
chemicals often exhibit spectra of adverse effects rather than the same critical toxic
effect (criterion 1) (Mileson et al., 1998).
Knowledge of a chemical's mode of action implies a general understanding of
the key toxicodynamic events that occur at a tissue level, rather than a detailed
description of the cascade of events at the cellular or molecular level such as is
suggested by the term "mechanism of action." For chemical mixtures, the term,
"common mode of action", implies that chemicals exhibit a common toxicologic
outcome in the same tissue when tested. However, the toxicodynamic events that lead
to this common outcome after the chemicals reach the target site are not well
understood; they may be the same (or similar) or not (it is simply not known). A
common mode of action is sufficient justification to consider or employ a dose additive
model. The terms "mode of action" and "mechanism of action" represent degrees of
scientific understanding of toxicodynamic events underlying observed toxic responses
rather than separate categories.
The distinction between these two terms is discussed here using a hypothetical
cancer assessment to illustrate when dose additive models, such as RPFs, can be used
and when they should not be used. (RPFs are relatively simple mixture risk models
typically developed from empirical bases; as additional detailed toxicodynamic data are
generated for mixture components, these simple models are likely to be replaced by
16
-------
biologically-based mixture risk models.) Tumors occurring in a specific liver tissue in an
animal bioassay may arise through a number of different modes of action. Consider two
examples.
Example Chemical 1:
Repeated episodes of chemical-induced liver cell necrosis may result in random
DMA replication errors as the surviving cells undergo compensatory
reproduction. These random DMA replication errors may occur in genes critical to
control of cell replication (e.g., tumor suppressor genes and proto-oncogenes)
and become "fixed" in the genome through replication, ultimately giving rise to
liver tumors.
Example Chemical 2:
A mutagen may interact directly with liver cell DMA that codes for genes in the
cell replication cycle and cause a mutation that gets fixed in the DMA after a
round of replication. Some of these mutations reduce the cells' ability to properly
regulate their own replication and this lack of replicative control ultimately results
in tumor development after a series of additional mutations and changes occur in
the affected cells.
These two chemicals do not share a common mechanism of action because the first
induces carcinogenesis through necrosis and the second induces carcinogenesis
through mutation of the target tissue.
Now, assume that two chemicals that comprise an environmental mixture both
cause necrosis in the same hepatic tissue when tested individually in separate animal
bioassays. The ultimate result of the liver tissue necrosis that occurs when each
17
-------
chemical is tested in a bioassay is the formation of observable liver tumors in the same
tissues (as in Example Chemical 1 in the preceding paragraph, the tumors form when
random errors in DNA replication occur in genes that control the cell cycle get "fixed"
during compensatory liver cell replication). The same bioassay outcome (i.e., liver
tumor formation arising from a specific tissue when each individual chemical is tested)
may occur through a number of different possible necrotic processes that lead to dead
liver cells:
1) The chemicals may cause liver tissue cell necrosis by the same mechanism of
toxic action. The chemicals may be shown to cause the same sequence of
necrotic events in affected liver cells after the chemicals reach the target tissue.
This is clearly a case of chemicals exhibiting a common mechanism of action.
Lacking the level of mechanistic detail provided in this description, analysts could
still logically conclude that the chemicals may share a common mode of action
based on the occurrence of liver tumors arising in the same hepatic tissue.
2) The chemicals may cause tissue necrosis in the same liver cells by different
necrotic mechanisms (i.e., either different toxicodynamic events or different
sequences of toxicodynamic events that are observed to lead to cell
death...ultimately resulting in tumor formation through random errors in
compensatory replication in remaining living cells). In this case, one could
reasonably judge that the chemicals still exhibit a common mechanism of action.
Lacking the mechanistic detail, analysts could still logically judge that the
chemicals share a common mode of action because of the occurrence of liver
tumors arising in the same hepatic tissues.
18
-------
For the two cases above, RPFs for the chemicals could be developed (given
appropriate data).
3) If the chemicals cause tumors in different types of cells of the same organ, then,
based on evidence from animal bioassays, it is concluded that the chemicals do
not share a common mode of action. Because they are not causing necrosis in
the same types of cells, it could be concluded that the chemicals cause toxicity
through different modes of action.This outcome could occur because of
toxicokinetic differences between the chemicals, toxicodynamic differences
between the chemicals, or both. In any case, it is not appropriate to use RPFs
for the assessment of risk posed by this mixture, based on the available
toxicodynamic information.5
5ln practice, U.S. EPA (2000) suggests use of the Hazard Index (HI) method as an indicator of
risk when mixture components cause toxicity in the same target organ. In this case dose addition is
loosely defined to accomodate the lack of accessible mechanistic data.
19
-------
4. CHOICE OF DOSE METRIC IN CHARACTERIZING MIXTURE
TOXICITY BY DOSE ADDITION
Two separate issues are discussed in this section. F:irst, the potential
significance of using kinetic data in the development of relative potency factors is
described. If kinetic differences exist between test species and humans, relative
potency factors will change when modeling risks on the basis of a administered dose
versus an internal dose. Second, a discussion is presented regarding choice of dose
metric in an RPF-based approach. In modeling human health risks posed by exposure
to a mixture by the RPF method, the type of dose measures employed do not appear to
alter the outcome of the risk estimation procedure. Two dose measures commonly used
for delivered dose are units of mass (mg/kg) or moles (mmol/kg). The key is to be
consistent in development of an RPF application, using either mass measures or molar
measures.
4.1. RPF DOSE ISSUES
Measures of either an administered dose or internal dose may provide the basis
for estimation of relative potency for a chemical group. Administered or applied doses
are the amount of a substance applied to an external body barrier and available for
absorption. Administered doses include those doses applied to external body
membranes such as the gastrointestinal tract, the lungs and the skin. Internal doses
measure or estimate the quantity of a contaminant that is present in an internal tissue
(U.S. EPA, 1992). The entire administered dose may not cross the barrier. Tissue
concentrations of interest could include those occurring at either toxicologic target
tissues and or tissues not targeted by the chemical.
20
-------
4.1.1. Administered Dose. Most applications of RPFs in the literature are based on
measures of administered doses. For example, the EPA has developed four sets of
RPFs that estimate the toxicity of a mixture of related compounds based upon
administered dose measures for individual compounds: the dioxins, the polychlorinated
biphenyls, the polycyclic aromatic hydrocarbons, and the organophosphorus pesticides
(OP) (U.S. EPA, 2000, 2001 b). In each case, the risk estimates based on RPFs were
described as interim, pending the emergence of additional chemical mixture-specific
toxicokinetic and toxicodynamic data. The type of dose upon which the RPFs are based
will not alter the interim nature of the risk estimate. Ultimately, biologically-based
mixtures risk models will likely be developed for each case; these models will replace
the simpler RPF models and be based upon the emergence of additional chemical
mixture-specific toxicokinetic and toxicodynamic data.
4.1.2. Internal Dose. Measures or estimates of internal doses may provide an
improved basis both for estimating risks posed by chemical mixtures that occur through
multiple exposure routes and for estimating human health risks for some mixtures by
the same exposure route. To date, RPFs based on internal doses have not been
developed because the ability to predict internal organ or tissue doses through
physiologically-based pharmacokinetic (PBPK) models is relatively new or because,
given the simplistic assumptions of the RPF approach, refined estimates of dose would
provide little resolution to overall uncertainty.
4.1.3. Mixtures Exposures Through Multiple Exposure Routes. In 2002, U.S. EPA
completed a report showing that a multiple exposure route mixtures risk assessment
can be conducted based on internal dose estimates developed in both test animals and
21
-------
humans for toxicants that do not cause portal of entry effects (U.S. EPA, 2002c). The
document combines exposure modeling results, PBPK modeling results, and the RPF
mixtures risk assessment approach. Human internal doses (e.g., blood, tissue, and
organ concentrations) were estimated using PBPK models, accounting for external
exposures from multiple routes (as dictated by the exposure scenario) and human PK
processes. Hypothetical RPFs were developed for a subset of chemicals based on test
animal data. Although the application of a full PBPK model was recognized as the
preferred approach to estimating rodent internal doses (i.e., blood concentrations), for
the example data used in the report, administered doses were assumed to be 100%
bioavailable to the rat. The rodent response data were assumed to be constant
between internal and external exposures and were used to evaluate the human dose-
response relationship. The use of internal dose measures (i.e., blood concentrations in
both humans and rodents) both for developing the RPFs based on rodent data and as
an indicator of human multi-route exposure provides a necessary and consistent basis
for extrapolating across species. Clearly, these approaches should not be used and are
inappropriate for toxicants that elicit responses at points of contact with the body (e.g.,
skin, intestinal tract, and nasopharyngeal, bronchial and lung epithelium).
4.1.4. Mixtures Exposures Through a Single Exposure Route in Different Species.
For some mixtures, basing RPFs on internal doses may reduce some uncertainty in
applying RPFs for individual exposure routes. From a single route of exposure to a
given chemical mixture, the animal kinetics and human kinetics that give rise to
respective internal doses of the mixture components may result either in the same
internal doses or different internal doses, when the same amount of chemical is applied
22
-------
externally. If the kinetics result in the
same internal doses or internal doses
that differ consistently across the
mixture (i.e., comparisons of the ratios
of external to internal doses for each
component between test animal and
human are constant), then basing
RPFs on internal dose estimates is not
necessary, because the relative
potencies will not change. When
kinetic differences between humans
and test animals lead to non-constant
differences in internal dose
concentrations across a chemical class,
then basing RPFs on internal doses
provides a more scientifically sound
basis for applying RPFs (see Text
Boxes 4-1 and 4-2).
Consider the same 2 component
mixture example presented in Text Box
3-1 where chemical 1 again serves as
the index chemical. Rodent data exist
Text Box 4-1
Mathematical Representations and Formulas for RPF
Based on Internal Doses to Rats (test animal)
Let:
d, = exposure to chemical 1 as a result of its presence
in a mixture (units not specified)
d2 = exposure to chemical 2 as a result of its presence
in a mixture (units not specified; consistent with d,)
I, = internal dose of chemical 1 present in a mixture
(units not specified)
I2 = internal dose of chemical 2 present in a mixture
(units not specified; consistent with I,)
ICED, = index chemical equivalent dose based on
relative potency estimates (units consistent for I,, I2)
f,(*)=dose-response function of the index chemical
for response(s) common to chemicals 1 and 2 (units
consistent with I, and I2; they are based on internal
measures of dose but use the same response
measures as developed in Text Box 3-1)
h(I,,I2) = mixture hazard or risk from joint exposure
of dose d, to chemical 1 and dose d2 to chemical 2;
however, these doses are based on internal measures
I, and I2 rather than administered doses d, and d2.
[ED)0]j, = internal dose of chemical 1 that results in a
10% response, either as a fraction of exposed test
animals that respond, or as a fractional change in a
measured physiological value.
[ED10]I2 = internal dose of chemical 2 that also
results in the same 10% response
Then, designating chemical 1 as the index chemical
in the internal dose based RPF approach,
RPF2I = [ED10]n / [ED10]I2
ICED, = I, + (RPF2* I2)
h(I1)I2)=f,(ICED,)
23
-------
such that a RPF2 can be developed based
on the administered doses (RPF2E) or the
internal doses (RPF2I) of chemical 1 and
chemical 2. Response data are available
for the test animals only, and the human
mode of action is considered to be the
same as that in the test animal. The ratio,
RPF2E/RPF2I, in the rodent will either
approximately equal the ratio of human
administered dose to human internal dose
or not. If these ratios are equal, then, when
estimating risk using the RPF approach for
a single exposure route, it does not matter
whether external or internal doses are
used as the basis of the RPF. If these
ratios are not equal, then, when estimating
risk using the RPF approach for a single
exposure route, it matters whether external
or internal doses are used as the basis of
the RPF. The RPFs should be based on
internal doses because the
Text Box 4-2
Potential Use Of Internal Dose Based RPFs
Assume that the toxicodynamics are the same for
humans and rats. Let:
K1R= I,/d, in Rat for chemical 1
K2R= I2/d2,in Rat for chemical 2
K1H= I,/d, in Human for chemical 1
K2H= Vdzjin Human for chemical 2
From Text Box 3-1, the mixture risk in rats is
h(d,,d2)=f1(ICED)
This is based upon ICED = d, + (RPF2* d2), where
RPF2 = [ED10]1/[ED10]2.
An implicit assumption in the Chemical Mixture
Guidance is that RPF2 is the same in rodents and
humans. Thus, the human ICED for d2 is calculated
as the product of the human administered dose and
RPF2.
The risk posed to humans from this mixture is
estimated to be h(d1,d2)=f,(ICED),
where ICED = d, + (RPF2* d2) and_RPF2 = [ED10], /
[ED,0]2. The ratio of [ED10]S is calculated from the
rodent administered dose data.
Proposal:If K1R == K1H and K2R * K2H=» RPF2 is not
a valid estimate of the relative potency of chemical
2 for the human.
Proof: Let chemical 2 be converted to chemical 1
on a 2 to 1 molar basis in the rat (i.e., 2 moles of
chemical 2 is converted thru some kinetic process
into 1 mole of chemical 1 in the rat). For an RPF
model, chemical 2 would be one-half as toxic
relative to chemical 1 based on the administered
doses =» RPF2 = 0.5, when chemical 1 is the index
chemical and RPF( = 1.
Let the conversion of chemical 2 to chemical 1
cause toxicity of chemical 2 in the human also and
assume that the toxicodynamics of chemical 1 are
identical for humans and rats.
Because K2R * K2H, the conversion of chemical 2
into chemical 1 will not exhibit a 2 to 1 ratio, the
RPF2 estimated from rodent external data * the
human RPF2. The kinetic differences between
humans and rodents lead to different internal tissue
doses which influence the toxicity of chemical 2
relative to chemical 1.
Further Implication
If K1R/K1H = K2R/K2H => It is valid to apply RPF2
estimated from rat data to human administered dose
data due to kinetic differences. The kinetic
differences between species do not change the
relative potency of Chemical 2 to Chemical 1.
24
-------
pharmacokinetic differences result in inaccuracies when the RPFs are developed in test
animals and applied to humans.
4.2. CHOICE OF DOSE MEASURES
For modeling of a mixture's toxicity or joint action under the assumptions of
relative potency factors, representation of dose as either a molecular (molar)
representation of dose or a representation by chemical mass does not matter in the
conduct of the risk assessment. It does not matter because the molecular weights of
the compounds relative to each other are constant.
Consider two compounds, C1 and C2, that exhibit a common mechanism of toxic
action. Let the molecular weight of C2 be twice that of C1. Administration of 1 milligram
of C1 elicits the same response in test animals as administration of 2 milligrams of C2.
(Molecules of C1 and C2 are equally potent.) If the experimental evidence for RPFs is
based on single chemical experiments where dose is measured in milligrams, then the
relative potency of C2 to C1 will be 0.5. If the experimental evidence for RPFs is based
on single chemical experiments where dose is measured in moles, then the relative
potency of C2 to C1 will be 1. Because a molecule of C2 has twice the mass of C1, the
conversion of mass doses to molar doses in a risk assessment will result in an RPF for
C2 of 0.5 (i.e., = Y2). Equivalent human exposures (resulting in the same predicted risk)
result from exposures to 1 mole of each chemical or some mass of C1 and Yz the same
mass of C2. Thus, the chemical potency comparisons when applied to estimate human
risk will be the same regardless of whether the measures are based on moles or
masses.
25
-------
5. BIOSTATISTICAL DOSE-RESPONSE MODELING FOR CUMULATIVE RISK
Biostatistical modeling results can be integrated with exposures to calculate
cumulative risk estimates depending on expected toxicological action of the mixture
components. Three methods discussed in this section:
1) Dose Addition: When the chemicals of interest act in accordance with a common
mode of action, a dose addition approach can be employed. Dose Addition is a
chemical mixtures risk assessment method in which doses are summed (after
scaling for relative potency) across chemicals that have a similar mode of action;
risk is then estimated using the combined total dose.
2) Integration of Dose Addition and Response Addition: When mixture components
can be classified into subgroups within which a common mode of action exists,
then, by definition, independence of toxic action is expected between subgroups.
Response addition is a chemical mixtures risk assessment method applied to
chemicals whose modes of action are independent of each other (i.e., the
presence of one chemical in the body does not influence the effects caused by
another chemical); risk of a whole body effect (e.g., non-specific cancer), is then
estimated by summing the risks (e.g., skin cancer, liver cancer) of the individual
chemicals. Integrating dose addition and response addition in this case means to
estimate the subgroup risks and then sum them to estimate cumulative risks
(U.S. EPA, 2002c).
26
-------
3) Joint Dose-Response Model: Finally, a joint dose-response model using scaled
doses is applied when commonality of toxic mode of action is uncertain. This
method produces a range of cumulative risk estimates.
EPA-sponsored research on the use of dose-addition in cumulative risk assessment,
focusing on the issue of similarly shaped component dose-response curves, has
resulted in the publication of two papers by Chen et al. (2001, 2003). The information
in this chapter relies heavily on the research presented in the Chen et al. papers, which
are reproduced in their entirety in Appendices A and B. The first paper (Chen et al.,
2001) demonstrates methods for dichotomous data using the log probit and logistic
dose-response functions. The second paper (Chen et al., 2003) further extends the
statistical methods to continuous endpoints, using cholinesterase inhibition as an
example. To demonstrate use of these models in cumulative risk assessment, without
loss of generality, the discussions in this section are limited to dichotomous data using
the log probit dose-response function.
5.1. DOSE-RESPONSE MODEL FOR COMBINED EXPOSURES
To begin discussion of dose-addition as a tool for risk assessment, let F^ and F2
be the dose-response functions for chemical 1 and chemical 2, respectively. Under
dose addition, the response, R, to the combination of doses d, and d2 for chemicals 1
and 2, respectively, is
R(d1td2) = Ff(cft + p d2}= F^djp +c/2) (5-1)
where p is the relative potency of chemical 2 to chemical 1. When one chemical acts as
if it is a simple dilution or concentration of the other, then the relative potency between
the two chemicals is constant. In other words, for all response levels, the effective dose
27
-------
of one chemical is a constant multiple of the effective dose of the other chemical.
Hewlett and Plackett (1959) viewed the concept of dose addition (similar action) in a
slightly broader sense than requiring a constant relative potency between two
chemicals. Mathematically, their characterization can be interpreted as allowing the
relative potency factor to be different for different response levels. Thus, the biological
bases and mathematical models required to characterize an RPF-based assessment
are different depending on whether or not constant relative potency is assumed.
Dose addition allows for summing the individual doses into an equivalent dose in
terms of an index chemical and using the index chemical's dose-response function to
estimate the mixture response from the equivalent total mixture dose. A dose-response
function for binary response data, denoted P/of)= F, relates the probability of response
to the dose, d, of chemical i, where F is a probability distribution function. The general
model can be expressed in the logarithm of dose as
(5-2)
A commonly used dose-response model, used throughout this disscussion to illustrate
the methods, is the probit function, which is,
P(d) = c + (1 - c)r09-=exp(- 1/2 f 2)dt (5-3)
J-» V27T V '
where the parameter c represents background effect and P(d) is defined to be c when
d = 0. The parameters a and P are the intercept and slope parameters of the
dose-response function under its inverse, F~1(P(d)). For the rest of this discussion, the
log probit function for binary data will be used to demonstrate dose addition methods;
28
-------
however, other functions and continuous endpoints can also be utilized in these
approaches (see Appendices A and B).
For an example with two chemicals, if the relative potency of chemical 2 to
chemical 1 is constant, then the dose-response for one chemical can be expressed in
terms of the equivalent dose of the other chemical by using a relative potency factor. In
this case, p = (di/ cfe) (i.e., Pi(cfi) = P2(di/p) = P^(pd2) = P2(cfe)), where the dose 0(1 of
chemical 1 and 0(2 of chemical 2 are equal effective doses (i.e., they cause the same
magnitude of response). Now, given that Pi(ch) = P^(d^/p}, then
a, + # log^ = a2 + P2 log(
-------
Hence, because Equations 5-6 and 5-7 are both true, P1 = (32 , and it can be shown that
two chemicals have a constant relative potency if and only if the slopes of the (log)
dose-response functions are equal. (See Appendix A for a more complete proof.)
5.1.1. Constant Relative Potency. The term, constant relative potency, implies that
for all response levels, the effective dose of one chemical is a constant multiple of the
effective dose of the other chemical. Constant relative potency is a desired condition to
conduct an RPF based risk assessment, at least for the dose ranges pertinent to the
exposure of interest (see Section 2).
5.1.1.1. Dose Addition If two chemicals have a constant relative potency
and if the joint response is dose-additive, then the dose-response function from
exposure to di of chemical 1 and cfe of chemical 2, using chemical 1 as the index
chemical is,
(5-8)
For a group of m chemicals in which the relative potency between any two chemicals is
constant, the joint response of the m chemicals can be derived in the same way as
Equation 5-8, using a relative potency factor pt for each component as it is paired with
the index chemical(s).
F(dl,...dm)=F
as + 0 log ds
(5-9)
where, pt = exp[ (a, - as) / P ] for t * s. In this case, the estimated risk at any set of
doses does not depend on the choice of index chemical (i.e., when constant relative
30
-------
potency is operational, the risk estimate will be the same regardless of the choice of
index chemical).
5.1.2. Nonconstant Relative Potency. Constant relative potency is a fairly restrictive
assumption that may not hold true for many mixtures. Thus, if the relative potency
between chemical 1 and chemical 2 is different for different response levels, then the
slopes of the dose-response functions for the two chemicals will be different and the
modes of action for the two chemicals may also differ. In this case, at the equal
effective doses of ofi for chemical 1 and cfefor chemical 2 such that Pi(ofi) = P2(of2), it
can be shown that the equivalent dose of chemical 2 in terms of chemical 1 is,
(5-10)
and the equivalent dose of chemical 1 in terms of chemical 2 is,
n ,, (5-11)
P2
Under these conditions, the joint response can still be estimated by an index chemical
approach, using doses adjusted by a ratio of the slopes. The joint dose-response from
an exposure to 0(1 of chemical 1 and cfe of chemical 2 in terms of chemical 1 as the
index chemical is,
(5-12)
31
-------
where w = P2 / p^ and p12 = exp[(a2 - a1 ) / PJ. On the other hand, the joint response in
terms of chemical 2 as the index chemical is,
F(dl,d2)= P2(d2 + d2(dl))=F(a2 + p2 Iog(d2 + p2ld2/w)) (5-13)
where w = P2 / PL and p21 = exp^c^ - a2 ) / P2]. Note that the joint response predicted
from chemical 1 , Pi(ofi +c/i(cfe)), will differ from that predicted from chemical 2, P2(d2 +
c/2(c/i)). For m chemicals, the combined response in terms of chemical s can be derived
as,
( } ( ( m }}
F(dl,...,dm) = P\ ds + £ pstd»« = F\as + & log I pad?- (5-14)
The pst = exp[(a, - as) / PJ is a potency ratio of chemical t to the index chemical s, and
wst = Pt / ps, is the slope ratio, where t = 1 m, and t *s.
5.1.3. Constant and Nonconstant Relative Potencies in the Same Mixture. In
many cases, a mixture may be comprised of component subsets, where within each
subset a constant relative potency may exist (dose addition for common modes of
action), but where nonconstant relative potencies occur between subsets (response
addition for independence of action between subsets). In this case, a set of m
chemicals can be clustered into several subclasses of constant relative potency. For
example, the set of six chemicals,
{{C1,C2,C3},{C4,C5},{C6}},
represents a set where the chemicals C1, C2, and C3 in the first subclass have
constant relative potency with respect to each other, as do the chemicals C4 and C5 in
32
-------
the second subclass; the relative potency factor between the last chemical C6 and the
other chemicals is different at different response levels. Two approaches are proposed
here for evaluating a set of chemicals with varying relative potencies.
5.1.3.1. Integrating Dose Addition and Response Addition The first
approach is appropriate to apply when data on the toxic modes of action are available
so there is some certainty that the subclasses represent groups of chemicals with a
common mode of action distinctly different from the other subclasses. The toxicity
associated with each subclass is produced independently from the other subclasses.
The statistical method is then to estimate the dose-response function for the chemicals
within each subclass under dose addition, using a different index chemical from within
each subclass, and calculate the joint cumulative risk under response addition as the
sum of the subclass risk estimates. Hence, the joint dose-response function is
expressed as,
F(dl,...dm) = P\d, + pnd2 + ..]+...+ Pcl[dq + pM+Irf,+1 + ...]+...Pm[
-------
selecting an index chemical from a separate subclass. Based on Equation 5-14
developed above, the joint response for m chemicals can be expressed in terms of a
single index chemical 1 for the entire mixture (i.e., including all subclasses) as,
F(dlt...dm) = P\(d, + p2J2 + ...)+-+(/₯/r/ + PMd£ + ..)+...+ pmd] (5-16)
The chemicals in the same subclass will have the same slope ratio w t = (Pt / p.,). Also,
the chemicals within the same subclass will have the same cumulative risk estimate,
regardless of the choice of index chemical. (The complete derivation for Equation 5-16
can be found in Appendix A.) However, the estimated combined response will depend
on the subclass in which the index chemical is selected, a different subclass will predict
a different risk estimate. Thus a range of risk estimates can be produced, reflecting the
uncertainty in the mode of action determinations.
5.2. STATISTICAL ALGORITHMS FOR SUBCLASS GROUPINGS WITHIN A
MIXTURE
Two classification algorithms are proposed to cluster mixture components into
subclasses such that the chemicals in the same subclass have a common slope. The
joint response is estimated by fitting the dose-response model of the mixture under
dose addition. Chemicals within subclasses are first combined using simple dose
addition (constant relative potency), and then subclasses of chemicals are combined
using a general form of dose addition (non-constant relative potency). Thus, the
proposed method allows one to estimate the joint toxic response for chemicals having
different dose-response slopes. (A complete example of the classification algorithms
and subsequent response calculations for six hypothetical pesticides in a mixture are
shown in Section 4 of Appendix B.)
34
-------
Since two chemicals have a constant relative potency if and only if the slopes of
the (log) dose-response functions are equal, the clustering algorithm is based on testing
for the equality of the slopes of dose-response functions. Either the likelihood ratio test
or the analysis of variance F test can be used for the comparison. (See Appendix B for
more information on these tests.) The clustering algorithms begin with a fitting of each
s* s*. *>
individual dose-response function for the m chemicals. Let, ft 15/? 2,...fi m denote the
maximum likelihood estimates of the dose-response functions. The estimates of the m
slopes can be arranged in an ascending order:
P c< P C2<.< P cm.
That is, the chemical ci has the smallest slope estimate, the chemical 02 has the second
smallest slope estimate, and so on. The classification algorithms are applied to this
ordered set. These iterative (stepwise) processes systematically test the adjacent
chemicals in an ordered set for equal slopes and end up with subclasses of chemicals
that can be characterized as having the same slope. The top-down approach begins
with the assumption that all of the slopes are different and uses an iterative process to
group chemicals with common slopes into subclasses; the bottom-up approach begins
with the assumption that all of the slopes are equal and uses an iterative process to
divide the chemicals into subclasses that have different slopes.
In classical statistics, when the null hypothesis is rejected, this result does not
imply that the null is then true and can be accepted. For example, in the bottom-up
approach, the procedure keeps dividing the chemicals into RPF subclasses until the
null hypothesis is not rejected. We complete the procedure when we can accept the
35
-------
null hypothesis that dose-response slopes among chemicals are the same. In the top-
down approach, the procedure keeps grouping the chemicals until the null model is
rejected. We complete the procedure when we can reject the null hypothesis that dose-
response slopes among chemicals are the same. Thus, the top-down approach may
be a preferred method because there, the procedure is more consistent with traditional
statistics. For this application, however, useful information is gained using either
approach regarding how different two or more curves might be, offering a quantitative
method to assess similarity in dose-response beyond the more typical visual check
using graphics. Because we want to "travel up" the dose-response curve of the index
chemical to predict mixture risk, we need some comfort level that the dose-response
curves of the subclass chemicals share a common shape.
5.2.1. Top-Down Approach. In the top-down classification, the procedure begins
using an initial model in which the slopes of the m chemicals are assumed to all be
different. Figure 5-1 illustrates the iterative procedure followed using the top-down
approach. (See also Table 3 in Appendix B for example calculations.) The initial
model, MO, of chemicals is denoted by the partition set MO = {{C1}, {C2}, (C3), {C4},
{C5}, {C6}}. Consider the null and alternative hypotheses, comparing two adjacent
slopes,
Hoq: Pc,q = Pc,q+i versus Haq: pc,q * (3c,q+1 (5-17)
for q = 1, 2 ,..., m-1. Under the null hypothesis, a joint dose-response function can be
fit for the mixture of chemicals Cq and Cq+1, using a constant relative potency model,
based on Equation (5-8) of,
36
-------
IT)
UJ
a:
o
CO
2
0.
Q.
I
Q
-e
CD
JI
O
_o
LL
37
-------
(5-18)
The null model Hot? can be represented by the partition set,
B1 = {{C1},... {Cq = Cq+1},... {Cm}}. (5-19)
The hypothesis of comparing two adjacent slopes, equivalently, can be expressed in
terms of testing the two models, the null model (B1) vs. the initial model (MO):
Hoq: B1 = {{C1},... {Cq = Cq+1},... {Cm}} versus Haq: MO = {{C1}, {C2},..., {Cm}}.
Let poq be the p-value associated with the test H^ versus Haq, for q = 1, 2 ,..., m-1; and
let pcr= Max { pc1 pc2 pcm} (i.e., pcr is the largest p value associated with testing for a
common slope between two adjacent chemicals in the set). When the largest value, pcr,
is less than a pre-specified significance level, say, ak then the procedure stops, we
reject the null model that the chemicals can be further grouped, and the model MO that
the slopes of the m chemicals are different is concluded. On the other hand, if pcr is
greater than the significance level, then we cannot reject the null model, so the
chemicals Grand Cru are classified into one subclass. That is, a new "initial" model, M1
= {{C1},... {Cq = Cq+1},... {Cm}}, is formed and the procedure continues to the next step.
Under the model M1, the two chemicals Grand 0-1 can be treated as one
chemical. Let,/?cr denote the maximum likelihood estimate of the common slope for the
two chemicals Cr and cr*-i. The m-1 slope estimates are now arranged in ascending
order as:
38
-------
That is, the two individual slope estimates, /3cr and /?cr+I are replaced by their common
slope estimate, & . The same algorithm is applied by performing m-2 comparisons of
two adjacent estimates. The hypothesis can be expressed as
Ho(?:B2 versus Hag:M1
where
B2 = {.... {Cq ,Cq+1},..., {Cr,Cr+1}, ...} if q * (r - 1)or q * (r + 1)
= {..., {Cr ,Cr+1, Cr+2}, ...} ifq = (r+1)
Again, if the largest p-value is less than the significance level, then the procedure stops,
the null hypothesis that the slopes are the same is rejected, and the model M1 is
concluded. If the largest p-value is greater than the significance level, then the null
model is adopted as a new "initial" model and the procedure continues to the next step.
The procedure keeps grouping the chemicals until the null model is rejected. Note that
in the last step, if the null hypothesis is not rejected, then the model {C1, C2,...,Cm},
that all slopes are equal, is used for the risk assessment.
5.2.2. Bottom-Up Approach. In the bottom-up classification, the procedure starts with
the initial model, MO, where the slopes of the m chemicals are equal, denoted as the
partition set, MO = {C1, C2 Cm}. (The same notation is used to illustrate the
parallelism between the two classification schemes.) Figure 5-2 illustrates the iterative
procedure followed using the bottom-up approach. (See also Table 4 in Appendix B for
example calculations.) We now form a new model B1 = {{C1,... Cq}, {Cq+1,..., Cm}}
constructed by the split of MO into two subclasses. Consider the hypothesis of a
39
-------
LO
HI
=>
O
o
CD
2
0.
Q.
Q.
Z)
E
o
CD
-e
CD
O
40
-------
constant relative potency model MO against the alternative model B1 of two subclasses
of constant relative potency factors:
Hog:MO versus HagiBL
To test every possible combination of two subclasses while holding the order of the
slopes constant, there are (m-1) tests. Let pc, be the p-value associated with the test
Hog versus Hag, for q = 1,..., m-1, and let pcr= Min { pc1 p^ pcm} (i.e., pcr is the smallest
p value associated with testing for a common slope between two adjacent subclasses
of chemicals). If pcr is greater than a pre-specified significance level, say, ab, then the
procedure stops, and the initial model MO where all the slopes are the same is
accepted. On the other hand, if pcr is less than the significance level, then the
corresponding alternative model dividing the chemicals into two RPF groups, M1 =
{{C1,... Cq}, {Cq+1,..., Cm}} is accepted, and the procedure continues to the next step.
The algorithm repeats until a null model is accepted. Note that in the last step, if the null
hypothesis is rejected, then the model that all slopes are different is concluded, {{C1},
{C2}, {C3}, {C4}, {C5}, {C6}}.
The two clustering schemes described above are tree structure classifications.
The top-down algorithm forms the tree from the top. It assumes that the slopes of the
chemicals are different. In each step, a chemical (or subclass of chemicals) is
combined with another chemicals (or subclass of chemicals) to form a new subclass.
Therefore, the number of subclasses at each step is one less than the previous step.
On the other hand, the bottom-up algorithm forms a tree in a division fashion. It
assumes that the slopes of the chemicals are equal. A new subclass is formed in each
step. These two algorithms may result in different tree structures. In both procedures,
41
-------
a goodness-of-fit test (a global test) can be performed on the terminal tree against the
two trivial trees {{C1}, {C2}, {C3}, {C4}, {C5}, {C6}} and {{C1, C2, C3, C4, C5, C6}}.
5.3. CUMULATIVE RISK ASSESSMENT
The fitted dose-response model for the mixture from multiple chemical
exposures can be used for quantitative risk estimation in terms of the equivalent total
mixture dose of the index chemical. For a group of m chemicals in which the relative
potency factor between any two chemicals is constant, the estimated cumulative risk
from exposure to the specific doses d10,...,dm0, for chemicals 1, m, respectively, is
derived as,
( ( m }}
F(dwt...9dm0) = F\ as -I- ft log £ pstdt0 (5-20)
whereds,{l,pst are the maximum likelihood estimates of the model parameters, and
D = (psidlQ + ...,psmdm0J is the equivalent total mixture in terms of the index chemical
s, and pss = 1 . The cumulative risk can be expressed as a response of the mixture
dose in terms of the dose-response function of the index chemical,
P(D) = F(as + ft logrf) (5-21)
Using this equation, either the effective dose (EDpJ for a given response level p% or an
acceptable dose level D* corresponding to a given risk level rcan be computed (i.e.,
P(EDp) = p% or P(D*) = r). In general, when the relative potency factor is not constant,
42
-------
the estimated cumulative risk will depend on the index chemical. In this case, the
average risk or the maximum risk over all possible index chemicals can be calculated.
5.3.1. Mixtures Reference Dose. The equations developed using RPFs may be
useful in calculating a mixtures Reference Dose (RfD). The RfD is a "safe" level for
environmental pollutants, which represents a human exposure level below which
deleterious non-cancer effects are not expected to occur (U.S. EPA, 2003b). The RfD
has traditionally been derived by dividing an experimental dose level, a No-Observed-
Adverse-Effect Level (NOAEL) or a Lowest-Observed-Adverse-Effect Level (LOAEL)
from an animal toxicity study by several uncertainty factors (UFs), and a modifying
factor (MF):
NOAEL or LOAEL
RfD = (5-22)
J UFsXMF V '
An alternative method is to replace the NOAEL or LOAEL by a modeled benchmark
dose (e.g., the lower 95% confidence limit on an ED10, that is, an effective dose that
produces a 10% response). These UFs are used to specifically account for uncertainty
in the RfD estimate due to extrapolations across species (UFA), within species (UFH),
across durations of exposure (UFS), between experimental dose levels (UFL) and from
weak to strong databases (MF). In the absence of statistical treatment, the default
value of these UFs has typically been set equal to 10. For a single chemical, a
benchmark dose (e.g., ED10) often serves as the point-of departure for low-dose
extrapolation in order to minimize model dependency at low dose levels.
43
-------
Using the mixture dose response models in this section, a mixtures reference
dose (RfDJ can be developed. For a mixture of components with the same mode of
action, Equation 5-21 can be used to calculate the point-of-departure for the mixture.
The RfDm in terms of an index chemical is defined as RfDm = £Dp/UFm; where EDp is
the mixture dose corresponding to a risk level of p% and UFm is the uncertainty factor
for the mixture. The UFm would need to consider all of the same UFs shown above for
the single chemicals RfD development. For given exposure doses, risks above the
RfDm can be calculated using an appropriate mixture dose response model (Wilkinson
et al., 2000). (A complete example of the this procedure is shown in Appendix A.)
44
-------
6. CONCLUSIONS
An important question in mixtures risk assessment research is how to assess a
mixture containing some chemicals that share a common toxic mode of action and
other chemicals that do not. Current additivity methods have evolved to handle either
the former (dose addition) or the latter (response addition). Alternatively, the risk
assessor may choose to do the assessment based on whole mixture data. The
biostatistical methods developed in this report provide alternative methods to evaluate a
mixture under three scenarios. The simple case occurs when there is certainty that a
common toxic mode of action is operating, so a dose addition approach can be applied.
The second case occurs when the mixtures can be divided into independent mode of
action subclasses; dose addition and response addition can be integrated to make the
assessment. The third case occurs when mode of action is uncertain, so a joint
dose-response modeling procedure is used to create a range of risk estimates. Thus,
these approaches enrich the available library of mixture risk assessment methods
beyond what is currently published by the U.S. EPA (1986, 2000). Further, these
approaches are available if needed for the evaluation of additional pesticide mixtures
under FQPA. Finally, the results presented here are generalizable to assessments of
other environmental mixtures; the risk assessments that support environmental
regulations of important environmental mixtures such as dioxins, polychlorinated
biphenyls, and OPs are based on concepts of additivity (U.S. EPA, 1989b, 2000,
2001 b).
The research results in this report can be applied to reduce uncertainties in
RPF-based risk assessments of chemical mixtures. These results also show how
45
-------
mixtures risk assessments can be conducted using additivity concepts. Various sources
of uncertainty exist in most mixtures risk assessments, including uncertainties
addressed in this report regarding several factors:
Common mode of action across mixture components (Sections 2, 3)
Similarly shaped dose-response curves across mixture components (Sections
2,5)
Value of internal vs. external dose estimates for developing RPFs (Section 4)
Choice of dose metric (moles vs. mass) to use in a cumulative risk assessment
(Section 4)
Cross-species extrapolation of relative potency factors (Section 4)
Estimating risks for a mixture with two or more common mode of action
subclasses (Section 5).
Biostatistical modeling in this report presents ways to combine dose-response
information, partitioning the mixtures into common mode of action subclasses. These
models can then be used to estimate risks for specific exposure scenarios or used to
develop toxicity values, such as a reference dose for the mixture. Three RPF-based
methods are discussed, reflecting what is known or uncertain about the mixture
toxicology. These approaches can be applied using internal or external doses.
Development of approaches based on internal doses may reduce some toxicokinetic
uncertainties associated with RPFs based on administered doses. In the Chen et al.
papers (2001, 2003) in Appendices A and B, external doses were used to develop
statistical methods for grouping components into common mode of action subclasses.
The next step in this process is to use RPFs based on internal doses and compare
subclass groupings and modeling results with those developed using external doses.
Recommended future RPF research on pesticide mixtures is to:
46
-------
1) Develop kinetic models for pesticide mixtures in rodents.
2) Using experimental cholinesterase inhibition measures, determine RPFs based
on both external and internal dose estimates for the rodent.
3) Determine if the RPFs based on internal dose estimates significantly differ from
RPFs developed from external doses for the rodent.
4) Apply the biostatistical methods for grouping by common dose-response curves
using RPFs based on internal and external doses and compare the groupings
that result.
5) Develop kinetic models for pesticide mixtures in humans.
6) Estimate human risks using rodent cholinesterase inhibition responses, RPFs
based on rodent internal doses, and human internal dose estimates using the
three approaches presented in Chen et al. (2001, 2003), as appropriate.
7) Compare subclass groupings and human risk estimates for all scenarios of
internal and external RPFs.
8) Evaluate the toxicity of different human exposure scenarios with the RPF models
developed.
This research was undertaken to continue exploring and developing cumulative
risk assessment strategies based on dose addition concepts beyond current
applications and is intended to improve future applications of RPF based risk
assessments.
47
-------
7. REFERENCES
Chen, J.J., Y.J. Chen, G. Rice et al. 2001. Using dose addition to estimate cumulative
risks from exposures to multiple chemicals. Reg. Toxicol. Pharmol. 34(1):35-41.
Chen, J.J., Y.J. Chen, L.K. Teuschler et al. 2003. Cumulative risk assessment for
quantitative response data. Environmetrics. 14:339-353. (DOI:10.1002/env587)
Finney, D.J. 1971. Probit Analysis, 3rd ed. Cambridge University Press, Cambridge,
England, p. 269-282.
Hewlett, P.S. and R.L. Plackett. 1959. A unified theory for quantal responses to
mixtures of drugs: Non-interactive action. Biometrics. 15:591-610.
Mileson, B.E., J.E. Chambers, W.L. Chen et al. 1998. Common mechanism of toxicity:
A case study of organophosphorus pesticides. Toxicol. Sci. 41(1):8-10.
NRC (National Research Council). 1988. Complex mixtures: Methods for in vivo
toxicity testing. National Academy Press, Washington, DC.
U.S. EPA. 1980. Comprehensive Environmental Response, Compensation, and
Liability Act (CERCLA or Superfund). 42 U.S.C. s/s 9601 et seq.
U.S. EPA. 1986. Guidelines for Health Risk Assessment of Chemical Mixtures.
Federal Register. 51(185):34014-34025.
U.S. EPA. 1989a. Risk Assessment Guidance for Superfund. Vol. 1. Human Health
Evaluation Manual (Part A). EPA/540/1-89/002.
U.S. EPA. 19896. Interim Procedures for Estimating Risks Associated with Exposures
to Mixtures of Chlorinated Dibenzo-p-dioxins and -dibenzofurans (CDDs and CDFs) and
1989 Update. Risk Assessment Forum. EPA/625/3-89/016.
U.S. EPA. 1992. Guidelines for Exposure Assessment. Federal Register
57(104):22888-22938.
U.S. EPA. 1996. Safe Drinking Water Act Amendments. National Drinking Water
Clearinghouse. Online, http://www.epa.gov/safewater/sdwa/text.html
U.S. EPA. 1997. The Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA) and
Federal Food, Drug, and Cosmetic Act (FFDCA) As Amended by the Food Quality
Protection Act (FQPA) of August 3,1996; U.S. Environmental Protection Agency, Office
of Pesticide Programs, document # 730L97001, March, 1997. Food Quality Protection
Act (FQPA) Public Law 104-170. Online, http://www.epa.gov/oppfead1/fgpa/
48
-------
U.S. EPA. 2000. Supplementary Guidance for Conducting Health Risk Assessment of
Chemical Mixtures. Office of Research and Development, Washington, DC.
EPA/630/R-00/002. Available in PDF format at: www.epa.gov/NCEA/raf/chem mix.htm
U.S. EPA. 2001 a. National-Scale Air Toxics Assessment for 1996. Science Advisory
Board Preliminary Draft. EPA-453/R-01-003 Office of Air Quality Standards and
Planning, RTP, NC. Online, http://www.epa.qov/ttn/atw/nata/natsaov.html
U.S. EPA. 2001 b. Preliminary Cumulative Risk Assessment for the Organophosphorus
Pesticides. Office of Pesticide Programs, Washington, DC.
U.S. EPA. 2002a. Framework for Cumulative Risk Assessment. EPA/630/P-02/001A.
Risk Assessment Forum, Washington, DC.
U.S. EPA. 2002b. Guidance on Cumulative Risk Assessment of Pesticide Chemicals
That Have a Common Mechanism of Toxicity. OPP, Washington, DC. Online.
http://www.epa.gov/oppfead1/trac/science/cumulative guidance.pdf
U.S. EPA. 2002c. The Feasibility of Performing Cumulative Risk Assessments for
Mixtures of Disinfection By-Products in Drinking Water. EPA/600/R-03/051 Final Draft.
U.S. EPA. 2003a. Regional/ORD Workshop on Cumulative Risk Assessment, Dallas,
TX, Nov. 4-8, 2002. Washington, DC.
U.S. EPA. 2003b. Integrated Risk Information System. Office of Research and
Development, National Center for Environmental Assessment, Washington, DC.
Online, http://www.epa.gov/iris
Wilkinson, C.F., G.R. Christoph, E. Julien et al. 2000. Assessing the risks of
exposures to multiple chemicals with a common mechanism of toxicity: How to
cumulate? Reg. Toxicol. Pharmol. 31:30-43.
49
-------
APPENDIX A
CHEN ET AL., 2001
USING DOSE ADDITION TO ESTIMATE
CUMULATIVE RISKS FROM EXPOSURES TO MULTIPLE CHEMICALS
A-1
-------
Using Dose Addition to Estimate Cumulative Risks from
Exposures to Multiple Chemicals
James J. Chen1, Yi-Ju Chen1, Glenn Rice2, Linda K. Teuschler2,
Karen Hamernik3, Alberto Protzel3, and Ralph L. Kodell1
1 Division of Biometry and Risk Assessment
National Center for Toxicological Research
U.S. Food and Drug Administration
Jefferson, Arkansas 72079
2 National Center for Environmental Assessment
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
3 Health Effects Division
U.S. Environmental Protection Agency
Washington, DC 20460
Send correspondence to:
*Dr. James J. Chen
Division of Biometry and Risk Assessment
NCTR/FDA/HFT-20
Jefferson, AR 72079
Tel:(870)-543-7007; Fax:(870)-543-7662; E-mail: jchen@nctr.fda.gov
* The views presented in this paper are those of the authors and do not necessarily represent those
of the U.S. Food and Drug Administration or U.S. Environmental Protection Agency
-------
SUMMARY
The Food Quality Protection Act (FQPA) of 1996 requires the EPA to consider the cumulative
risk from exposure to multiple chemicals that have a common mechanism of toxicity. Three
methods, hazard index (HI), point of departure index (PODI), and toxicity equivalence factor
(TEF), have commonly been considered to estimate the cumulative risk. These methods are
based on estimates of EDio (point of departure) and reference doses from the dose response
functions of individual chemicals. They do not incorporate the actual dose response function of
the mixture from multiple chemical exposures. Dose addition is considered to be an appropriate
approach to cumulative risk assessment because it assumes that the chemicals of interest act
in accordance with a common mode of action (a similar action). This paper proposes a formal
statistical procedure to estimate the cumulative risk by fitting the dose response model of the
mixture under dose addition. The relative potency between two chemicals is estimated directly
from the joint dose response model of the mixture. An example data set of four drugs representing
four chemicals is used to illustrate the proposed procedure and compare it to the HI, PODI, and
TEF methods.
Key Words: Chemical mixture; Low-dose extrapolation; Relative potency factor (RPF); Similar
action; Toxicity equivalence factor (TEF);
-------
1. Introduction
Regulatory agencies use risk assessment to derive acceptable levels of exposure to chemicals
that may exist as contaminants in food, drinking water, air, or the environment. Risk assessment
for toxic agents is usually conducted to evaluate the potential risks from exposure to a single
toxic agent through a single route of exposure. Although it is important to establish safe levels
of exposure for humans for each toxic agent, people frequently are exposed to many chemicals
simultaneously or in sequence by different routes. The exposures to multiple chemicals could
cause unexpected cumulative potential effects through various media. The risks may combine
additively, multiplicatively or in some other fashion. The combined risk may be greater, or less
than what would be predicted from data on individual chemicals. Concerns about the problems
of multiple chemical exposure have been an important issue. The risk associated with exposure
to more than one toxic chemical by different routes may be characterized by cumulative exposure
and risk assessments.
Assessing the cumulative toxicological effects of multiple chemicals has been addressed from
time to time (NRC, 1988; EPA, 1986, 1999a). Methods and data, which can be used to estimate
the risk of exposures to multiple chemicals, have been developed over the years. But there is no
consensus on appropriate statistical methods for cumulative risk assessments (CRA). The Food
Quality Protection Act (FQPA) of 1996 requires that, in future risk assessments, the EPA must
consider not only the risk of a single pesticide chemical residue, but also the risk of exposures to
other pesticide residues and substances that have a common mechanism of toxicity. The FQPA
specifically focuses on available information concerning the potential cumulative effects of such
exposures.
The issue of a common mechanism of toxicity has recently been addressed by a working group
of experts convened by the ILSI Risk Science Institute (RSI) (Mileson et al., 1998). The working
group presented three criteria to describe a common mechanism of toxicity: 1) cause the same
critical toxic effect; 2) act on the same molecular target at the same target tissue; and 3) act by
-------
the same biochemical mechanism of action, or share a common toxic intermediate. The working
group agreed that all three points are useful to apply to chemicals that may act by a common
mechanism of toxicity, but did not state whether all three points must be met before a firm com-
mon mechanism of toxicity determination can be reached. It is recognized, however, that precise
mechanistic information on animal or human effects of pesticide chemicals is scant. Common
mechanism determinations will therefore be difficult to establish with these three points because
chemicals often exhibit a different spectrum of adverse effects in different organs and tissues
(Mileson et al. 1998).
Wilkinson, et al., (2000) evaluated three methods of assessment of cumulative risk from ex-
posures to multiple chemicals: hazard index (HI), point of departure index (PODI), and toxicity
equivalence factor (TEF). They also considered two the other methods of assessment: the margin
of exposure (MOE) and cumulative risk index (CRI) that are the reciprocals of the PODI and
HI approaches, respectively. The approach of these methods is based on estimates of reference
doses or point-of-departure doses (e.g., EDio) from the fitted individual dose response functions.
There is no attempt to incorporate the dose response function of the mixture from combined
exposures to multiple chemicals. In this paper, we propose a quantitative approach to estimating
the cumulative risk by directly fitting the dose-response function of the mixture through the dose
addition model.
Under the assumption of a common mode of action (chemicals are non-interactive and act on
similar biological systems in eliciting a common response) for multiple chemicals, the chemicals
are commonly assumed to act as if one is a simple dilution of the other. The joint action of
the chemicals, then, can be described by "dose addition" (Finney, 1971). The assumption of
addition of individual exposures (dose addition) to predict a cumulative toxic effect is reasonable
(Wilkinson, et al., 2000). Furthermore, dose additivity is consonant with EPA policy that "pes-
ticide chemicals that cause related pharmacological effects will be regarded, in the absence of
evidence to the contrary, as having an additive deleterious actions" (CFR, 1998); also the EPA
-------
(1986) recommended no-interaction approaches of dose addition for risk assessment of mixtures.
Let FI and F2 be the dose response functions for chemical 1 and chemical 2, respectively.
Under dose-addition, the response to the combination of d\ and d2 for chemical 1 and chemical
2, respectively, is
R(d1,d2) = Fl(dl+pd2)
where p is the relative potency of chemical 2 to chemical 1. When one chemical acts as if it is a
simple dilution of the other, then the relative potency between the two chemicals is constant. In
other words, for all response levels, the effective dose of one chemical is a constant multiple of
the effective dose of the other chemical. Hewlett and Plackett (1959) viewed the concept of dose
addition (similar action) in a slightly broader sense than requiring a constant relative potency
between two chemicals. Mathematically, their characterization can be interpreted as allowing
the relative potency factor to be different for different response levels.
Dose addition allows for summing the individual doses into an equivalent dose in terms of an
index chemical, and using the index chemical's dose-response function to estimate the response
from the equivalent total mixture dose. Dose addition is considered to be an appropriate ap-
proach to cumulative risk assessment because it assumes that the chemicals of interest act in
accordance with a common mechanism of toxicity. The main purpose of this paper is to pro-
pose an approach to calculating cumulative risk under the broader definition of dose addition in
which the relative potency is not constant (Hewlett and Plackett, 1959). The approach involves
estimating the relative potencies between chemicals from the joint dose response function of the
mixture through addition of the doses of individual compounds.
-------
2. Dose Response Model for Combined Exposures
A dose response function for binary response data, denoted P(d) = F, relates the probability
of response to the dose, d, where F is a probability distribution function. The general model can
be expressed in the logarithm of dose as
d>0,
or in the un-transformed dose as
Two commonly used dose response models are the probit model and the logistic model. The
log-probit model is
P(d] = c+ (1 - c) r+ Qg -^=exp(-l/2t2)dt
Joo v2?r
and the log-logistic model is
, /-, ^ exp(a +/31ogd)
v 'l + exp(a + £logd)'
where the parameter c represents background effect and P(d) is defined to be c when d = 0.
The parameters a and /3 are the intercept and slope of the dose response models under F-1(P(d)).
Consider only two chemicals and denote the dose response functions for chemical 1 and
chemical 2 as
and
If the relative potency p of chemical 2 to chemical 1 is constant, then the dose response for one
chemical can be expressed in terms of the equivalent dose of the other chemical, i.e., Pi(di) =
Pz(di/p) P\(pd
-------
The above equality holds for all rfj. In particular, letting di = 1, the equation becomes cti =
a2 falogp. This implies logp = (a2 ai)/fa. Similarly, If P2(d2) Pi(pd2), then
a2 + $2logd2 = ai + /?ilogd2p, for all d2.
It implies analogously that logp = (a2 a\)/P\. Hence, fl\ = fa. Conversely, assume that the
slopes of the dose response functions are equal (f3\ = fa = /?). If Pi(di) = ^2(^2) then
ai + /31ogdi = a2 + /31ogd2.
The relative potency of chemical 2 to chemical 1 is logp = («2 ai)//3. Thus, the relative potency
p between the two chemicals is constant for all dose (response) levels. We have shown that two
chemicals have a constant relative potency if and only if the slopes of the (log) dose response
functions are equal.
If the dose-response functions are modeled in terms of un-transformed doses instead of log
doses, then the relative potency is constant if and only if the intercepts of the dose-response
functions are equal, where the relative potency is the ratio of the slopes. The remainder of this
paper will address only log-dose models.
2.1 Constant Relative Potency
If two chemicals have a constant relative potency and if the joint response is dose-additive,
then the dose-response function from exposure to d\ of chemical 1 and d2 of chemical 2 is
F(dl,d2) = Pl(dl+pd2}
For a group of m chemicals in which the relative potency between any two chemicals is constant,
the joint response of the m chemicals can be derived as
m
F(d1,---,dm] = PiCdi+
t=2
i=2
-------
where pt = exp[(at Q.\)/f3\ is the relative potency of chemical t to the index chemical 1,
t = 2, , m. The joint response can also be expressed in terms of any other chemical as an
index chemical s,
= F(as + (3log(ds
where p't = exp[(at as)//3}. It can be seen that p't = pt/ps for t 1, -,m, where p\ = 1. The
two models are equivalent, i.e., the estimated risk at any set of doses does not depend on the
choice of index chemical.
2.2 Non-Constant Relative Potency
If the relative potency factor between chemical 1 and chemical 2 is different for different
response levels, then the slopes of the dose response functions for the two chemicals are different.
At the equal effective doses of d\ for chemical 1 and d2 for chemical 2 such that Pi(di) = P2(d2),
it can be shown that the equivalent dose of chemical 2 in terms of chemical 1 is
i
and the equivalent dose of chemical 1 in terms of chemical 2 is
j fj \ fa\ a2\,/3
d2(di) = exp( - - K
P2
Under dose- addition, the joint response from an exposure to d'i of chemical 1 and d2 of chemical
2 in terms of chemical 1 is
where w = fal&\, and p12 = exp[(a2 a\}/P\[. On the other hand, the joint response in terms
of chemical 2 is
F(di,d2) = P2(d2(d!) + d2)
-------
where £21 = exp[(cci 02) /Az]- Note that the joint response predicted from chemical 1, P\(d\ +
^1(^2)), wm differ from that predicted from chemical 2, P2(<^2(^i) + ^2))-
For m chemicals, the combined response in terms of chemical s can be derived as
t+s
The pst = exp[(at as)//3s] is a potency ratio of chemical t to the index chemical 5, and
is the slope ratio, t = 1, , m, and t ^ s.
-------
2.3 General Cases
For a set of m chemicals, the chemicals can be clustered into several subclasses of constant
relative potency. For example, the set {{Cl, C2, ..}, {Cl, C(l+l)..}, .. {Cm}} represents that the
chemicals 1, 2, .. in the first subclass have constant relative potency with respect to each other
as do the chemicals Cl, C(l+l) .. in the second subclass; the relative potency factor between
the last chemical Cm and the other chemicals is different at different response levels. For this
example, the joint response in terms of chemical 1 is
F(dlj , dm) = PiUdj + P2d + ...) + ... + (pldT + pi-Kfili + -) + - + PmC")-
The chemicals in the same subclass will have the same slope ratio wt (= 0tlPi)- Also, the chemi-
cals in the same subclass will have the same cumulative risk estimate, regardless of which is used
as the index chemical.
3. Cumulative Risk Estimation
The fitted dose response model for the mixture from multiple chemical exposures can be used
for quantitative risk estimation in terms of the equivalent total mixture dose of the index chemical.
For a group of m chemicals in which the relative potency factor between any two chemicals is
constant, the estimated cumulative risk from exposure to the specific doses dio,---,dmO for
chemicals 1, . . ., m, respectively, is
m
F(di0, , dm0) = F(as + /31og(]T) (5stdto)),
t=i
where as, /3, pst are the maximum likelihood estimates of the model parameters, and D = psidiG+
' iPsmdmo) is the equivalent total mixture in terms of the index chemical s, and pss = 1. The
cumulative risk can be expressed as a response of the mixture dose in terms of the dose response
function of the index chemical
10
-------
Using this equation, either the EDP for a given response level p% or an acceptable dose level D*
corresponding to a given risk level r can be computed, i.e., P(EDP) = p% or P(D*} = r.
In general, when the relative potency factor is not constant, the estimated cumulative risk
will depend on the index chemical. In this case, the average risk or the maximum risk over all
possible index chemicals can be used.
For a single chemical, a benchmark dose (e.g., ED10) often serves as the so-called point-of-
departure for low-dose extrapolation in order to minimize model dependency at low dose levels.
The above equation can be used to calculate the point-of-departure. The reference dose for the
mixture in terms of an index chemical is defined as
Ref = EDP/GUF,
where EDP is the mixture dose corresponding to a risk level of p% and GUP is the group uncer-
tainty factor. For given exposure doses, the estimated risk unit with respective to the risk at the
reference dose can be calculated (Wilkinson, et al. 2000).
4. An Example for Cumulative Risk Estimation
A data set of four analgesics given by Finney (1971, Chapter 6, p 104) is used as an example to
illustrate the proposed procedure. These represent typical toxicological data obtained from dose
response experiments. The four analgesics can be regarded as four chemicals having a common
mode of toxicity. The logistic dose response function is used in the analysis,
r>(j\ (i \ exp(a + fllogd)
1 + exp(a + (3logd}.
Table 1 contains the maximum likelihood estimates with standard error estimates in paren-
theses and the maximum value of the log-likelihood (LL) of the fitted logistic dose response
11
-------
function for the four chemicals. The EDio, ED.io, and specific exposure doses with corre-
sponding predicted risk of the four chemicals are also listed in Table 1, The EDio and ED.10
are used later to describe the three cumulative risk assessment methods presented by Wilkin-
son et al. (2000). We are interested in estimating the cumulative risk at the exposure doses
d10 = .005, d20 = .010, d30 = .005, d40 = .010. The sum of the four individual risks is 6.67 x 10~5.
The likelihood ratio (LR) test is used to test for the equality of the slopes. The LL value under
a common slope model is -729.225. The LR %2 statistic under the null hypothesis is 2(729.225-
(209.358+157.447+139.797+221.716)] = 1.814. The x2 value shows no evidence of any differences
among the four slopes.
The data set of the four chemicals is fitted to the model of constant relative potency given
by
0*2, 0*3,04) = C+ (1 -C)-
exp(as
where psi is the relative potency factor of chemical t to the index chemical s. Table 2 contains
the maximum likelihood estimates with standard error estimates of the coefficients of the dose
response function, the equivalent exposure dose D with the predicted cumulative risk, and the
EDio and ED.i0 using four different index chemicals (s 1,2. 3,4). Note that pa,pf>, and pc are
the estimates of the relative potency factors between chemicals relative to the index chemical. For
example, when s = 1, then pa = p12, Pb = pis, pc = Pu- The maximum likelihood estimates of
the model parameters are c = .056,6; = 2.605,4 1-90, pi2 = 1.26, pis = 3.61, and pu = 0.34.
The total mixture dose is D = .005 + 1.26 x .010 + 3.61 x .005 + 0.34 x .010 = 0.0391. The
predicted cumulative risk is 1.47 x 10~4. The predicted risk can be computed using a different
index chemical. Table 2 shows that risk estimate is the same regardless of which chemical is se-
lected as the index chemical. For a convex dose response function, the estimated (low dose) risk
based on simply summing the individual risks (6.67x 10~5 shown in Table 1) will underestimate
the cumulative risk through dose addition (1.47 x 10~4 shown in Table 2) under a model of a
12
-------
common mode of action.
Alternatively, using the ED\Q as the point-of-departure, the reference dose for the mixture
in terms of the index chemical 1 can be calculated by
Ref= 1.2820/GUF.
If GUF = 50, then Ref = 1.2820/50 - 0.026. This value is smaller than the mixture dose 0.039.
Similarly, the reference doses for the mixture in terms of other index chemicals 2, 3, and 4 are
0.020, 0.007, and 0.076 respectively. These values are smaller than their corresponding mixture
doses shown in Table 2.
For illustration purposes, assume that the relative potency factors between chemicals 1, 3,
and 4 (with each other) are constant, and the relative potency factors between chemical 2 and
chemicals 1, 3, and 4 are different. The four chemicals are grouped into two subclasses { {1,3,4},
{2} }. If chemical 1 is used as the index chemical (to represent the subset {1,3,4}), then the
joint dose response function is
p/ , , , , x ,(, , exp(ai
P(di,d2, d3, d4) = c+(l- c) - -.
1 + exp(a
If chemical 2 is used as the index chemical, then dose response function becomes
, , ,x , ^ exp(a2 + /?2log(d2
Table 3 contains the maximum likelihood estimates of the model parameters. Table 3 shows
that chemicals 1, 3, and 4 give the same predicted risk (1.39 x 10~4). But the cumulative risk
predicted by chemical 2 is 1.75 x 10~4. The estimated slope ratio between the chemical 2 to
chemical 1 (or 3, 4) is w = 1.12 = 1/.89.
5. Discussion
Wilkinson et al. (2000) described the three methods, HI, PODI, and TEF, of cumulative
risk assessment based on the estimates of the EDio and reference doses of individual chemicals.
13
-------
For given exposure doses, the risk unit estimate can be obtained by multiplying an uncertainty
factor (UF) for the chemical. In the present context, using the EDi0 as the POD, the risk unit
for the three methods is
HI = UF x (0.005/0.9110 + 0.010/1.4214 + 0.005/0.3397 + 0.010/2.9082)
= UF x 0.031 (= PODI = TEF),
where UF is the common uncertainty factor for the four chemicals. The risk unit estimate is 0.31
when UF=40, and it is 3.10 when UF = 100. The ED.io can also be used as POD to calculate
the HI, PODI, and TEF but with UF = 1, the risk unit is HI (0.005/0.0462 + 0.010/0.1855 +
0.005/0.0311 + 0.010/0.1733) = 0.380 (= PODI = TEF).
The ED.io can also be used as the reference dose in the TEF method as in the context of
the Wilkinson et al. (2000) examples. When the EDio is used as POD and ED.jo as reference
dose, applying the TEF method to estimate the risk unit will depend on the choice of the index
chemicals. For example, the risk unit estimate for TEF method in terms of the index chemical
1 is
0.9110 x (0.005/0.9110 + 0.010/1.4214 + 0.005/0.3397 + 0.010/2.9082) 4
00462 6.05x10 .
In the same way, the calculated risk units are 5.15 x 10~4, 3.34 x 10~4, and 2.35 x 10~4 for
chemicals 2, 3, and 4 as the index chemical. The risk predicted from the proposed dose-addition
model given in Table 2 is 1.47 x 10~4 irrespective of which chemical is selected as the index
chemical.
The HI, PODI, and TEF methods all assume that the dose response functions for the chem-
icals considered have a similar slope. The relative potency factors among chemicals are often
based on a particular effective dose EDP (e.g., ED10) of individual dose response functions. In
this approach, the relative potency estimate will depend on the choice of the particular effective
dose if the slopes are not estimated to be equal. For example, the relative potency between
chemical 3 and chemical 1 is 0.9110/0.3397 = 2.68 based on ED10, and it is 0.0462/0.0311 =
14
-------
1.49 based on ED.io (Table 1). Because the proposed approach takes into account a common
slope in fitting the joint dose response function, the estimate of the relative potency for a subset
of chemicals that have the same slope is invariant to the choice of effective doses or the index
chemicals. In Table 2, for example, the estimated relative potency of chemical 3 to chemical 1 is
3.61. This value can be also computed from the ratio of the ED10 or ED.io of the chemical 1 to
chemical 3.
The proposed approach of fitting a single joint dose-response function to the dose response
data (from all chemicals) is consistent with the current approach to a single chemical risk as-
sessment. The fitted dose-respopnse function can be used to estimate the cumulative risk for a
given set of exposure doses or to derive a reference mixture dose from a benchmark dose from
the index chemical. The proposed approach is similar to the TEF method. But, unlike the
TEF method, the proposed method will give the same predicted risk regardless of the choice of
the index chemical under the constant relative potency model. Perhaps most importantly, the
proposed approach can be used when the relative potency factor differs for different subclasses
of chemicals. This flexibility, which is based on a broader than usual concept of dose addition,
makes the procedure broadly applicable for estimating cumulative risk.
References
CFR (1998). Code of Federal Regulations, 40, 180.3, July 1, 1998.
EPA (1986). Guidance for Health Risk from Exposure to Chemical Mixtures. U.S. Envi-
ronmental Protection Agency. Fed. Reg. 51, 34014.
EPA (1999a). Guidance for Conducting Health Risk Assessment of Chemical Mixtures.
U.S. Environmental Protection Agency, Washington, D.C., April 1999. Unpublished
draft document.
15
-------
EPA (1999b). Proposed Guidance on Cumulative Risk Assessment of Pesticide Chemi-
cals That Have a Common Mechanism of Toxicity. U.S. Environmental Protection
Agency, Washington, D.C., August 1999. Unpublished draft document.
Finney (1971). Probit Analysis, Third Edition. Cambridge University Press, Cambridge.
Hewlett, P. S. and Plackett, R. L. (1959). A unified theory for quantal responses to mix-
tures of drugs: non-interactive action. Biometrics, 15, 591-610.
Mileson, B. E., Chambers, J. E., Chen, W. L., Dettbarn, W., Ehrich, M., Eldefrawi, A.
T., Gaylor, D. W., Hamernik, K., Hodgson, E., Karc2mar, A., Padilla, S., Pope,
C., Richardson, R. J., Saunders, D. R., Sheets, L. P., Sultatos, L. G., and Wallace,
K. B. (1998). Common mechanism of toxicity: A case study of organophosphorus
pesticides. Toxicol. Sci. 41, 8-20.
National Research Council (NRC) (1988). Complex Mixtures: Methods for in Vivo Toxicity
Testing. Natl. Acad. Press, Washington, D. C.
Wilkinson, C. F., Christoph, G. R., Julien, E., Kelley, J. M.. Kronenberg, J., McCarthy,
J., and Reiss, R. (2000). Assessing the risks of exposures to multiple chemicals with
a common mechanism of toxicity: How to cumulate? Reg. Toxicol. and Pharmacol.
31, 30-43.
16
-------
Table 1. The maximum likelihood estimates (standard errors) of the coefficients of the logistic
dose-response model, and the estimated ED10, ED.io and maximized log-likelihood value for the
four chemicals.
Chemical c
I
2
3
4
Sum
0.00
(0.27)
0.12
(0.15)
0.00
(0.59)
0.00
(0.33)
a.
-2.05
(1.54)
-2.87
(1.31)
-0.07
(1.41)
-3.98
(2.59)
13 LL
1.58 -209.358
(0.71)
2.32 -157.447
(0.71)
1.97 -139.797
(0.88)
1.67 -221.716
(0.77)
ED 10 ED. 10 Exposure Pred.
0.9110 0.0462 0.005 2.98xlO~5
1.4214 0.1855 0.010 0.11 xlO~5
0.3397 0.0311 0.005 2.73xlQ-5
2.9082 0.1733 0.010 0.85xHT5
6.67xKT5
17
-------
Table 2. The maximum likelihood estimates (standard errors) of the coefficients of the joint dose
response function from multiple exposures of chemicals having constant relative potency factors.
a P pa pb pc D Pred. EDi0 ED
.10
1 0.056 -2.605 1.90 1.26 3.61 0.34 0.0391 1.47x 10~4 1.2820 0.1071
(0.09) (0.67) (0.30) (0.39) (0.03) (0.13)
2 0.056 -2.165 1.90 0.79 2.86 0.27 0.0310 1.47x 10~4 1.0170 0.0850
(0.09) (0.60) (0.30) (0.08) (0.32) (0.03)
3 0.056 -0.167 1.90 0.28 0.35 0.09 0.0108 1.47x 10~4 0.3553 0.0297
(0.09) (0.32) (0.30) (0.03) (0.01) (0.04)
4 0.056 -4.674 1.90 2.97 3.75 10.72 0.1160 ].47x 10~4 3.8090 0.3183
(0.09) (0.97) (0.30) (0.29) (1.14) (0.38)
18
-------
Table 3. The maximum likelihood estimates (standard errors) of the coefficients of the joint
dose response function from multiple exposures of chemicals that do not have constant relative
potency factors.
s c a P pa Pb PC w D Pred. ED10 ED
.10
1 0.054 -2.535 1.84 1.08 3.64 0.34 1.12 0.0328 1.39x 10~4 1.2426 0.0958
(0.10) (0.67) (0.31) (0.41) (0.03) (0.28) (0.20)
3 0.054 -0.153 1.84 0.27 0.30 0.09 1.12 0.0090 1.39x 10~4 0.3405 0.0262
(0.10) (0.32) (0.31) (0.03) (0.01) (0.08) (0.20)
4 0.054 -4.541 1.84 2.97 3.21 10.80 1.12 0.0973 1.39x 10~4 3.6966 0.2849
(0.10) (0.98) (0.31) (0.29) (1.18) (0.84) (0.20)
2 0.054 -2.389 2.08 0.93 2.93 0.36 0.89 0.0505 1.75x 10~4 1.1297 0.1170
(0.10) (0.72) (0.43) (0.23) (0.32) (0.14) (0.16)
19
-------
Data set of four chemicals from Finney (1971)
Chemical
1
1
1
2
2
2
3
3
3
4
4
4
4
4
Dose
1.50
3.00
6.00
1.50
3.00
6.00
0.75
1.50
3.00
5.00
7.50
10.00
15.00
20.00
Response
19
53
83
14
54
81
31
54
80
13
27
32
55
44
Total
103
120
123
60
110
100
90
80
90
60
85
60
90
60
20
-------
APPENDIX B
CHEN ET AL, 2003
CUMULATIVE RISK ASSESSMENT FOR QUANTITATIVE RESPONSE DATA
B-1
-------
Cumulative Risk Assessment for
Quantitative Response Data
James J. Chen1, Yi-Ju Chen1, Linda K. Teuschler2, Glenn Rice2,
Karen Hamernik3, Alberto Protzel3, and Ralph L. Kodell1
1 Division of Biometry and Risk Assessment
National Center for Toxicological Research
U.S. Food and Drug Administration
Jefferson, Arkansas 72079
2 National Center for Environmental Assessment
Office of Research Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
3 Health Effects Division
Office of Pesticide Programs
U.S. Environmental Protection Agency
Washington, DC 20460
Send correspondence to:
*Dr. James J. Chen
Division of Biometry and Risk Assessment
NCTR/FDA/HFT-20
Jefferson, AR 72079
Tel:(870)-543-7007; Fax:(870)-543-7662; E-mail: jchen@nctr.fda.gov
* The views presented in this paper are those of the authors and do not necessarily represent those
of the U.S. Food and Drug Administration or U.S. Environmental Protection Agency
-------
SUMMARY
The Relative Potency Factor approach (RPF) is used to normalize and combine different toxic
potencies among a group of chemicals selected for cumulative risk assessment. The RPF method
assumes that the slopes of the dose response functions are all equal; but this method depends
on the choice of the index chemical, i.e., different index chemicals will give different predicted
mean estimates. This paper is part of an approach to explore and develop cumulative risk
assessment strategies. As part of this approach this paper proposes a procedure for cumulative
risk assessment from exposure to multiple chemicals that have a common mechanism of toxicity.
We propose two classification algorithms to cluster the chemicals into subclasses such that the
chemicals in the same subclass have a common slope. The joint response is estimated by fitting
the dose response model of the mixture under dose addition. The proposed method will give the
same predicted mean response regardless of the selection of the index chemical for the chemicals
in the same subclass. The proposed method also allows one to estimate the joint response for
chemicals having different slopes. An example data set of six hypothetical pesticide chemicals is
used to illustrate the proposed procedure.
Key Words: Chemical mixture; Classification tree; Point of departure (POD); Relative potency
factor (RPF); Similar action.
-------
1. Introduction
Quantitative risk assessment is used to derive acceptable exposure levels or to estimate the
risks from exposure to chemicals that may exist as contaminants in food, drinking water, air, or
the environment. Estimation of potential risks for toxic agents is usually conducted on a single
toxin by a single route of exposure. However, people frequently are exposed to many chemicals
simultaneously or in sequence by different routes from different sources. Exposures to multiple
chemicals could cause unexpected potential adverse effects through a variety of toxicological in-
teractions. Various chemical components may induce similar or dissimilar effects over time. The
Food Quality Protection Act (FQPA) of 1996 requires the Environmental Protection Agency
(EPA) to consider not only the risk of a single pesticide chemical residue but also the risk of
exposures to other pesticide residues and substances that have a common mechanism of toxic-
ity. The FQPA specifically states the available information concerning the potential cumulative
effects of such exposures. The process of risk assessment of concurrent exposure by all relevant
routes for a group of compounds that cause a common toxic effect by a common mechanism is
designated as cumulative risk assessment.
The issue of determining a common mechanism of toxicity has been addressed by a working
group of experts convened by the International Life Sciences Institute (ILSI) Risk Science Insti-
tute (RSI) (Milesonet al., 1998). Subsequently, the EPA (EPA, 1999; http:/www.epa.gov/oppfeadl/
trac/science/) has issued a guidance document for identifying pesticide chemical that have a com-
mon mechanism of toxicity. Recently, the EPA issued the results of the revised cumulative risk
assessment for organophosphorus pesticides [http;//www.epa.gov/pesticides/cumulative/]. The
current paper is part of an approach to continue exploring and developing cumulative risk assess-
ment strategies. In this paper, we assume that common mechanism groups can be satisfactorily
determined. In this context, a common mechanism group is defined as a group of pesticides
determined to cause a common toxic effect by a common mechanism of toxicity. Such chemicals
are said to occupy the same "risk cup" (EPA, 1999).
-------
One important issue in cumulative risk assessment is how to incorporate the probability model
for estimating cumulative risk. Methods and data, which can be used to conduct risk assessment
of exposures to multiple chemical mixtures, have been developed over the years (NRC, 1988;
EPA, 1986, 1989, 1999). Because of complexity of evaluating multiple chemicals there are no
statistical methods for assessing risks from multiple chemicals that can be routinely applied to
all chemical mixtures. Methods for risk assessment of chemical mixtures fall into two general
approaches: 1) whole mixture of concern, and 2) component-based. The whole mixture approach
involves either direct evaluation of the mixture of concern or an assessment of the mixture of
concern using data available on a sufficiently similar mixture. The component-based approach
considers the additive or interactive actions among the mixture components. The existing toxico-
logical database for pesticides contains data generated primarily to evaluate the hazard potential
of individual chemicals. The most widely used component-based methods are dose addition and
response addition. Dose addition assumes that the chemicals act on the same biological site,
similar biological systems and behave similarly in terms of the primary physiologic processes
(absorption, metabolism, distribution, elimination), and elicit a common response (EPA, 2000a).
Response addition assumes that the chemicals behave independently of one another, so that the
body's response to the first chemical is the same whether or not the second chemical is present;
in simplest terms, a response addition model is described by statistical independence. Given that
cumulative risk assessment will be based on the chemicals sharing a common toxic effect that
arises by a common mechanism of toxicity, dose addition is considered to be the most appropriate
model to use for estimating cumulative risk.
Dose-addition models presented in the literature are often in terms of a probability measure
(e.g., Finney, 1971; EPA, 1986). Let FI and F2 be the dose-response functions for chemical 1
and chemical 2, respectively. Under dose addition, the response to the combination of di and
d-2 for chemical 1 and chemical 2 is Fi(di + pd2) = F2(di/p + da), where p is the relative po-
tency of chemical 2 to chemical 1. FI and F2 are the probability of occurrence of a toxic effect
for chemical 1 and chemical 2, respectively. The commonly used models are the probit, logis-
-------
tic, and multistage models. The data for a probability model are quantal responses measured
by the presence or absence of a toxic endpoint such as death. Recently, Chen et al. (2001)
applied the dose-addition model approach to estimating cumulative risk for quantal effects by
directly fitting the combined dose-response function for a set of chemicals in the same "risk cup".
The toxic responses from exposures to pesticide residues often are measured by a continuous
quantitative value, such as altered blood concentration or altered neurological function. In the
context of the FQPA, EPA has recently concluded that the organophosphorus pesticides act by
a common mechanism of toxicity, which is manifested through inhibition of acetylcholinesterase
(Mileson et al., 1998). The common endpoints measured in cholinesterase bioassays are plasma,
red blood cell, and brain cholinesterase activity levels. In this paper, we develop a dose-addition
model for quantitative response data to estimate cumulative risk.
Risk is customarily defined as the statistical probability of the occurrence of an adverse effect
at a level of exposure. Dose-response models for adverse quantal response data are well defined
since an adverse effect is self-evident, that is, the occurrence of an adverse effect is observed on
individual subjects empirically. By contrast, a clear-cut adverse effect for continuous quantitative
responses is difficult both to define and to observe unequivocally. The characterization of risk
for continuous quantitative responses in terms of probability of occurrence does not naturally
follow. Methods for risk estimation of continuous quantitative response data for a single toxin
have been proposed by many authors (e.g., Crump, 1984; Gaylor and Slikker, 1990; Chen and
Gaylor, 1992; Kodell and West, 1993; Chen et al., 1996). Dose response modeling of continuous
quantitative data for cumulative risk assessment has not been developed. The main purpose of
this paper is to propose an approach to estimating the cumulative response and cumulative risk
of an adverse continuous quantitative effect for an individual concurrently exposed to pesticides
in a common mechanism group.
2. Dose Response Model for Combined Exposure
-------
Let y(d] be a control-adjusted response variable (after a proper scaling or transformation,
if necessary) of an individual exposed to a chemical at dose d. The control-adjusted response
y(d) is calculated either by subtracting the control mean from responses in the treatment groups
(difference scale) or by dividing the responses by the control mean (ratio scale). Assume that
y(d) has a normal distribution with mean E(y(d)) = /u(d) and variance a.2 (Note that we assume
a constant variance across dose groups of a chemical.) The mean response is often expressed as
a linear function of the natural logarithm of dose,
fj,(d) = a + (3 log d,
where a is the response for d = 1. The parameters a and J3 are the intercept and slope of the
log-dose response function, respectively.
Without loss of generality, suppose c is a critical value for an abnormally low level of response,
a level below which a response is considered to be atypical. For example, c may be a certain
threshold such as a 3 standard deviation reduction (difference) from the control mean or 20%
reduction relative to the control mean. Under the difference scale, c can alternatively be expressed
as c ka, where k is appropriately chosen to yield a specific low percentage point of the
distribution of unexposed individuals. For exposure to a given dose d, the proportion of the
individuals with response y(d) below the critical value c = ka is given by
P(d) = P[y(d)
-------
value c. By expressing c in terms of k and a the probability of an adverse effect can be calculated.
2.1 Dose Addition Model
Consider only two chemicals and denote the dose response functions for chemical 1 and
chemical 2, respectively, as
and
If n\(di) = ^2(^2), the ratio of the equally effective doses pi2 = d\/d2 is called the relative
potency of chemical 2 to chemical 1. Chen et al. (2001) showed that two chemicals have a
constant relative potency if and only if the slopes of the (log) dose response functions are equal,
i.e., /?! = /32. The combined mean response can be derived through addition of doses of chemical
1 and chemical 2 based on the relative potency factor. Briefly, under dose addition, if two
chemicals have a constant relative potency, then the dose-response function from exposure to di
of chemical 1 and d2 of chemical 2 is
If the relative potency factor between chemical 1 and chemical 2 is different for different response
levels, the joint response from exposure to di of chemical 1 and d2 of chemical 2 in terms of
chemical 1 is
where ty12 = /?2/A> and /o12 = exp[(a2 - ai)//?i]. The cumulative response from exposure to
chemical 1 and chemical 2 can also be expressed in terms of chemical 2. However, if the relative
potency is not constant, then the response predicted based on chemical 1 will differ from that
-------
predicted based on chemical 2.
For a set of m chemicals, the chemicals can be clustered into several subclasses of constant
relative potency {81,82,..., Sk}, where each Si consists of chemicals having constant relative po-
tency. For example, the set {{ci, c2,..}, {cg, c9+i-.}, ..{c}} represents that the chemicals GI, c2, ..
in the first subclass have constant relative potency with respect to each other as do the chemicals
cq, Cg+i,.. in the second subclass; the relative potency factor between the last chemical c and the
other chemicals is different at different response levels. For notation simplification, let c, = i. The
joint dose response function from exposure to the set of m chemicals {{1, 2,..}, {q, q + 1..}, --{m}}
in terms of chemical 1 (called the index chemical) is
/z(di, , dm) = 0i [fa + pl2di + ...) + ... + (piqd?1' + Pi(,+i)
-------
number of subjects in dose group i from chemical /, and g\ is the number of dose groups from
chemical /. Suppose y^\ is normally distributed with mean ni(du) and variance of. Estimation of
the mean and variance parameters for an individual chemical can be obtained by the maximum
likelihood method. The log-likelihood function for the chemical / is
where /J,i(du) = ai + fy log dn. The log- likelihood function for the m chemicals in terms of the
chemical s (the index chemical) is
" 1=1 i=l j=l
where ns(Du) = as + /3S log Dit and Dit = dis + YT^s Pstdtst.
Denote the maximum likelihood estimate (MLE) of as, /3S, pst, wst, and of as ds, (3S, p~st, wst,
and of, respectively. If the control-adjusted response y^i is measured on the difference scale,
then the estimated cumulative risk from exposure to the m chemicals in terms of the chemical s
can be derived from
=,[-*-
If y^i is measured on the ratio scale, then the risk estimate is given by
In both cases, the estimated probability -P(-D) will depend on the standard deviation of a selected
index chemical.
3. Tree Classification Algorithms
In this section, we propose two classification algorithms to cluster a group of chemicals into
subclasses of constant relative potency factors. Since two chemicals have a constant relative
9
-------
potency if and only if the slopes of the (log) dose response functions are equal, the clustering
algorithm is based on testing for the equality of the slopes of dose response functions. Either the
likelihood ratio test (LR) or the analysis of variance F test can be used for the comparison.
The procedure begins with a fitting of each individual dose response function for the m
chemicals. Let /3j, /32, , An denote the MLEs of the slopes of the dose response functions. The
estimates of the m slopes can be arranged in an ascending order:
MCm-
That is, the chemical c\ has the smallest slope estimate, the chemical c2 has the second smallest
slope estimate, and so on. Two tree classification algorithms, top-down and bottom-up, are
proposed.
In the top-down classification, the procedure starts with the model that the slopes of the m
chemicals are all different, denoted as MO = {{!}, {2}, , {m}}. Consider the hypothesis of
comparing two adjacent slopes,
H0g : &, = (3Cg+1 versus Hag : (3Cq ^ /3Cq+1
for q = 1, 2, , m 1. Under the null hypothesis Hog, the dose addition model for the mixture
of chemical cq and chemical cq+\ is
The null model H0g can be represented by the partition set Bl= {{ci}, ...{cg,cg+1 }, ...{cm}}.
The hypothesis of comparing two adjacent slopes, equivalently, can be expressed in terms of
testing the two models:
H0g : Bl = {{d}, ..., {c9,c9+i},..., {cm}} versus Ha(? : MO = {{ci}, {c2}, , {cm}}.
Let pCq be the p- value associated with the test Hog versus Ha?, for q = 1, 2, , m 1; and let pCr
= Max (pcnPc2i ' ' ' iPcm_i}- If Pcr is IGSS than a pre-specified significance level, say, at, then the
10
-------
procedure stops, and the model MO that the slopes of the m chemicals are different is concluded.
On the other hand, if pCr is greater than the significance level, then the chemicals cr and cr+\
can be classified into the one subclass. That is, the model Ml= {{ci}, ...,{ CT,CT+\ }, ...} is
accepted, and the procedure continues to the next step.
Under the model Ml, the two chemicals CT and cr+1 can be treated as one chemical. Let J3'Cr
be the MLE of the common slope for the two chemicals CT and cr+\. The (m 1) slope estimates
listed in the ascending order become
That is, the two individual slope estimates /?Cr and /3Cr+1 are replaced by their common slope
estimate 0'^. The same algorithm is applied by performing m 1 comparisons of two adjacent
estimates. The hypothesis can be expressed as
H0g : B2 versus Hag : Ml
where
B2= {...,{cq, cg+1},...,{cr, cr+l}, ...}, if g + (r - 1) or q ± (r + 1)
= {-,{CT-I, CT, cr+1},...}, if q = (r - 1)
= {...,{cr,cr+i,cr+2}, ...}, if q = (r + 1).
Again, if the largest p- value is less than the significance level, then the procedure stops, and the
model Ml is concluded. If the largest p-value is greater than the significance level, then the null
model is accepted and the procedure continues to the next step. Note that in the last step, if
the null hypothesis is not rejected, then the model {{ ci, c2, , cm}} that all slopes are equal is
accepted.
In the bottom-up classification, the procedure starts with the model that the slopes of the
m chemicals are equal, denoted as MO = {{ci,c2, ,cm}}. (We use the same notations to
illustrate the parallelism between the two classification schemes.) Consider the model Bl =
11
-------
{{GI, ...cg}, {cg+1, , Cm}} constructed by the split of MO into two subclasses, q = 1, 2, , m1.
Consider the hypothesis of a constant relative potency model MO against the alternative model
Bl of two subclasses of constant relative potency factors:
H0g : MO versus Haq : Bl.
There are (m-1) tests. Let pCq be the p-value associated with the test H09 versus Hag, for
q = 1, ,m 1, and let pCr = Min {pcl,pC2, ,Pcm_i}- If P^ [S greater than a pre-specified
significance level, say, a^ then the procedure stops and the model MO is accepted. On the
other hand, if p^ is less than the significance level, then the corresponding alternative model
Ml= {{CI...CT}, {cr+i, , Cm}} is accepted, and the procedure continues to the next step. The
algorithm repeats until a null model is accepted. Note that in the last step, if the null hypothesis
is rejected, then the model that all slopes are different is concluded, {{ci}, {02}, , {cm}}.
The two clustering schemes described above are tree structure classifications. The top-down
algorithm forms the tree from the top. It assumes that the slopes of the chemicals are different.
In each step, a chemical (or subclass of chemicals) is combined with another chemicals (or sub-
class of chemicals) to form a new subclass. Therefore, the number of subclasses at each step is
one less than the previous step. On the other hand, the bottom-up algorithm forms a tree in a
division fashion. It assumes that the slopes of the chemicals are equal. A new subclass is formed
in each step. These two algorithms may result in different tree structures. In both procedures, a
goodness-of-fit test (a global test) can be performed on the terminal tree against the two trivial
trees {l,2,...,m} and {{l,2,...,m}}.
4. An Example
A data set consisting of a group of six chemicals was constructed for the example. The data
are the measures of different cholinesterase activity levels. These data represent typical endpoints
measured in a cholinesterase bioassay. Table 1 shows the sample size (n), mean response, and
12
-------
standard error (S.E.) for each of the five dose groups of the six chemicals. The control means for
the six chemicals are 340, 345, 334, 304, 359, and 450. The Bartlett test indicates that a constant
variance model among dose groups is rejected for every chemical. Therefore, a natural logarithmic
transformation of the response is applied to achieve a constant variance. The constant variance
model for a given chemical appears to be adequate for the transformed data (Bartlett test). The
transformed data are then adjusted by subtracting their respective control means. The linear
dose-response function using the natural logarithm of the dose,
/i(d) = a + /3 log(d).
is fit to the control-adjusted data for each chemical. Table 2 contains the maximum likelihood
estimates (MLEs) with standard error estimates in parentheses and the log-likelihood (LL) of
the fitted dose response function for each of the six chemicals. The six slope estimates listed in
ascending order are given as
/?3(-0.289) < /34(-0.260) < /?5(-0.232) < ^(-0.221) < &(-0.212) < #$(-0.169).
The likelihood ratio test is used in the analysis. The significance level for the top-down approach
is set to be at=0.25, and for the bottom-up approach is a.b = 0.05.
In the first step of the top-down classification the different relative potency model M0=
{{3},{4},{5},{2},{1},{6}} is compared with each of the five models: Blj ={{3,4},{5},{2},{1},
{6}}, B12={{3},{4,5},{2},{1},{6}}, B13={{3},{4},{5,2},{1},{6}}, B14={{3},{4},{5},{2,1},
{6}}, and B15={{3},{4},{5},{2},{1,6}}. The model B13 gives the largest p-value 0.6048 (>
0.25). Therefore, the model Bis is used as the null model in the next step, and the procedure
continues. Table 3 provides the details of the analysis in each step. This procedure concludes
that the six chemicals are classified into three subclasses as {{3,4},{5,2,1},{6}}.
In the first step of the bottom-up classification, the constant relative potency model MO =
{{3,4,5,2,1,6}} is compared with each of the five models: Bli ={{3},{4,5,2,1,6}}, B12={{3,4},{5,
2,1,6}}, B13={{3,4,5},{2,1,6}}, B14={{3,4,5,2},{1,6}}, B15={{3,4,5,2,1},{6}}. The details of
13
-------
analysis in given in Table 4. The bottom-up classification comes to the same three subclasses of
constant relative potency model, {{3,4},{5,2,1},{6}}. In this example, the top-down algorithm
requires four steps, while the bottom-up algorithm requires three steps.
The goodness-of-fit test can be performed using the likelihood ratio test to compare the termi-
nal tree {{3,4},{5, 2,1},{6}} against the trivial trees {{3},{4},{5},{2},{1},{6}} and {{3,4,5,2,1,6}}
for the top-town and bottom-up procedures, respectively. In the top-down procedure, the p-
value associated with the test of comparing the null model {{3,4},{5,2,1},6} and the alternative
model {{3},{4},{5},{2},{1},{6}} is greater than the significance level 0.05 (p-value=0.4984).
Therefore, we conclude that the model with the three subclasses of constant relative potency
{{3,4},{5,2,1},{6}} is adequate. Similarly, the goodness-of-fit test indicates a significant fit of
the same model with the p-value 0.00246 (< 0.05) by testing the null model {{3,4,5,2,1,6}}
against the alternative model {{3,4},{5,2,1},{6}} for the bottom-up classification.
Both classification algorithms indicate that the six chemicals can be grouped into the three
subclasses {3,4},{5,2,1},{6} of constant relative potency factors. The data set of six chemicals
can be fitted based on the three subclasses. For example, if chemical 1 is used as the index
chemical (to represent the subset {5,2,1}), then the joint dose-response function is
Using chemical 2 or chemical 5 as an index chemical, it will have a similar dose response function
and give the same prediction at given exposure levels. If chemical 3 is chosen as the index
chemical (to represent the subclass {3,4}), the joint dose-response function becomes
Finally if chemical 6 is used to be the index chemical, then the joint dose-response function is
given by
, , d6) - «6 + /36log(d6
14
-------
Table 5 (columns 1-11) contains the maximum likelihood estimates with standard errors of
the model parameters for the different index chemicals. The notations pa, pb, pc, pd, pe, wa, and
Wb denote the relative potency factors and slope ratios between chemicals relative to the index
chemical, and a is the standard deviation of the index chemical. Suppose we are interested in a
cumulative risk assessment at the exposure doses d\ = 0.030, d? = 0.035, d3 = 0.020, d± = 0.020,
d5 = 0.030, and de = 0.002. The equivalent exposure dose D can be estimated using an index
chemical. For instance, when the index chemical s 1, the maximum likelihood estimates of
the coefficients are p\2 = 1-032, p\$ = 1.600, p\3 = 0.437, p\4 = 0.273, p\6 = 4.718, w13 = 1.215,
w\6 = 0.762, and al = 0.171. The total mixture dose is D = 0.030+1.032x0.035+1.600x0.020+
0.437 x (0.020)1-215 + 0.273 x (0.030)1'215 + 4.718 x (0.002)0-762 = 0.2560. The predicted mean
response is -0.4585 or, taking anti-logarithm, a 36.8% reduction of activity of cholinesterase. The
total mixture dose and predicted responses are shown in the last two columns of Table 5. It can
be seen that the chemicals 1, 2, and 5 give the same predicted mean response of -0.4585 as do
the chemicals 3 and 4 (-0.5247).
Alternatively, the combined response may be computed for each subclasses of chemicals with
the joint dose-response function being the sum of the three dose-response functions for the three
subclasses
i , , de) = [«! + /?ilog(d! + pi2d2 + pi5d5)] + [a3 + /%log(d3 + p^d^} + [a6 + /%logde)].
The mixture dose for the subclass {1,2,5} is D = 0.030 + 1.032 x 0.035 + 1.600 x 0.020 = 0.1141
with chemical 1 as index chemical. The predictive response is -0.2796. Similarly, the mixture
dose for the subclass {3,4} is D = 0.3360 (chemical 3 as index chemical) with the predictive
response -0.2844, and the predictive response for chemical 6 is -0.0548. The estimated cumula-
tive response becomes (-0.2796)+(-0.2833)+(-0.0548)=-0.6177. This alternative approach uses a
response addition to combine results from the dose-additive subclasses.
15
-------
The estimate of adverse probability based on the joint dose-response function from exposure
to the six chemicals can be calculated in terms of the critical value c k
-------
generally defined as a point estimate of the dose or exposure level that is used to depart from
the observed range of empirical response (or incidence) data for the purpose of extrapolation
(EPA, 2000b). In the case of a cumulative risk assessment, POD is a dose reflecting a uniform
response for the common toxic effect for each chemical. The RPF is defined as the ratio of
the POD of the index chemical to that of each other chemical in the group. The exposure
dose to each chemical is multiplied by the RPF to express all exposures in terms of the index
chemical. The summation of these values provides a total combined exposure dose expressed in
terms of the index chemical for prediction. In the present context, suppose that the estimated
dose corresponding to the predicted mean response of -0.05 is defined to be the POD, such
that a + ft log(POD) = 0.05. For the given exposure doses considered in this example, Table 7
contains the estimate of POD, the total combined (equivalent) exposure dose, predicted response,
and the cumulative risk estimate for each index chemical. For example, the total exposure
normalized to the chemical 1 is
dRpp = 0.030(0.0327/0.0327) + 0.035(0.0327/0.0387) + 0.020(0.0327/0.1782)
+ 0.020(0.0327/0.1894) + 0.030(0.0327/0.0315) + 0.002(0.0327/0.0019) - 0.1965.
The predicted mean response associated with the total combined exposure &RPF can be estimated
by using the individual dose response model of the index chemical 1
= -0.774 + (-0.212) x log(0.1965) = -0.4290.
The cumulative risk estimates using the RPF method is calculated as
P(cW) = $ [-3 - ~"14?°1 = 0.3169.
Tables 6 and 7 show that the risk estimates obtained from the RPF method are, on average,
slightly smaller than those obtained from the proposed model. On the other hand, the estimated
risk based on simply summing the individual probabilities (0.0155, second column of Table 6)
will heavily understate the risk estimated either from RPF method or from the proposed method,
17
-------
as does the predicted mean response (-0.3001, shown in Table 2). The alternative version of
the proposed approach, which combines dose addition and response addition, gives substantially
higher risk estimates than the version that employs dose addition only.
The proposed dose addition model is similar to the RPF method. Although the RPF method
assumes that the dose response functions for all chemicals have a similar slope (a constant relative
potency), different index chemicals will give different predicted mean estimates. The proposed
method does incorporate the actual dose response function of the mixture from multiple chemical
exposures. The method allows one to estimate the joint response for the chemicals in a common
mechanism group but having different relative potency factors. ]t will give the same predicted
mean response regardless of the selection of the index chemical for the chemicals in the same
subclass, but risk estimates will depend on the variance of the index chemical.
18
-------
References
CFR (1998). Code of Federal Regulations, 40, 180.3, July 1, 1998.
Chen, J. J., Chen, Y-J, Rice, G., Teuschler, L. K, Hamernik, K., Protzel, A., and Kodell,
R. L. (2001). Using Dose Addition to Estimate Cumulative Risks from Exposures to
Multiple Chemicals. Reg. Toxicol. and Pharmacoi, 34, 35-41.
Chen, J. J. and Gaylor, D. W. (1992). Dose response modeling of quantitative response
data for risk assessment. Commun. Stat. Theory Methods, 21, 2367-2381.
Chen, J. J., Kodell, R. L., and Gaylor, D. W. (1996). Risk assessment for nonquantal toxic
effects. Toxicology and Risk Assessment, 503-513.
Crump, K. S. (1984). A new method for determining allowable daily intake. Fundam.
Appl. Toxicol., 4, 854-871.
Environmental Protection Agency (1986). Guidance for Health Risk from Exposure to
Chemical Mixtures. Fed. Reg., 51, 34014.
Environmental Protection Agency (1999). Guidance for identifying Pesticide Chemicals
and Other Substances that have a Common Mechanism of Toxicity. Fed. Reg. 64,
5795-5796.
Environmental Protection Agency (2000a). Supplementary Guidance for Conducting Health
*
Risk Assessment of Chemical Mixtures. U.S. Environmental Protection Agency, Risk
Assessment Forum. EPA/630/R-00/002.
Environmental Protection Agency (2000b). Proposed Guidance on Cumulative Risk As-
sessment of Pesticide Chemicals That Have a Common Mechanism of Toxicity. U.S.
Environmental Protection Agency, Washington, D.C., June 2000. Unpublished draft
document.
Finney (1971). Probit Analysis, Third Edition. Cambridge University Press, Cambridge.
19
-------
Gaylor. D. W. and W. L. Slikker (1990). Risk assessment for neurotoxic effects. Neuro-
toxicology, 11, 211-218.
Hewlett, P. S. and Plackett, R. L. (1959). A unified theory for quantal responses to mix-
tures of drugs: non-interactive action. Biometrics, 15, 591-610.
Kodell, R. L. and R. W. West (1993). Upper confidence limits on excess risk for quantita-
tive responses. Risk Anal, 13, 177-182.
Mileson, B. E., Chambers, J. E., Chen, W. L., Dettbarn, W., Elhrich, M., Eldefrawi, A.
T., Gaylor, D. W., Hamernik, K., Hodgson, E., Karczmar, A., Padilla, S., Pope,
C., Richardson, R. J., Saunders, D. R., Sheets, L. P., Sulta,tos, L. G., and Wallace,
K. B. (1998). Common mechanism of toxicity: A case study of organophosphorus
pesticides. Toxicol. Sci., 41, 8-20.
National Research Council (NRC) (1988). Complex Mixtures: Methods for in Vivo Toxicity
Testing. Natl. Acad. Press, Washington, D. C.
Wilkinson, C. F., Christoph, G. R., Julien, E., Kelley, J. M., Kronenberg, J., McCarthy,
J., and Reiss, R. (2000). Assessing the risks of exposures to multiple chemicals with
a common mechanism of toxicity: How to cumulate? Reg. Toxicol. and Pharmacol.,
31, 30-43.
20
-------
Table 1: A hypothetical group of six chemicals*
Chemical Dose
1 control
0.02
2.3
22.5
213
2 control
0.017
1.7
17.0
177
3 control
0.05
2.0
19.0
205
n
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
Mean*
340.0
323.8
167.0
80.0
45.6
345.0
360.8
187.4
74.4
50.2
334.0
360.8
268.8
68.6
38.0
S.E.
6.97
15.19
11.63
3.41
1.63
15.20
26.58
12.92
1.50
3.80
7.52
8.05
8.71
1.99
2.77
Chemical Dose
4 control
0.03
1.1
15.0
168
5 control
0.019
1.3
13.8
189
6 control
0.01
0.1
10.8
250
n
10
10
10
10
10
5
5
5
5
5
5
5
5
5
5
Mean
304.0
382.3
266.4
87.6
44.4
359.0
299.8
220.0
92.6
35.0
450.0
301.6
264.2
104.6
59.6
S.E.
5.65
4.93
6.27
1.87
1.51
9.75
18.57
13.49
1.86
2.55
13.03
24.24
21.23
6.09
8.89
* Data represent hypothetical events for inhibition of the activity of the enzyme of
cholinesterase in laboratory animals treated with increasing doses of six different
chemicals.
f Mean activity of cholinesterase after dosing.
21
-------
Table 2: The Maximum Likelihood Estimates (Standard Errors) of the coefficients of the
individual dose response model, and Log-likelihood values for the six chemicals
Chemical
1
2
3
4
5
6
sum
a
-0.774
(0.041)
-0.768
(0.047)
-0.548
(0.080)
-0.483
(0.039)
-0.853
(0.072)
-1.104
(0.056)
0
-0.212
(0.011)
-0.221
(0.013)
-0.289
(0.023)
-0.260
(0.012)
-0.232
(0.020)
-0.169
(0.014)
a LL d
0.170 7.0439 0.030
(0.027)
0.201 3.6799 0.035
(0.032)
0.322 -5.6999 0.020
(0.051)
0.233 1.5159 0.020
(0.026)
.0.307 -4.7730 0.030
(0.049)
0.248 -0.4775 0.002
(0.039)
1.2891 0.1202
Pred(d)*
-0.0316
-0.0278
-0.0832
-0.0642
-0.0385
-0.0548
-0.3001
* Pred(d) is the natural logarithm of the predicted response.
22
-------
c
o
1
o
-1-3
CD
CO
OH
CD
CO
CD
-u
i-t
^O
C/3
!I|
.2
-t-3
o
rj
* i
CD
CO
a
o
ex
CO
CD
CD
CO
O
'S 2
£ r^
QJ O
_ ( Q
"^3 S-4
a a
CO
CD
J3
"g
S
§
CO
"8
'o
£|3
CD
O
O
"o
CO
w
s
EH
co
rS
-Q
EH
CD
j=J
>
a,
^
<^
.
CD
13
O
s
CD
_I3
a
it
CD
i
C^J
O
s
3
^
CO
CD
a
o
To
'o
CD
""Q
6
PH
cu
-1-3
CO
""vf* t~-
m co
m i i
CM CM
O O
CM O>
CM in
^ CM
co m
o o
OJ O
CD m
CM CM
O O
^^
(-*->
CO
^ '
^^~
(
^
CM
^_J^
Q
"
r*"u
W^J
^
^A^
. co
^^
^^ r^
^-A\ / * ^
CD CD
/-**> / * ^
lH r 1
~ ^
( * \ / * i
CM CM
i£L *°-
" ^L
CjjT^ T^
r^
CO CO
«- f J ^ T "*
to
^
V
^~i.
V
r£?
^Q.
V
r*"?
V
gj
V
m
i i
« 0
O oo
co m
6 °
tN CD
1C "H
S 3
r-5 ^
CM S
tN CM
C5 0
1
^^ ^^
CO CO
r-*^ ^
I 1 1 1
^ CM"
r^-^ v *-*
in" m
*-- r * »-- »
H^, r^
^ T^
T^ »^
/-^-N (-*^
CO CO
O
T 1
O
0
r-H
i-H
S
t-H
1
t-
oo
"^
co"
CQ_
V
i l
V
x ^
(N
V^_
||
II
Q^^
V
^
V
CO
CM
oo £2
CM CO
0 CO
0 o
00 00
CD -ii
7 d
CM tN
C3 CJ
1
r^-^ r^
CD CO
^~^ ^C1
» " » i " \
V ' ^
* Cvi
m" ^_^
^ "^
V V
^J^ ^^
CO CO
o
i \
o
o
o
in
CM
r l
CM
l
00
r 1
O
^
CO_
1 1
^**^
/~^
CM
m"
^
Tt4
V '
r^^
CO
W
kO
CN
6
2
0
iH
0
O5
CO
tN
C5
1
f-* ^
r-*!
CO
^
i 1
CM
in"
~
CHH^
^J
^^T
*
CO
V_^J
r^-^
CO
^ '
^
/ \
T-H
CM"
in"
'-
* * i
"^
co"
_^j
^O,
V
i 1
C^
Q^_
II
L
0^5
V
V
co
i i
CM
O
o
o
co
05
05
co
co
co
CM
c>
r^
CD
* *>
*~~
r -\
T-t
in^
^
* i *
r-^
CO
-v>
'-v'
in
CM
0
O
0
O5
CO
oo
co
m
o
CM
O
r-*^
co^
^
1 ;,
in"
^
"^
^ '
l_*^i
CO
CD CM
o o
p o
0 o
5
^ o
CM CM
9 o
r-1*^
co
Ti
csT
iC*
~
/^"7p
^v~
co
'-v-'
r-*-. r-^
/-*~» r-^-i
CO CO
^ T-H
°i Q
m" /:
»~ r~^^
"^1 "^1.
co' co"
oS
V
, s
Q5
II
II
oS"
^-i
ii
ii
S£
V
5
CO
""'
^
-------
CD
1
i.
^
ex
d
1
g
M
o
+3
o
,0
CD
.3 ,±3
1 ^
i i
£ -d
o
CD O r~""t
-S S ^g
t! o
s a
0 ^
(-1 1
1 £
1
^
13
a
CO
G co
CD CD
y CX
£ -i
CD "^
O <*->
y O
f , . j^
0 CD
3 0
CD
H
ll^
_: O5 05
o co co
_ ? _ _ s 3 ?1
LO rH b- b- IN ^
o X oo 05 ,_; ^n i i
CM *7 T- 1 i 1 'Y CM CM
CT O.TOCD ,-TCDCD
LW i TH | i O | i
^ fr- S ^ o" S t-~ CM" IS ^-" CM"
OOOS^CM CO^CMCO 'NcMCO
i-i r-j Q CM ^d0"!0? dcsi<:s!
CD CD ! CD CD I CD CD I CD CD
1 1 _> 1 1 ^-T^ | 1 _"^ | 1
- Qj - - OS ~ - (35
O O5 fn O5 O5 go O5 O5 tf\ O5 O5
LOLOJKoo ooXJcoco Kcoco
CMCM'-ICM CM'-ICMCM I;:CMCM
CDoOcD CD'OCDCD OCDCD
iiit i i i i iii
/^ r^-, r^
r^-^ f^ r-^ r^-> ^ CO^ CO^
r ^ r^-s r-^-i f~*^-\ ' r^ ^-^ w-r-'
^^^ / *-\ r-^-> r^\ CO CO CO CO jT ,T .T
co" 'co" ccT co" "~t ^ ^ ""1 '"1 ^ *~1
r-T r-T ^n" T H" ^ C? '"* ^ (N ^^ ^
^C1 CM" CM" CM" i^ CM" CM r_^ {£j CM rJ^
^p ^^ LO" LO" ^^ LO LO" LO r^ LO" LO
LO" LO"^ "^^^^ "^<^-
»- »- 1 " 1 ' 1 ' » ' » * \ / " » f * \ ^^"^ / * I / * S
T^ T^ "^ "~ ^^~ ^JH -^ T^ ^" T^l ^JH
co"co"co"co coco"co"co" c-oco"co"
r-^-,
r^-< ^0
' "" ^"^
^H. /-»-ii
I 1 II
CM" c^T
LO" 10"
^ ^
co" co"
^ ^ CO
Q^ ~>-
|| X
^-L -i.
II II
Q^s Cf^
HI j
II
m 10
Q") CO
- - - -
V V
II II
CO CO
CM CO
-------
"cS
-u f *
CO Q
CD O-
S "O
w g
a OH
X
CD
cu
is- ^
4-3
s
.
o b
>
o Cu
'f CD
>H »!-H ^
£3 43 ex
!2, -^
CD Q^
'S -u
OG3 "O
-u cx
CO CO
+3 (3
S3 O
.2 O
o
fP! 9?
M i !> u
CD co QJ^
8 w
f i . -4-i
o o
'co" _
(H O ~
20 £
>-*
T3
o3
""£3 C3
S c^.
-2
CO
CO
C3
i-J CJj_
S
CD
LO S
JH
f-l CO
LO
oo
LO
^1*
0
i
0
CD
CM
0
i 1
£
i t
CD
CM
CO
^
CD
LO
1 1
CM
i I
oo
t*-
<*
CO
£"
CM
CD
N-
co
CD
CD
O
i H
CM
co
o
T-H
I 1
CM
CM
CD
i
O
^O
£^_
CD
r-H
CD
CM
CD
CD
CM"
f1^.
o
0
s '
^~
t^.
o
CD
T I
O
^*-
T H
CM"
O5
O
CD
_^-^
LO
CD
i t
CD
'
co"
LO
CD
CM
t--
CO
f"^
C~}
1 i
0
CD
oo"
LO
o
s,
LO
oo
LO
^J*
CD
i
05
l>-
CM
CD
0
0
CM
CD
CM
CO
0
LO
T 1
CM
V t
o
LO
-*
LO
CO
CM
CD
CO
CM
^
CD
CD
LO
LO
I 1
05
CO
CD
i I
CM
CM
CD
l
tr-
CD
CD
1
CM
i 1
co
CD
CD
CM"
t~
o
0
** '
'^
t*
o
f~~]
O5
^xh
CO
, 1
OO"
oo
o
o
^ ^
^ ^
C55
LO
T 1
O
^
oT
LO
LO
CD
O5
CO
(~~1
c"~^
, i
0
CD
LO
O
e,
LO
oo
LO
^
CD
1
O
O
i l
CD
CO
O
CO
CD
CM
^O
f1^.
O
LO
1 t
CM
r-H
O5
T^
O5
CM
T 1
t^
T 1
O
co
CM
CD
IO
CO
CD
LO
CM
CO
CD
CM
CM
CD
i
CO
OO
CD
i
LO
CO
^
o
0^
CM"
f^.
CD
CD
^
o"
CD
CD
co"
CD
CD
i i
oo"
LO
0
CD
** '
^^
"^
o
t *
o
^
oo
co
CM
CD
LO"
CM
CM
CD
, t
CD
CD
LO
O
s.
J^
CM
LO
CD
i
O
i l
oo
oq
CD
o
CM
co
CD
t^
CM
CO
O
CO
CM
oq
CD
i l
05
CD
CM
i t
05
CM
O
CO
o
CM
OO
05
T t
O
oo
CO
o
05
co
CM
CD
i
LO
0
CO
(^
CM
LO
CD
i
oo
LO
O5
CM
i-H
o" CM
LO CO
O CM
S- ^
oo" b~
LO CM
O CD
O CD
^ '
i^ co
-xh CM
o oo
S- ^
hT <3>
° ^
T~~l .
£i S
^ CM
t- 00
OO CM
O ^*
^
^ ^
O co
i-i oo
CD O5
O CM
'
t-- C75
05 0
LO O5
CD, CM
CD i 1
t t*~-
i t ^t1
O T 1
o" °5
T 1 CO
S CM
CD 0
ocS" £2
LO ^r
O "*
e °
^
LO
CM
O
CD
OO"
LO
o
d>
x *'
t^
^
o
o
LO"
0*1
Is""
CN
CM"
i-H
r 1
^4
^ '
^~^
LO
t-;
CD
"^ ^
oT
LO
o
o
OO
CO
c3
o"
rH
o
o
i-H
o
CD^
O
CO
CO
CO
O
1
CD
CM
T 1
O
CD
f-^.
T^
CM
CD
^
05
LO
i l
CM
! (
co
i i
^f
CM
0
CD
*
^
O
CD
CM
CM
0
CO
CO
CD
r<
CO
1 1
CD
05
CD
r- 1
O
1
^
O
T 1
^
CO
CD
CO
o
CD^
oo"
I 1
CD
^ '
"^T
CM
11-
0^
co"
1 t
o
o^
LO"
CM
o
CD
S '
_^ ^
O
CM
-------
Table 6: The estimated cumulative risks from the individual model and
the two proposed dose addition approaches for the six chemicals
Individual model Dose- addition model
Chemical
1
2
5
3
4
6
sum
P(d)
0.0024
0.0021
0.0020
0.0031
0.0032
0.0027
0.0155
P(D]
0.3748
0.2396
0.0666
0.0961
0.2544
0.0645
Pa(D)
0.7368
0.5353
0.1616
0.1397
0.3679
0.3052
-------
Table 7: The estimates of the POD, total exposure dose
predicted response (Pred(d#pp)), and cumulative risk
for the six chemicals from the RPF method
Chemical
1
2
3
4
5
6
POD
0.0327
0.0387
0.1782
0.1894
0.0315
0.0019
dRPF
0.1965
0.2324
1.0701
1.1370
0.1892
0.0114
Pred(d/jpF)
-0.4290
-0.4455
-0.5676
-0.5164
-0.4668
-0.3480
P(dHPF)
0.3169
0.2166
0.1079
0.2166
0.0695
0.0552
-------
U.S. Environmental Protection Agency
Region 5, Library (PL-12J)
77 West Jackson Boulevard, 12th Fkxa
Chicago, II 60604-3590
-------
xvEPA
United States
Environmental Protection
Agency
Please make all necessary changes on the below label,
detach or copy, and return to the address in the upper
left-hand corner
If you do not wish to receive these reports CHECK HERE I I.
detach, or copy this cover, and return to the address in the
upper left-hand corner
PRESORTED STANDARD
POSTAGE & FEES PAID
EPA
PERMIT No. G-35
Office of Research and Development
National Center for Environmental
Assessment
Cincinnati, OH 45268
Official Business
Penalty for Private Use
$300
EPA/600/R-03/052
September 2003
www.epa.gov
Recycled/Recyclable
Printed with vegetable-based ink on
paper that contains a minimum of
50% post-consumer fiber content
processed chlorine free
------- |