&EPA
T,
Statistical Policy
ASA/EPA Conferences on
Interpretation of
Environmental Data
I. Current Assessment^
Combined Toxicant Effects
May 5-6, 1986
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PREFACE
This volume is a compendium of the papers and commentaries that were presented at
the first of a series of conferences on interpretation of environmental data conducted by
the American Statistical Association and the U. S. Environmental Protection Agency's
Statistical Policy Branch of the Office of Standards and Regulations/Office of Policy,
Planning, and Evaluation.
The purpose of these conferences is to provide a forum in which professionals from
the academic, private, and public sectors can exchange ideas on statistical problems that
confront EPA in its charge to protect the public and the environment through regulation
of toxic exposures. They provide a unique opportunity for Agency statisticians and
scientists to interact with their counterparts in the private sector.
The holding of a research conference and preparation of papers for publication
requires the efforts of many people. Gratitude is expressed to the ASA Committee on
Statistics and the Environment which was instrumental in developing this series of
conferences. Thanks are also owed to members of the ASA staff and, particularly, Ede
Denenberg, who supported the entire effort. Although there was no provision for a formal
peer review, thanks are also due to the reviewers who assessed the articles for their
scientific merit and raised questions which were submitted to the authors for their
consideration.
The views presented in this conference are those of the individual writers and should
not be construed as reflecting the official position of any agency or organization.
Following the first conference on "Current Assessment of Combined Toxicant
Effects," in May 1986, a second was held in October 1986 on "Statistical Issues in
Combining Environmental Studies," from which a proceedings volume will also be
published. The subject of the next conference, scheduled for May 1987, will be
"Sampling and Site Selection for Environmental Studies."
Emanuel Landau, Editor
American Public Health Association
Dorothy G. Wellington, Co-Editor
Environmental Protection Agency
U.S. Environmental Protection Agency
GLNPO Library Collection (PL-12J)
77 West Jackson Boulevard,
Chicago, IL 60604-3590
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INDEX OF AUTHORS .
AHDERSOH, Perry 30 LITT, Bertram D 44
BRODERIUS, Steven J 45 MACHADO, S.G 22
CHAMOY, Gail 9 MARGOSCHES, Elizabeth H 83
CHEN, Chao 28 MOSKA, Carl 30
CHEN, J.J 78 PATIL, G.P 63
CHRISTENSEH, Erik R 66 SHELTON, Dennis 30
FEDER, Paul 1 19 TAILLIE, C 63
HASS, B.S 78 THORSLUND, Todd W 9
HEFLICH, R.H 78 WEBER, Lavern J 30
HERTZBERG, Richard C 75 WYZGA, Ronald E 84
KODELL, Ralph L 1 YINGER, Elizabeth 30
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TABLE OF CONTENTS
Preface iii
Index of Authors iv
Modeling the Joint Action of Toxicants: Basic Concepts &.
Approaches. RALPH L. KODELL, National Center for lexicological Research 1
Use of the Multistage Model to Predict the Carcinogenic Response
Associated with Time-Dependent Exposures to Multiple Agents. TODD W.
THORSLUND, GAIL CHARNLEY, ICF Clement Associates 9
Discussion. PAUL 1. FEDER, Battelle Columbus Labs 19
Assessment of Interaction in Long-Term Experiments. S.G. MACHADO,
Science Applications International Corporation 22
Discussion. CHAO W. CHEN, U.S. Environmental Protection Agency 28
Concentration and Response Addition of Mixtures of Toxicants Using
Lethality, Growth, and Organ System Studies. LAVERN J. WEBER, PERRY
ANDERSON, CARL MUSKA, ELIZABETH YINGER, DENNIS SHELTON, Oregon
State University 30
Discussion. BERTRAM D. LITT, Office of Pesticides, U.S. Environmental
Protection Agency 44
Joint Aquatic Toxicity of Chemical Mixtures and Structure-Toxicity
Relationships. STEVEN J. BRODERIUS, U.S. Environmental Protection
Agency, Environmental Research Laboratory, Duluth 45
Discussion. G.P. PATIL, C. TAILLIE, Center for Statistical Ecology
and Environmental Statistics, Pennsylvania State University 63
Development of Models for Combined Toxicant Effects. ERIK R. CHRJSTENSEN,
University of Wisconsin-Milwaukee 66
Discussion. RICHARD C. HERTZBERG, U.S. Environmental Protection Agency 75
A Response-Additive Model for Assessing the Joint Action of Mixtures. J.J. CHEN,
B.S. HASS, R.H. HEFLICH, National Center for Toxicological Research 78
Discussion. ELIZABETH H. MARGOSCHES, U.S. Environmental Protection Agency 83
Statistical Directions to Assess Effects of Combined Toxicants. RONALD E. WYZGA,
Electric Power Research Institute 84
Appendix A: ASA/EPA Conference on Current Assessment of Combined Toxicant
Effects Program 89, 90
Appendix B: Conference Participants 91
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MODELING THE JOINT ACTION OF TOXICAHTS: BASIC CONCEPTS AND APPROACHES
Ralph L. Kodell, National Center for Toxicological Research
Introduction
The problem of modeling the joint action of
drags and environmental toxicant* ha* aa*a a
reanrgence of interact recently, dna to a
heightened awareness of the need to protect
haalth and environment, and the attendent
regulatory consideration*. The assessment of
combined toxicant effects falls into the general
framework of a mixture problem. There is a body
of literature that deals with finding optimal
mixtures of various components through the use of
response surface methodology (Cornell, 1981).
This approach has been used successfully, for
example, to describe the effects of cancer
chemotherapy treatments (Carter e_t al_, 1984). In
general, however, the assessment of mixtures of
agents such as drugs and pesticides has tended to
follow a more specialized approach (Kodell and
Pounds, 1985). Most current efforts to study
this type of joint action are based on the
seminal work of practitioners such as Bliss
(1939), Gaddura (1949), Hewlett and Plackett
(1950), Finney (1952), and Loewe (1953). In drug
development, the interest lies both in enhancing
efficacious joint effects and in limiting toxic
joint effects. In pesticide development, the
interest lies in enhancing toxic effects to a
targeted population, while limiting those toxic
effects to untargeted populations. This is
illustrated in Figure 1. In addition, it is
important to know of any inhibitory effects of
one beneficial drug or pesticide on another.
Generally speaking, in modeling the joint
toxic action of agents administered in
combination, the toxic endpoint produced by
individual agents is known, and the objective is
to determine whether the joint toxic action of
two or more agents is in some sense "additive,*
. as opposed to being "synergistlc" or
"antagonistic." In addition to basic research
and development considerations, this has
application in determining acceptable levels of
exposure to environmental toxicants. Various
scientific disciplines are involved, including
biostatistics, pharmacology, toxicology and
epidemiology.
Joint Action Nomenclature
In looking into the problem of investigating
the Joint action of toxicants, one immediately
senses a lack of consistency among investigators
with respect to the nomenclature used to
characterize various types of joint action. For
example, some authors use the term "synergism"
very loosely to describe any enhanced joint
effect, while others use a term "potentiation" to
describe certain types of enhancement and
synergism to describe others. The term
"additivity* Implies the absence of synergism to
some, but is a special case of synergism to
others. Berenbaum (1977) has described the
inconsistent terminology surrounding synergism
quite succinctly, although a bit harshly:
"Synergy, however, is a topic on which confusion
reigns. The relevant pharmacological literature
is often obscure (some papers, indeed, are models
of incomprehensibility) and is profusely littered
with technical terms that are not always clearly
defined. Several different terms are used to
dascrlb* the came phenomenon and the same term
Man* different thing* to different author*."
Wail* clearly there is no consensus with
respect to Joint action nomenclature, there does
seem to be a tendency to classify various types
of joint action into either of two broad
categories, namely, "interactive" and
"noninteractive" action. Under the latter
• category, the concepts of "addition" and
"independence" underlie various null models of
joint action (Table 1). To the pharmacologist
TABLE 1. .Concepts a=d nomenclature associated
with the broad classifications of non-
interactive and interactive joint action.
Noninteractive Action
Addition Independence
Concentration Response Response
Addition Multiplication
Similar Action
Response
Independence
Interactive Action
Synergism Antagonism—
Potentiation
Enhancement
Supra-Addition•
Inhibition
Attenuation
Infra-Addition
and toxicologist, the concept of addition or
"additivity" can imply something about either the
doses (concentrations) or the responses (effects)
of toxicants acting together. To the
blostatistician, addition of doses is In line
with the concept of "similar action," whereas
addition of responses is related to the notion of
"independence" of action. To the epidemiologist,
the concept of additivity relates only to the
responses of jointly acting toxicants, and stems
from the notion of independence of action. The
epidemiologist includes the concept of
"multiplication" of responses as a form of
noninteractive joint action, in the sense that it
can be interpreted as a type of independence of
action. Table 2 gives a cross-classification of
basic concepts by scientific disciplines.
In the category of Interactive joint action
are included the various departures from additive
and Independent joint action. These interactions
are often classified as either "synergistic" or
"antagonistic," although Increased effects are
sometimes described as exhibiting "potentiation"
or "enhancement" rather then synergism, and
decreased effects as exhibiting "inhibition" or
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• -v< ' ...,.V f. , -', • ' , • ''' " . ' "' ' ' "V" ' " " ."
^•~-^visu^^
TABLE 2. Concepts of noninteractive joint action,
cf.egorized by scientific disciplines in
which they are used. Cell entries
represent terms or notions within each
discipline chat are conmonly used to
describe the concepts of noninteraction.
An empty call implies that the discipline
does not embrace the concept.
"X. Null
X.todel
Disciplines.
Toxicology/
Pharmacology
Epidemiology
Biostatistics
Concentra-
tion
Addition
Addicivity
Simple
Similar
Action
Response
Addition
Summation
Additivity
Uncondi-
tional
Independence
Response
Multipli-
cation
Multipli-
cation
Conditional
Independence
"attenuation" rather than antagonism (Table 1).
Numerous other terms have been used to describe
interactive joint action, including supra- and
infra-addition, super- and sub-addition, hyper-
and hypo-addition and hyper- and
hypo-multiplication.
Null Models for Noninteractive Joint Action
The primary focus of this paper will be on
null models of concentration and response
additivlty as applied in a pharmacological /
toxicological context. These models and concepts
win be discussed initially. Following this, a
.less-detailed discussion of the additive and
multiplicative models of relative risk employed
in epidemiology studies will be given.
The basic approach to modeling the' joint
action of two (or more) toxicants is founded on
tolerance distribution theory. That is,
individuals are presumed to have varying degrees
of tolerance to a particular toxicant, thus
implying a probability distribution of
tolerances. Dose-response models are formulated
without attempting to Identify specific
underlying mechanisms of action of the toxicants
under study. Pharmacological foundations for
joint action studies are often attributed to
Gaddum (1949) and Loewe (1953, 1957), while
biostatistical modeling has been developed by
Bliss (1939), Flnney (1952, 1971), Hewlett and
Plackett (1950, 1959), Plackett and Hewlett
(1948, 1967), Hewlett (1969), Ashford (1958) and
Ashford and Smith (1965). There has been some
attempt to formulate more refined models in terms
of their biological basis. For example, Ashford
and Cobby (1974) developed a class of joint
action models based on receptor theory and the
law of mass action, following work by Plackett
and Hewlett (1967) and citing the early work of
Gaddum (1936). This work was followed—up by
Ashford (1981). Although there has been some
application of this theoretical approach (e.g.
Chou and Talalay, 1983; Svensgaard and Crofton,
1985), virtually all practical investigations of
joint toxic action have followed the tolerance
distribution approach.
As alluded to above, generally the
dose—response models that have been* formulated
for noninteractive joist action are based either
on concentration addition or on response
addition, or at least they include theae types of
joint action as special eases. Among the author*
who have adopted the concept of concentration
addition in modeling noninteractive joint action
are Smyth vt^ al. (1969), Casarett and Doull
(1975), Piserchia and Shah (1976), Berenbaum
(1977), Eby (1981), and Unkelbach and Wolf
(1984). Among those who have modeled
noninteractive joint action on the basis of
response addition are Webb (1963), Holtzman et
al. (1979), Wahrendorf et al. (1981), Ozanne and"
Mathieu (1983) and Machado and Bailey (1985).
Authors who have aodeled on the basis of both
concentration addition and response addition
include Broderiua and Smith (1979)', Shelton and
Weber (1981), Chou and Talalay (1983), Kodell and
Pounds (1985), Christenaen and Chen (1985), and
Chen et al. (1985). The terms "concentration
addition" and "response addition" were introduced
by Shelton and Weber (1981). Their idea of
response additivity is slightly more general than
its use in this paper. Loewe (1953) used the
terms "iso-addition" and "hetero-addition" to
describe a broad concept of concentration
addition and a narrow concept of response
addition, respectively. Steel and Pecknan (1979)
introduced the notion of an "envelope of
additivity" that is bounded by Loewe's iso- and
hetero-additivity.
Concentration JVdditivity
Some of the principles and concepts that
underlie concentration addition will be given
prior to presenting a formal mathematical
definition. Under the broad category of similar
action, Bliss (1939), Pinney (1971) and Hewlett
and Plackett (1959) all expressed the principle
that two toxicants have the same site of primary
action, while Ashford and Cobby (1974) expressed
the principle that both toxicants act at all the
same sites. Hewlett and Plackett (1959) regarded
similar action as meaning that the physiological
effects leading to the response are additive. In
this sense of additivity, they allowed for
imperfect correlation of tolerances to the two
toxicants. In the narrower sense of additivity
used In pharmacology, the tolerances are
completely positively correlated, but apparently
one toxicant is not necessarily a simple dilution
of the other (Hewlett and Plackett, 1959). In
the narrowest sense of additivity (similar
action) is the concept of concentration
additivity (simple similar action) (Bliss, 1939;
Finney, 1952; Hewlett and Plackett, 1959), in
which one toxicant is simply a dilution of the
other with respect to administrated dose. This
concentration additivity is also characterized by
the perfect positive correlation of the
individual tolerances to the two toxicants
(Flnney, 1971; Hewlett and Plackett, 1959).
Let P(dp denote the probability of a toxic
response to concentration dj^ of toxicant i
(i-1,2) such that
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S^^
for some monotonic function. T (I-1.2)'
toxlSt is a dilution of the1 oth.r, then dl -
«d where p is the relative potency of toxicant
P'to toxicant 1. The probability of a toxi c
response to the combination of ^ and dj,
Illuming concentration addition, Is
The pharmacological approach to asses.ing
addltivity has been through the use
grams (Hewlett, 1969), which are plots
, of dose, of the two toxicants that
y give fixed levels of toxic response. The
tit represents a given constant response
alied an isobols (Figure 2). Under the broad
definition of additivity, these isoboles are
straight lines, but they are not necessarily
Parallel. Under the narrow definition ot
'concentration additivity, vith perfect positive
correlation of tolerances, these isoboles are
parallel straight lines with slope equal to the
neaative of the relative potency.
The biostatistical approach to assessing con-
centration additivity has involved the fitting of
dose-response models. As a simple illustration,
cln-ider the parallel line assay technique
whereby a suitable linearizing transformation
(e.g., probit), Ff) - .^ lo« V 1-
(Flaney, 1971). Setting ^ • 32 yields p -
exp[(a2-ai)/B]. Another simple method^is the
slope ratio assay technique whereby PI •
.
response to d. and d2 is predicted using either
F or P. with estimated parameter values, and the
goodnesl-of-fit of the model is assessed (Kodell
ST Pounds. 1985). Often models °f greater
complexity have been used (Hewlett and Plackett,
1959; Christensen and Chen, 1985).
n.anonse Addltjvit?
- Afl above, some of the principles and concepts
that underlie response addition will be given
orior to presenting a formal mathematical
definition. Under the broad category of
^indent action, Bliss (1939) and Finney
(1971) expressed the principle that two toxicants
have different modes of action, whereas Hewlett
and Plackett (1959) and Ashford (1981) pressed
the principle that the toxicants have different
sites of action. Hewlett and Plackett (1959)
.odeled biological independence without assuming
•tati.tical independence. That 1., their
definition of Independent action allowed for
correlation of tolerances to the two toxicants.
More narrowly, some early investigators (e.g.
Gaddum 1949) modeled independence of action in
the sense of 'absence of synergism," aasuming
perfect positive or negative correlation of
tolerances. In the narrowest sense of indepen-
dence is the concept of simple independent action
(Bliss, 1939; Finney, 1971), which is also called
response additivity. This response additivity is
characterized by zero correlation of the Individ-
ual tolerances to the two toxicants (Bliss , 1S-J9,
Finney, 1971; Ashford and Cobby, 1974).
With P(d.) as defined above, the probability
of a joint toxic response, assuming response
additivity, is
PU^) - P(dt) + [l-P(dl)]P(d2)
- P(d2) + [!-P(d2)]P(d1) .
That is, the response to the second toxicant over
and above that of the first is .imply an added
effect based on the proportion not responding to
the first toxicant, and vice versa. Note that
P(d1+d2) - P(dx) + P(d2) - P(d1)*P(d2) ,
which corresponds to the probability of the union
of statistically independent events. Although
response additivity doesn't mean simply adding
response probabilities, the last expression above
indicates that if these probabilities are small,
then the product, P(d,)*P(d0), will not greatly
Influence the joint ''response. However, some
authors have just added responses, without regard
to their magnitude (Holtrman £t _al_. , 1979; Ozanne
and Mathieu, 1983). This latter approach Is
equivalent to hypothesizing independent action
with perfect negative correlation of tolerances.
The use of isobolograms to identify response
additivity has not been popular, perhaps because
of a lack of agreement as to the shape and
location of isoboles. For example, Webb (1963)
and Hewlett (1969) suggest conflicting shapes and
locations of isoboles for response additivity.
Indeed, Christensen and Chen (1985) demonstrated
various shapes of isoboles under response
additivity.
The biostatistical approach to assessing
response additivity has involved the fitting of
dose-response models. For example, a simple
procedure has been to formulate P(d.+d.) as
W + *2(d2} " Vk^W' for suitably
chosen P. (e.g., Kodell and Pounds, 1985).
P(d.+d2) is predicted from separately estimated
F (d.) functions, and the goodness-of-fIt of the
response additivity model is assessed. Often,
more general models of response additivity have
been used (Hewlett and Plackett, 1959; Shelton
and Weber, 1981).
Application of Concentration and Response
Additivity
The setting of water quality standards for
multiple contaminants is an example of an
activity that requires either knowledge of or
assumption, about the Joint action of these
contaminants. Citing insufficient information on
mixtures of environmental contaminants, the Safe
Drinking Water Committee of the-National Research
Council (1980) stated that estimates of toxicity
from acute exposures will, out of necessity, have
to be based on a nonconservative assumption of
additivity. The Committee went on to cite the
work of Smyth et^ al. (1969), which is based on
concentration additivity, as pertinent.
With respect to carcinogenic effects from
chronic exposure, the Committee favored response
additivity, stating that to estimate
quantitatively the cumulative carcinogenic risk
of several carcinogen., the individual risks
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^&&£&!f^
might b« added. The Committee stated chat this
approach assume* Chat Interactions are not
present and that the risks are small enough so
Chat adjustments for joint probabilities are not
needed.
Let D, and D, denote exposure levels of
toxicants 1 and 2, respectively, that correspond
individually to an acceptable level of risk, R.
To insure an acceptable level of risk, R, to a
combination, dj+dj, of toxicants 1 and 2 under
concentration additivity, then dj^ and dj must
satisfy (Finney, 1971)
Equivalently,
where it1 and IT, are the respective proportions of
toxicants 1 and 2 in the mixture. Under response
additivity, if R la an acceptable level of risk.
for a conibination, d^+dj, of toxicants 1 and 2 ,
then d cannot pose an individual risk exceeding
R and d- cannot pose an individual risk
where
-
exceeding ^
It should be noted that there is a case for
which concentration addition and response
addition are indistinguishable mathematically,
i.e., their predicted joint responses are
mathematically identical. This is the case of
the one-hit model. Suppose that
P(d2) • F2(d2) - 1
With a double logarithmic linearizing transforma-
tion, parallel lines with slope- 1 are obtained,
enabling estimation of X , \2 and the relative
potency, p - ^/ \, where d^jp . Thus, under
an assumed concentration-additive joint response,
d)]
1 -
- X2d2] ,
However, assuming a response-additive joint
response ,
P (dj-hlj) • F^) + F2(d2) - F1(d1)*F2(d2)
- 1 - exp[-X1d1] -I- 1 - exp[-X2d2] - 1
Thus the assumption of either concentration or
response additivity leads to the same predicted
mathematical joint response function. Of course,
this is true also for a strictly linear dose
response model, which Is the limiting form of the
one-hit model aa the dose approaches sero.
Interaction
As indicated earlier, there is no clear
consensus as to what constitutes "interaction" of
drugs or toxicants. In a broad sense, several
authors have expressed the concept that
interaction is characterized by one agent's
influencing the biological action of the other
(Bliss, 1939; Hewlett and Plackett, 1959;
Ashford, 1981). However, there is disagreement
when this broad concept is made more specific.
Plackett and Hewlett (1967) pointed out
differences between their concept of interaction
and that of Ashford and Smith (1965), quoting
their definition of interaction fron an earlier
paper (Plackect and Hewlett, 1952) as follows:
"[Drugs] A and B are said to interact if the
presence of A influences the amount of B reaching
B's site of action, or the changes produced by B
at B's site of action; and/or reversely, with A
and B interchanged." Plackett and Hewlett (1967)
contended that Ashford and Smith's (1965)
definition of "noninteractive" action included
only simple similar action with complete positive
correlation of tolerances and independent action
with zero correlation of tolerances, whereas
their own'definition would include both siailar
action with incomplete correlation of tolerances
and independent action with nonzero correlation
of tolerances as noninteractive.
The use of isobolograms to characterize
"interactive" departures from additivity has
suffered from Inconsistent nomenclature, as
pointed out by Hewlett (1969). Interestingly,
Hewlett (1969) reserved the term synergism to
describe an enhanced effect when only one of two
agents is active individually, using the term
potentiation to describe an enhanced joint effect
for two separately active agents- However, he
described a decreased joint effect in both cases
by the 'term antagonism. Also, Hewlett (1969)
described the joint action of two agents that are
separately inactive but jointly active as
"coalitive." Figure 3 illustrates some commonly
accepted isobolographic representations of
interactive joint action.
With respect to attempting to refine
characterizations of joint interactive effects,
Loewe (1957) seemed critical of the role that
biostatlatica has played in this effort. He was
probably correct, to the extent that he was
saying that tolerance distribution models that
depend on quanta! response bioassay data for
their resolution have limited ability to define
basic biological mechanisms. Plackett and
Hewlett (1967) commented on identiflability
limitations of tolerance distribution models.
The Additive and Multiplicative Models of
Relative Risk
Relative risk is defined as the ratio of the
risk due to a causal agent in the presence of
background risk factors to the risk due simply to
background factors. The additive model of
relative risk used in epidemiology studies
-------
corresponds to response additivity in
pharmacology/toxicology studies. It is based on
an approximation to a model of "unconditional"
independence of events, wherein causal agents and
background factors act independently of one
anther (lothman, 1976; Bogan at al., 1976).
Howavar, It corresponds alao to a model of
mutually exclusive (and therefore nonindepandant)
events (Xodell and Gaylor, 1986). Under the
additive modal of relative risk, the relative
risk due to two agents in combination is simply
the sum of their individual relative risks. More
specifically, B»u - RR1 + K*2 - 1. All
departures from this model are characterized as
either synergistic or antagonistic.
The multiplicative model of relative risk does
not have a corresponding null model in
pharmacology/toxicology studies. It Is based on
a model of "conditional" independence in a
statistical sense, for an event space
appropriately defined (Kodell and Gaylor, 1986),
having arisen originally froc the multiplication
of attributable risks (Walter, 1976; Walter and
Holford, 1978). As its naae implies, under the
multiplicative model of relative risk, the
relative risk due to two agents in combination is
simply the product of their Individual relative
risks. That is, RR^ - RR1 * RRj. Departures
from-this model are termed either synergistic or
antagonistic.
Hamilton (1979) reviewed various measures of
synergism that are employed with two-by-two
tables of cohort data from epidemiology studies.
All have been designed to detect departures from
the additive and multiplicative models of
relative risk. Investigators who have discussed
or used both the additive and multiplicative
models of relative risk are Kupper and Hogan
(1978), Koopman (1981), Thomas (1981),
Siemiatycki and Thomas (1981), Haailton (1982)
and Relf (1984), the latter three being concerned
specifically with Joint carcinogenic risk.
Notably, Hamilton and Hoel (1978) have considered
concentration additivity, response additivlty,
and response multiplication all in the same
context, namely, that of joint carcinogenic risk.
Siemiatycki and Thomas (1981) formulated
several examples of the additive and
multiplicative models in the context of the
multistage model of carcinogenesis. They also
demonstrated a nonidentiflability aspect of these
models, in that data can be consistent with a
particular model even though the underlying
conditions for that model are not met. Hamilton
(1982) also discussed nonldentlfiability aspects
of his postulated multistage model for joint
carcinogenic!ty. It should be noted that apart
from theoretical considerations of
nonidentiflability, simple two-by-two tables of
epidemiologic cohort data, upon which many
studies of interaction of disease risk factors
are (of necessity) based, contain limited
Information about the Joint action of these risk
factors.
Discussion
The study of the Joint action of agents
administered in combination is a very difficult
undertaking both conceptually and practically.
Even though there is common ground among
Investigators of joint toxic action, there It
also a great deal of inconsistency and
disagreement in nomenclature and concepts. It is
recommended that attempts to assess combined
toxicant affects be kept as simple as possible,
In light of the crude data generally available
for auch assessments. Investigators should ha
careful to define their own terms precisely and
to fully understand the terminology of othara.
Tents auch as additivity, independence,
synergism, and antagonism should not be used
loosely. As has been shown, departure from one
type of additivity, say concentration additivity,
might imply another type of additivity, say
response additivity, rather than a synergistic or
antagonistic form of interactive joint action
(Table 3).
TABLE 3. Illustration of incorrect conclusions
that can be reached if only one type of
"additivity" is considered as a model of
noninteractive joint action. The shape
of the underlying dose-response curves
governs the type of error that might be
made.
Dose-
Response
Convex
Convex
Concave
Concave
True
Situation
Concentration
Addition
Response
Addition
Concentration
Addition
Response
Addition
Null
Hypothesis
Response
Addition
Concentration
Addition
Response
Addition
Concentration
Addition
Incorrect
Conclusion
Synergism
Antagonism
Antagonism
Synergism
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-------
"7';'v;" ""--'V ^-'r •'" - ;r 'v .'•* '*' , •'' "•* '^~;-">''>•'**, *'''^_^-W''yp'lfRf";'-* ;"'M',_'vi'fv,^Tr>;7-i~T«^7j'^^\«,'*-'!y%-t *-—»r,rr 7^T^>w^y"^-!-rM'v»^v*rtr?^if'r A*'^**''-*
.;f^^Sl^!*s^^
S
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-------
i .V^-'-iJiO-- ., -. ...
'-.o-i ^-^VlVMA'- --' -'.-
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Joint Action Studies
1
Type of Agent
Drug
I
Type of Effect
Pesticide
1
Type of Effect
intended Adv"98
Nature of Effect
Adverse Intended
Nature of Effect
Therapeutic Toxic
Objective
Toxic Toxie
Objective
Optimal
Mixture
Safe
Mixture
Safe
Mixture
Optimal
Mixture
Safety
Assessment
Concerns
Health
Environment
Scientific Disciplines
T
Pharmacology
Toxicology
Blostatlstlcs
Epidemiology
Figure 1. Schematic representation of opposing objectives in joint action studies, along with
concerns that motivate assessment of combined toxicant effects, and scientific
discipline involved.
-------
Isoboles for
Simple Dilution
Figure 2. Isobologram for assessing joint action. An isobole is a plot of pairs of doses of
two toxicants that jointly give a fixed level of toxic response (e.g., 502). For
a simple dilution, isoboles for various response levels are parallel straight lines.
Isobole for
"Antagonism"
Isobole for
"Additivity"
Isobole for
"Synergism"
Figure 3. Isobologram depicting some commonly accepted, but not universally accepted,
representations of concentration additivity, synergism, and antagonism.
Isoboles for response additivity can lie anywhere within the square, depending
upon the underlying dose-response curves.
-------
USE OF THE MULTISTAGE MODEL TO PREDICT THE CARCINOGENIC
RESPONSE ASSOCIATED WITH TIME-DEPENDINT
EXPOSURES TO MULTIPLE AGENTS
Todd W. Tborsluad and Gail Charaley, ICF Clement Associates
Introduction
In a review of multiple agent dose-response
experiments, Filov et al. (1979) notes that the
observed interaction effects are usually highly
dose-dependent. As a result, such empirical
tests of interaction as proposed by Hamilton and
Hoel (1979), Machado et al. (1983), and Chen and
Kodell (1986) performed at one set of dose levels
may give very little information about interac-
tions at another set of dose levels.
The "high" dose levels for joint effects are
defined as the exposure values where statisti-
cally siznificant increases in cancer risk are
observed in either epider^iological studies or
cancer bioassays. Tor the most part, exposure
to complex mixtures of agents in the environment
is at "low" dose levels, i.e., at least three
orders of magnitude below those at which a cancer
response is observable in laboratory tests. As a
result, empirical tests of interaction observed
in bioassays give little insight into the effects
of complex mixtures at environmental levels of
exposure. To estimate effects at low dose lev-
els, it is necessary to postulate an underlying
theoretical construct for the carcinogenic pro-
cess that can be translated into a mathematical
dose-response model. Such a model will contain
parameters describing various elements of the
process. The joint effect of exposure to a com-
plex mixture is determined by the way in which
individual agents affect the parameters describ-
ing various elements of the process.
The agents in the complex mixture can interact
to affect the process in a variety of ways.
Chemical interaction between agents may create a
different carcinogenic agent. An example of this
in drinking water is the interaction of chlorine
used as a bactericide with naturally occurring
organic matter to form trihalomethanes (Bellar
et al. 1974, Rook 1974). New compounds may form
within the body as well. For example, nitrosa-
tion of certain compounds in fava beans by en-
dogenous nitrite, when both are present in the
gastric lumina, leads to the formation of a po-
tent, direct-acting mutagenic nitroso compound
(Vang et al. 1984).
Complex mixtures can also act to modify the
exposed individual so that the dose at the site
of action for one agent is dependent upon the
exposure levels of the other agents in the mix-
ture. Any event that affects the absorption,
distribution, metabolism, or elimination of a
compound will affect the level of that compound
that is available to react with DNA or other
target species. For example, simultaneous oral '
exposure to disulfiram (Antabuse) and inhalation
exposure to ethylene dibromide can greatly in-
crease the hepatocarcinogenicity of the latter.
This increase is thought to be a result of the
inhibition of acetaldehyde dehydrogenase by
disulfiram, leading to the buildup of toxic me-
tabolites of ethylene dibromide in the liver
(Wong et al. 1982). Another example is exposure
to cigarette smoke, which can induce the levels
of cytochrome P450 and aryl hydrocarbon hydro-
xylaae that metabolize polycyclic aromatic hy-
drocarbons (Conney et al. 1977), resulting in
higher intracellular levels of reactive deriva-
tives capable of forming adducts with DNA.
Another way in which biological interactions
can enhance initiation is possible saturation of
the enzyme systems responsible for the repair of
DNA adducts, allowing some to go unrepaired and
thus leading to mutation (Thilly 1983).
All such chemical-biological interactions are
the result of reactions at many cellular sites
with multiple molecules of the agents. As a re-
sult, mathematical models of the cancer response
that depend upon such mechanisms would be non-
linear at low doses. For example, if two chemi-
cals combined to tora a carcinogenic agent, the
rate of formation would be proportional to the
product of the concentrations of the two chemi-
cals. A linear reduction in the concentrations
of the chemicals would thus result in a quadratic
reduction in the formationof the carcinogenic
agent.
The nonlinearity of the typical chemical-
biological interaction strongly suggests that
mechanisms of carcinogenicity that depenc upon
such interactions are only marginally important
at environmental levels of exposure. Even so,
any information about chemical interactions or
exposure modification should be used in the
formulation of a model of the joint effects of
agents, if available, by estimating exposure at
the cellular and molecular levels. For the math-
ematical model of the carcinogenic response dis-
cussed in the next sections, it will be assumed
that the best available surrogate measure of dose
at the site of action is used as the dependent
variable.
Multistage Model
The most utilized quantitative model of the
carcinogenic process is the simple multistage
model described by Armitage and Doll (1954).
This multistage model provides a satisfactory
explanation of the power law for the age inci-
dence of many forms of epithelial carcinoma. It
also explains the time-dependent effects of vari-
able exposures, including cigarette smoking
(Armitage 1985). The multistage model is based
upon the assumption that the carcinogenic process
is a series of ordered, irreversible transforma-
tions in a single cell. After going through a
fixed number of transformations, a cell is con-
sidered to be a tumor that will grow and be ob-
served some time in the future.
If these transformations occur at the molec-
ular level, it is reasonable to assume that a
single molecule of an agent, if it enters the
critical reaction, can cause the transformation
from one stage to the next. Under this assump-
tion, the probability of a transformation is
-------
linearly related Co the degree of exposure at the
molecular level.
Tor constant exposure to a single agent, the
transformation rate from stage i to stage i+1 may
b* expressed as
more and Keller (1978) , we define the following
variables :
P. (t) - probability that a cell is in the
t\\
i stage at time t and
where
o. • background transformation rate,
0 - transformation rate per unit of expo-
sure , and
x • a constant that is directly proportional
to the best surrogate measure of expo-
sure at the site of action.
Assuming that there are a total of k stages and a
fixed time w fron the appearance of a cell in the
kth stage to deatr. by a tunor, the age-specific,
agent-induced cancer death rate [h(x,t)J is ex-
pressible as
k-1
h(x,t) • H (a.+B.x)
i-0
/(k-1)!, (2)
where
age attained.
The probability of death from a tumor by age t in
the absence of competing mortality is simply
P(x,t)
1-exp -/wh(x,v)dv -
(3)
1-exp - n (a.+B.x) (t-w)*Yk!
i-0
The derivation of these results is presented
clearly in the recent Armitage (1985) paper.
Generalization of Multistage Model to Account for
Variable Exposure to Multiple Agents
The multistage model has previously been gen-
eralized to account for either exposure to mul-
tiple agents or variable exposure over time.
Whittemore and Keller (1978) describe the complex
equations that can be used to obtain estimates of
risk under variable exposure conditions using the
multistage model. Day and Brown (1980) give re-
sults for the case where observation continues
after exposure ends. Crump and Howe (1984) de-
rive an expression for the special case where one
or two specified stages of the multistage process
are assumed to be exposure-dependent, and expo-
sure is taken to be a time-dependent step func-
tion. The multistage model has also been modi-
fied by Siemiatycki and Thomas (1981) , Hamilton
(1982) , and Reif (1984) to account for exposure
to multiple carcinogenic agents under constant
exposure conditions.
To generalize the multistage model to account
simultaneously for variable exposure and multiple
agents, we start with a time-dependent exposure
model. Following the approach taken by Whitte-
X.(t) • transition rate from the i to the 1+1
stage at tine t.
The probability that a cell is in the 1C stage at
time t (given that it is in the initial untrans-
formed state at t • 0) can be described by the
following set of simple differential equations:
dPQ(e)/dt — xQ(t) pQ(t) PQ(0) - 1
d?1(t)/dt — \1(t)P1(t) Pi(0) - 0
dP, (t)/dt
K.
X. ,(t)P. , (t) P, (0) » 0 U)
lC~ — K." 'i. K.
To account for exposure to multiple carcino-
genic agents, we define the transition rate to be
Xt(t)
(5)
where
" background transition for i. ' stage,
number of agents,
1 if the jth
.th
agent affects the i
"ii stage
J 0 if otherwise,
6. . • unit exposure transition rate for
j agent on i stage, and
x (t) » exposure to j agent at time t.
This formulation assumes that each of the mol-
ecules or produced radicals from all of the
agents are acting independently of each other
with regard to their probability of causing a
cell transformation. This is reasonable when
cell transformation probabilities for a single
cell are very small, as would be the case when
some individuals in the exposed population are
free of the tumor in question.
Since the probability that a single specified
cell will be transformed is very small, it fol-
lows that to a close approximation, PQ(O • !•
Using this assumption, Whittemore and Keller
(1978) showed that the preceding set of differen-
tial equations has the following approximate
iterative solution:
PQ(t) -
Pi(t) '
Xi-i(v)Pi-l(v)dv
(6)
In addition, we assume that
o The time required for a cell in its kth
transformed state to grow into a death-
-------
' '.. • ,.' •''."'.,' * "•'•':"''. (^'•,f
•&&$^^\&\*ii.^i fe if* r«^-^aS&S^iV^t<2^ii-::•.
causing tumor is approximately constant and
equal to the value w;
o The probability that a given cell will cause
• tumor death is very small;
o An organ contains H cells of a specified
type, each one of which is capable of caus-
ing a tumor death;
o H is very large;
o Each of the cells acts independently with
regard to undergoing transformations and
causing a tumor.
Then, the age-specific death rate associated with
a specific type of tumor in a given organ may be
expressed, to a close approximation, as
h(t) • N[dP, (t-w)/dt] « N'X. . (t-u)P, (t-w),
K tC~* K."~i
(7)
and the probability of death from that tumor by
age t in the absence of competing risk is
P(t) - 1 - exp - /Q h(v)dv .-
1 - exp - /* N[dPk(v-w)/dv]dv.
(8)
To illustrate how equations 5 through 8 can be
used to estimate the risk associated with mul-
tiple-agent, time-dependent exposures, several
simple examples will be presented in the follow-
ing sections.
Example of Interaction Effects for' Multiple
Agents with Continuous Exposures at Constant
Levels
For continuous, constant exposures, the trans-
ition rates are constants (over time) that are
obtained from equation 5 by substituting x-t for
x^(t). Using this notation, the transition rates
have the form
V ' xi' "i * Ji au Vj' (9)
and the possibility of a death from a tumor by
time t is
PCxj^....,*„.*£_• 1 - exp -
n X.(t-w)k/kl
i-0 1
At low environmental levels of exposure,
P(Xl,x2,...,Vt) : [JQ Xt]
(10)
t!, (11)
where
k-i k-i k-i t k-l
irXi M iroi + 2 U^aijAif 2 ^ *«*«• <12)
i«o i-o l-o I l-o ' •
since all higher-order exposure terms sre ap-
proximately equal to zero.
A number of important implications follow
from these results. When exposure to multiple
carcinogenic agents occurs, each agent may af-
fect one or more of the transition rates in one
or s»re cell types. If two agents affect dif-
ferent cell types, their effect on the produc-
tion of tuaors will be Independent if the appro-
priate mortality adjustment is made.
The probability of a tumor in this case is
one minus the product of the probabilities that
each agent does not cause a tumor. If the prob-
ability that each agent will cause a tumor is
low, the probability that the joint exposure will
produce a tumor is, to a very close approxima-
tion, equal to the sum of the probabilities that
each agent causes a tumor. Where two agents act
only on the same single stage of a cell type,
the probability tr.at joint exposure will produce
a tunor is equal tc the SUE of the probabilities
for each exposure. When tne agents act on dif-
ferent stages of :r.e sane cell type, there is a
multiplicative exzisure effect tarn as well as
the additive teras.
At high doses, the multiplicative ex-posure
effect term can dominate the carcinogenic joint
response, and the Joint effect can be much
greater than the sum of the individual effects.
However, if both exposures are reduced by sev-
eral orders of magnitude, the joint effect would
be, to a very close approximation, equal Co the
sum of the individual effects. The same results
hold when hundreds of compounds are combined.
If each one is reduced three or more orders of
magnitude, the deviation from additivity is not
an appreciable relative amount. As a result,
the multistage model predicts additivity at en-
vironmental exposure levels for almost all situ-
ations that would be routinely encountered.
The main exception to this rule is when one
of the agents remains at a high level. In these
•cases, the incremental risk associated with ex-
posure to low levels of an agent can be dominated
by its multiplicative interaction with exposure
to high levels of another agent. As a result,
particular concern must be paid to agents that
affect the same cell type as cigarettes, since
cigarettes are the single deliberately uncon-
trolled carcinogen to which we are exposed at a
high level in our environment.
To demonstrate the general premise that under
multistage theory, an observed extensive syner-
glstic effect in a multiple-agent bioassay does
not imply a major departure from low-dose addi-
tivity, the following numerical example is given.
Simplest Multistage Model that Results in a
Synergistic Effect
The simplest multistage model that results in
a greater than additive effect arises from the
assumption that each of two agents affects the
transition rates of different single stages in
the multistage process.
Thus, for two agents (m « 2), if the first
agent affects the ic^ and the second, the jtn
stage and no other transition rates are affected,
it follows that
-------
u
Example of Interaction Effects when Multiple-
Agent Exposures are not Continuous and
Concurrent over Time
Substituted Into equation 5, this gives the
result
Xi -
j
6
j2
Variable and noncontiguous exposure patterns
•ay be accounted for by treating the time-
dependent exposures, xj(t), aa specific step
functions that allow equation 4 to be solved in
a closed form. The following simple example il-
lustrates this general approach.
Consider the case where exposure is to two
agents (m - 2) with the following exposure
patterns:
Assuming that competing mortality from causes
other than the tumor under Investigation is min-
imal at the termination of the experiment, the
probability that a tumor will be observed may be
expressed as
Vc) - o
x2(t)
elsewhere
elsewhere
(15)
(13)
where
11
B2 '
s, » starting cizie of exposure to first
agent,
f. • stopping tine of exposure to first
agent,
Consider a model of the form of equation 13
that has the following properties:
s. - starting time of exposure to second
agent, and
o One agent is twice as potent as the other,
o 0.1 of one agent and 0.2 of the other gives
about a 9% response in a. bioassay if each
agent is given by itself,
o Responses at exposures of 1-10 of the
single agent values give a risk of 1-10-5
for each agent singularly and 4-10-5 for
joint exposure to both agents, and
o The background risk is about 5-10~6.
A numerical model that meets these conditions
f^ " stopping tiae of exposure to second
agent.
It is assumed that xi(t) affects the first stage
only and that X2(t) affects the last or kth
stage only. Under this assumption, the transi-
tion rates have the following time-dependent
form:
°0B01X1 91 * t « fl
P(xrx2)-l-exp (-0.000005) (1+189,
or
P(x , xJ-l-ex?-(0. 000005+0. 948640x +0.474320x2
+89,991.8x^2).
This model implies that to achieve a meaning-
ful (i.e., doubling) joint exposure effect at low
environmental doses, the joint experimental syn-
ergistic effect would have to be very large.
Two agents given together at levels of about
5% of the single-agent doses would produce about
a 992 response, while the single-level doses
given by themselves would yield about a 9% re-
sponse. An interaction of this magnitude is un-
precedented. This hypothetical situation is
depicted in Table 1.
In the next section, implications concerning
the ordering of exposure will be investigated.
X (t) - a s=l,2,...,k-2 0 < c < » (16)
S S
t < s.
(1)
\-lW ' X " Vl+Bk-1.2x2 Vt
-------
where
k-2
A- H a/(k-l)!.
J-0 J
for w - 0, Che age-specific rat* defined in
equation 7 is
h(t) - NX. ,(t) P. _.(t).
Since Pfc-iCt) ia functionally dependent upon
BI and f i and \t_i(t) is functionally dependent
upon 82 and f2, it follows that h(t) , as defined
in equation 16, is dependent upon the ordering
over time of sj,, f]., 32, and f2- For example,
if si
32
that
of \fc_i (t) and ?k-l(t) have the time-dependent
representation
X ? t f^t i
where the X and P are defined in equations
16 and 17, respectively. A schematic representa-
tion of equation 19 that illustrates how the
structural form of the age-specific rate.is time-
dependent is shown in Figure 1. Other structural
relationships can be derived in the same manner
for alternative orderings of the exposures.
To explore the effect of the timing of expo-
sure on the interaction or synergism of the
agents, we will estimate "relative risks" for the
following situation. It is assumed that agent
exposures were selected so that each of the
transition rates is increased by a relative fac-
tor of A during the exposure interval. This im-
plies that
301X1
3k-1.2*2
Vl
i.
equation 21 and used to obtain the relative risks
also depicted in Table 2.
The results obtained using this approach con-
form to one's intuitive sense of reasonableness.
Ho synergism (i.e., effect greater than one) ex-
ists if the exposure that affects the last stage
•ads before the exposure Chat affects Che first
stage begins. Also, Che greatest synergism ex-
ists when exposure that affects Che first stage
(18) ends before that which affects the last stage
starts. In this situation, the relative risk
rises slightly from I + A/3 to 1 + a/2, as the
number of stages increases from k - 2 to k » «.
In contrast, the relative risk decreases rapidly
from 1 + A/4 to 1 as the number of stages in-
creases from k » 2 to k » «, for the situation in
products which both exposures are given during the same
half of the time period. It is possible to de-
rive comparable results for any set of assump-
tions about the stages affected and any step
functions of exposure. However, the algebraic
fora aay be very cc-plex.
In the final section, the most important prac-
tical problem concerning joint exposure will be
investigated — nanely, how to cope with the
potential interaction of cigarette staoke and
other carcinogenic agents.
Joint Effect of Cigarette Smoke and Other
Agents on Respiratory Cancer
As a first step in attempting to estimate how
siEoking cigarettes tsocifies the quantitative ef-
fect of other agents on cancer rates, it is nec-
essary to develop a model for the effects of
cigarettes alone. Ideally, we would use the
combined data from as many sources as possible
in such an endeavor. Unfortunately, the only
data currently available in the open literature
in a form amenable for fitting with a multistage
model are found in the Doll and Peto (1978)
paper; they are reproduced here as Table 3. It
is recognized that a number of problems exist in
using these data. Among the more important are
the following:
o British cigarettes and/or smoking patterns
(20) are different from those in the United
States.
Under this assumption, the relative augmented
risk for the two exposures given together, as
compared to the sum of the two given separately,
can be derived. For most situations at environ-
mental levels of exposure, this relative risk in
the absence of competing risk may be expressed as
R*(0,t) - /C {h[x.(v),x,(v)]-h(0,0)} dv
0
* /C lh[x.(v),0]+h[0,x,(v)]
0
-2h(0,0)} dv. (21)
The age-specific cancer rates for the four
combinations of exposure depicted in Table 2 are
derived in a Banner analogous to the preceding
example. These rates are then substituted into
o The data are in a form that results in a
loss of information, since they are com-
bined into various groupings rather than
being presented for each individual.
o No information is given on rates after the
cessation of smoking.
It is hoped that the availability of addi-
tional U.S. data and more complete data for the
Doll and Peto (1978) cohort will eliminate these
problems in the future. However, for the present
we will fit the data given in Table 3 to various
forms of the multistage model to illustrate the
general approach for predicting the modifying
effect of cigarettes on the cancer potency
of other agents.
It is assumed that the 1 and k stage of a
k-stage model are affected by cigarettes. In
-------
;^
we assume that each individual in the
siting at age 91 and continued un-
Oor
til the end of the observation period. Also, we
I^a constant lag or weighting tt»e of length
? which will be estimated fro. the data. Under
thJUi S^Ptlona, the equations for the transi-
tion rates «y »• «*P""«d •»
6oixi(0
1 - 1,2,.... k-2 (22)
where the number of cigarettes smoked per day has
the functional form
x,(t)
sl - c
elsewhere.
„
To laconorac. a const.ut las f-ra of
»ith «-• 1° ••M
tory cancer may be written as
A(t-w)
k-1
w < t < S.-
h(x,t) »
(23)
A(t-w)
k-1
If k-4, then 13.9 < w < 23.3
If k-5, then 4.8 < w < 22.2
If k-6, then 0 < w < 14.2
However, l£k<3ork>7, the fit la statisti-
cally rejected at the 0.05 level for all values
of w. If the data on risks after the cessation
of smoking were available, it is likely that
only a k of 5 or 6 would fit the data; we would
expect a short lag because risks fall quite
quickly after smoking is stopped.
For the purpose of illustration, we will use
our best-fitting model to predict the effect of
smoking on the augmented risk associated with
another agent. If it is assumed that a second
agent affects the 1st stage of the multistage
process, the transition rate for the 1st stage
is expressed as
v° - v
For the case where x?(t) » X2 for all t, the age-
specific rate under this added assumption has the
form
A(t-w)k"1[l-t-B02x2] w < t < SL + w
h(x,,x,,t) - (25)
^k-l
^oiV^'V'
where
where
k-1
A • n a
3-0 3
The parameters A, BQ1, Bk_j. i, and w can be
estimated from the data in Table 3 using the max-
Srtikelihood method. To do so, it is assumed
that the observed number of respiratory cancer
detths in each cell has a Poisson distribution
££ mean hU.OFl, where PT is the total number
of oerson-years observed for each cell. The
°plrPameter estates that maximize the likelihood
are shown in Table A. The goodness of fit of the
Sel ^illustrated in Table 5. It is assumed
^hat for each cell, ^ equals 19.2, the average
age at which people started smoking for the en-
tirThe0parameters k and w are highly negatively
correlated, so that other estimates give almost
as good a fit. Models that contain values for
k and w that fall in the range shown below do
not give a statistically significant worse fit
at the 0.05 level, as measured by the log likeli-
hood criteria, than the best fit shown in
Table 4.
B02 * VV
To obtain information about the parameter
it is assumed that an animal bioassay is avail-
able. In terms of our previous parameters, the
probability of response for the animal may be
expressed as
P(x2,t)
BQ2x2
(t-w)*]
(26)
k
Of course, only the whole term, (A/k)Bn_(t-w)
can be estimated from the quantal animal data
alone; however, in conjunction with the human
data, 892 may be estimated separately.
The augmented risk associated with continuous
exposure to 12 while smoking x; cigarettes per
day from age S]^ to t under the assumption of no
competing risk may be expressed as
(27)
P(x2/x1,t)-[l-exp-;oh(x1,x2,v)dv]-
tl-exp-/Qh(x1>o,v)dv] .
For a low background rate, the augmented risk is,
to a close approximation,
.k
t-w)
s+w < t (28)
-------
To illustrate the general approach, w« shall
assume that the bioassay gave a linear tern esti-
mate of
f
t-w)* • 0.2.
Substituting this value and v - 13.642, t « 70,
• • 19.2, and BV-! 1 " 0.31044 into equation 28
gives the numerical result _ ^ t -,>
P(x2/x1,t-70)-0.2x2
D.31044x
•0.2X-+0.0618X.X-.
Let us assume that without cigarette use the
predicted risk is I'lO based only on the animal
bioassay. This implies that x_ equals 5'10~5.
"sine equation 29, we calculate the augmented
risk associated with the second agent alone in
the presence of cigarette smoke for individuals
who started sacking at age 19.2 and continued
until death or age 70. These results are de-
picted in Table 6.
Thus, a person who smokes tuo packs a day in-
creases his or her augmented risk by more than
one order of magnitude. The interesting philo-
sophical public health question arises: Does so-
ciety have the responsibility for protecting an
individual from a second agent that increases the
involuntary risk by about 1-10-^ if the individ-
ual smokes two. packs a day, when the voluntary
risk he or she assumes for smoking is about
1-10~1 or three orders of magnitude higher.
Ic summary, the approach suggested here to
adjust for cigarette use employs
o Human data to estimate the effects of ciga-
rettes,
o A""1""*1 data to estimate the effects asso-
ciated with the second agent, and
o Multistage theory to predict the joint ef-
fects of cigarettes and the second agent in
the absence of any actual joint exposure
data.
REFERENCES
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ARMITAGE, P., and DOLL, R. 1954. The age-
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CHEN, J.J., and KODELL, R.L. 1986. Analyses of
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CONNEY, A.H., PANTUCK, E.J., HSIAO, K.C., KUNTZ-
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CRUMP, K.S., and HOWE, R.B. 1984. The Multi-
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JNCI 64:977-989
DOLL, R., and PETO, R. 1978. Cigarette sacking
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non-smokers. J. Epideniol. Communitv Health
32:303-312
FILOV, V.A., GOLV3EV, A.A., LIl'ELINA, E.I., inc
TOLOKO;,TSIV, N.A., eds. 1979. Quantitative
Toxicology. John Wiley & Sons, New York
HAMILTON, M.A. 1982. Detection of interactive
effects in carcinogenesis. Blomed. J.
24:483-491
HAMILTON, M.A., and HOEL, D.G. 1979. Detection
of synergistic effects in carcinogenesis.
• Unpublished manuscript
MACHADO, S.G., SHELLABARGER, C.J., and LAND, C.E.
1983. Analysis of interactive effects between
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experiments. Unpublished manuscript
REIF, A.E. 1984.
JNCI 73:25-39
Synergism in carcinogenesis.
ROOK, J.J. 1974. Formation of haloforms during
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SIEMIATYCKI, J., and THOMAS, D.C. 1981. Bio-
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An example from multistage carcinogenesis.
Int. J. Epidemiol. 10:383-387
THILLY, W.G. 1983. Analysis of chemically in-
duced mutation in single cell populations.
In C.W. Lawrence, ed. Induced Mutagenesis:
Molecular Mechanisms and their Implications
for Environmental Protection. Plenum Press,
New York, pp. 337-378.
WHITTEMORE, A., and KELLER, J.B. 1978. Quanti-
tative theories of carcinogenesis. SLAM Rev.
20:1-30
WONG, L.C.K., WINSTON, J.M., HONG, C.B. and
PLOTNICK, H. 1982. Carcinogenicity and tox-
icity of 1,2-dibromoethane in the rat.
Toxicol. Appl. Pharmacol. 63:155-165
YANG, P., TANNENBAUM, S.R., BUCHI, G. , and LEE,
G.C.M. 1984. 4-Chloro-6-methoxyindole is the
precursor of a potent mutagen (4-:hloro-6-
methoxy-2-hydroxy-l-nitroso-indolin-3-one
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5:1219-1224
-------
^I2^^
FIGURE 1
SCHEMATIC REPRESENTATION OF THE TIME-DEPENDENT,
ACE-SPECIFIC DEATH RATE SHOWN IN EQUATION 19
WEI.
P(U
sl 32 f2
NOTE: X is defined in equation 16 and P , in equation 17.
TABLE 1
BIOASSAY DESIGN
Xl
x2 0 1.05414-10"5 4.8743-10"3 l-lfl"1
0 0 1-10"5 — 9.0503-10"2
2.10828«10~5 1-10"5 4-10"5
9.7486'10~3 — — 9.852-10"1
2.10"1 9.0503'10"2
NOTE: This is the design required to estimate an interaction
tern large enough to double the risk over that predicted
by additivity at environmental levels of exposure.
Underlining indicates a test group in the hypothetical
bioassay.
-------
>'.: ..:It&'':^:&&^
TABLE 2
RELATIVE AUGMENTED RISK {R*) OF JOINT EXPOSURE COMPARED WITH
SUM OF RISK ASSOCIATED WITH SINGLE EXPOSURES
0] + h(0,x2(v)l - 2h(0,0)|dv
Tine Interval
0 to t/2 t/2 to t
.. _____ Functional
No. x.(t) X2(t) x^t) ' Xj(t) Fora of R« k«2 k«5
10 0 x. x- 1 + A/2k I * •J 1 + A 1
2 0 x2 xj_ 0 1 111
3 Xj^ 0 0 x2 1+ A(2 fc
4 x, x, 0 0 1 + A/2*
TAOLZ 3
• tSPHUTOBt CANCER DATA rROM DOLL AND PETO (UH)
Elpoiuc* (Ci9*c«ttta p«r o>yl — «
H«0i«n A««
42. S y««t« old
•No. of eanetcs ob«*rv*d
No. e( p*r>on-ytar« ob>tfr«d
47. S y*>c« old
No. ot p«CBon-y««c» ooa«EV«d
S2.S y»«n old
No. o( eaneto ob»i**d
Ho. 0( p«rion-y«»r» obl«tv*d
51. S y««n old
No. o( ptcion-ytao oburvtd
t2.S year* old
Ho. of eancara ooa«rv*d
No. of patcon-yoaca obaocmd
»7.5 yvaca old
Ho. of camera obatrvod
No. of paraon-yoara obaocvod
72. S ycaca old
No. of cancats obatrvad
Ho. of p*raon-y*ara obmved
0.0
0.0
17,I4(.J
0.0
15, 132.5
1.0
12, 224.0
2. 0
1,105.5
0.0
«. 241.0
0.0
4,111.0
1.0
2,723.5
2.7
0.0
1,214.0
0. 0
1,000,5
0.0
153.5
1 0
1* u
425.0
1.0
505.5
0.0
3*2.5
1.0
242.0
4.4
0.0
2,041.5
0.0
1,745.0
0.0
1,542.5
0.0
1,355^0
1.0
1.0(1.0
1.0
143. J
2.0
494.5
11.)
1.0
3,795.5
1.0
3.205.0
2.0
2.727.0
"1.0
2,2(8.0
1.0
1.714.0
1.0
1,214.0
4.0
142.0
14.
0.
4.124.
|a
3,995.
4.
3,271.
Q^
2, 4<4l
2.
1,»29.
2.
1.217.
4.
413.
0
0
0
Q
0
0
J
g
S
0
:
0
0
0
S
20.
1.
7,044.
^
4,440.
4.
S.5I).
•
4.157.
11.
2.0(1.
12.
1.1)0.
10.
1,055.
4
0
0
Q
5
0
0
g
S
0
5
0
0
0
0
25.
0.
2,523.
7
2.545.
3.
2, (20.
C
2.101.
4.
l.SOt.
S.
974.
7.
527.
4
0
0
g
5
0
0
g
5
0
5
0
I
0
0
30.2
1.0
1.715.5
2 0
2.123.0
3.0
2,224.5
( 0
1, 923^0
11.0
1.1(2.0
9.0
7(1.5
2.0
317.5
31.0
0.0
192.5
0 0
1.150.0
3.0
1,211.0
4 Q
1.0(3.0
7.0
124.0
9.0
515.0
5.0
213.0
77.5 y*ara old
Ho. Of canctra obittv«d 2.0 0.0 0.0 4.0 5.0 7.0 4.0 2.0 2.0
HO. of paiaon-ycaca oba«c««d 1,772.0 201.5 517.5 547.0 370.5 912.0 209.5 130.0 11.5
NOTE: HO. of person-years obatrved cetera to the total nuaber oC peraon-yeara obaerved in that aqe group at
that expoaure level.
-------
TABLE 4
RESPIRATORY CANCER AND CIGARETTE SMOKING DATA:
MAXIMUM LIKELIHOOD ESTIMATES OF
PARAMETERS IN THE MULTISTAGE MODEL
Coefficient Maximum Likelihood Estimate
A 0.283404971489-10"10
BQ1 0.575320316865
Bk.1(]> 0.310436883121
Lag tine (w) 13.6420002494
NOTE: This is a five-stage model; stages 1 and 5 are affected
The age at the beginning of exposure is 19.2 years.
TABU 1
uuiurui u»cii AW ciuirm wuiw OATAI cooiwoi or rir or woci TO ouiiivu O»TA
14.0 10.1 31.4 18.3
41. 1 y.«f A old
•O. o* CAAC.lt oe«.l*»4 0.0 a. 9
41.1 r*A«A 014
•o. Of CAMdl <*MC~< I.I I.I 1. 1 1.1 '.» >-° !•> 1-1 °-°
••. t»i CAAgiH p r«<* •'»
•». 01 CA^c.n MunM 1.1 1.1 I.I 1.0 I.I •• I >•• I.I 4.1
••. *f «i«n«i» fCMlct^ 1. 13311 1. 13111 I.SI7S4 1.7041 1.113? 7.37M 4.1137 1.7344) 4.1431
ta. » r*A«« *14
•>. «l UAC.r. e>A.cra< 1.0 1.1 1.0 1.1 1.1 II. I '.I It. I 7.0
••. 4>f c«MC«(a r(*^kctM 1.3IM 1.11114 0.7li*l 3.3412 3. 1113 I.7f4l 1.4111 7. MSI 4.7731
47. S y«Ail »U
••. 01 CAAC.CI obMC<^4 I.I 1. 1 1.1 3.1 3.0 13.1 S.O 1.0 f.O
•a. of CAMMA pfMictAd 1.1371 1.31717 I. Ills 3.7)11 4.&3I4 10.147 7.23IS 7.3141 7.4411
73.1 y«A(A A14
1.0 4.0 4.9 11.0 7.0 3.9 1.0
77.1 TAAIA old
MO. Of CAOCAtA OOAAIVA4
NTTtl CAllA i«r. e*llAOAA« AO th«t tM *t««ict«« VAlwA 1A ACAACAC tbAA 4M ««I«A I to 3.S. If POAAlAtA. OAOCAAA of
TABLE 6
AUGMENTED RISK ASSOCIATED WITH SECOND AGENT
FOR VARIOUS SMOKING LEVELS
Cigarettes Smoked Augmented Risk
pec Day on Associated with
Average Second Agent
0 1.00-10*1
10 4.09'10~|
20 7.18-10~=
40 13.36-10"5
-------
;..,., •..«--,-.•• _ . ,f-\ • • ;.- ; ... . ,•••-:., ,,,>r.' -. ,,.,,'Ji-ij-'.. ,-• r-- -
^j!&'^L4:::^^^^^>i%^a^s-i^&:^
DISCUSSION
Paul I. Feder, Battelle Columbus Division
I enjoyed reading the Thorslund and Charnley
paper. It 1s well written and presents good
•ethodology and useful applications.
The main theme of the paper Is the description
and estimation of health risks associated with
low dose environmental exposures to «ult1ple
agent mixtures. Determination of the presence,
absence, nature, and extent of Interactions among
mixture components at low environmental exposure
levels 1s of considerable Importance. A key Idea
of the paper Is that the presence or absence of
empirically determined, high dose Interactions
observed 1n laboratory bloassays 1s Irrelevant to
Inferring the presence or absence of interactions
among mixture components at low environmental
levels of exposure.
In order to make definitive statements about
the presence and nature of interactions at low,
environmental exposure levels, 1t is necessary to
understand the biological and cheir.ical mechanisms
by which the mixture components interact with one
another and with the body. There may be chemical
interactions among mixture components;
differential behavior among components with
respect to environmental transformation and fate;
saturation of various Internal enzymatic
processes of metabolism, detoxification, or
genetic repair by some mixture comconents,
thereoy altering the effects of otr.ers. Certain
mixture components may modify the pharmacokinetic
characteristics of other components, thereby
altering their concentrations at the site of
action. Individual mixture components may not be
carcinogenic, Just combinations as with
Initiators and promoters. Any mechanistic
Information concerning the modes of action of the
mixture components and their Interrelations
should be Incorporated Into the dose-response
models that extrapolate the observed high dose
laboratory effects to predict health effects at
the low environmental exposure levels. Thorslund
and Charnley assume away many of these
mechanistic and pharmacokinetic considerations
when they state "...For the mathematical model of
the carcinogenic response...1t will be assumed
that the best available surrogate measure of dose
at the site of action 1s used as the Independent
variable...". This 1s easier to assume than to
verify. In all fairness though, the biological
mechanisms of action are often not very well
understood.
Thorslund and Charnley generalize the
multistage model to account for wltlple agents
and variable exposure. Their models are a class
of empirical dose response models that predict
health effects due to Joint exposure, based on
Individual component data. The models are
motivated by the mechanistic considerations
underlying the multistage model and provide a
plausible explanation of many high dose
Interactions that are observed 1n laboratory
data. In the absence of specific Information
about the nature and extent of the biological
mechanisms and interactions, this class of models
offers a workmanlike approach to describing the
low dose behavior of mixtures and the low dose
Interactions that are operative, among the
mixture components. It provides an empirical
extension of component add1t1v1ty to Incorporate
linear by linear Interaction terms Into the
predictions.
Thorslund and Charnley state "... At high
doses the Multiplicative exposure effect tern can
dominate... and the Joint effect can be much
greater than the sun of the Individual effects.
However, 1f both exposures are reduced by several
orders of magnitude, the joint effect would be,
to a very close approximation, equal to the sum
of the Individual effects... the multistage model
predicts add1t1v1ty at environmental exposure
levels for almost all situations that would be
routinely encountered".
While 1n principle the Thorslund and Charnley
model Implies low dose component addltivity, the
viewpoint above is somewhat of an overstatement.
It discounts pharmacokinetic interactions such as
saturation of elimination or repair processes anc
it ignores the question of *nat constitutes a
"low" dose. Several examples will be presented
below in which the Thorslunc and Charnley mocel
1s predictive of joint toxlcity of a two
component mixture at environmental levels of
exposure, but yet where component additlvity does
not hold. Thus, the Thorslund and Charnley model
1s not synonymous with component additlvity of
r1slcs~at Jow, environmental exposure levels.
Implications of the Thorslund and Charnley *
The simplest example "of tne Thorslunc ana
Charnley model corresponds to the case of a two
component mixture and two stages. Let U, and V
denote the concentrations of components 1 and 2;
assume that each component affects a different
stage. Equation (13) expresses the risk of a
tumor for this special case as
P(U,V) * 1 - exp[-A(l+BU)(l+CV)]
(13)
At low environmental exposure levels, P(U,V) can
be approximated as
P(U,V) s A + ABU + ACV + ABUCV
= POO + P10 + P01 + Pll.
In this expression POO represents the
background risk, P10 and P01 represent the
additional risks due to each component
separately, and Pll represents a linear by linear
Interaction term between components 1 and 2.
When Pll 1s small relative to P10 and P01, the
component additional risks are essentially
additive. Thus, to determine when component
additlvity 1s a reasonable assumption it 1s
necessary to determine conditions under which Pll
1s small relative to P10, P01. The expressions
for POO.PlO.POl.Pll, Imply that
Pll « P10P01/POO - (P10/POO)P01
- (P01/POO)P10.
Thus Pll 1s small relative to P10.P01 1f
P10/POO « 1 and P01/POO « 1.
Define a relative risk as the ratio of the
absolute risk to the background risk. That 1s,
let
-------
R(U,V) • P(U,V)/POO, RIO - P10/POO,
R01 • PO/POO, and Rll « Pll/POO. Then
R(U,V) • 1 + RIO + R01 + R10R01.
The product ter» 1s small If Rll x R10R01 «1.
Therefore, what constitutes a "low" dose In
the Thorslund and Charnley Model depends on the
level of background risk. To have additive
componentwise risks, the additional risks
associated with each component must be small
compared to the background risk, or equlvalently
the relative risks must be small compared to 1.
If the additional risks for each component are
large relative to background, the product term
will dominate; the component effects will appear
to Interact.
Re1f (1984) presents a number of
epldemiological examples that show the
relationship between joint effects and individual
component effects at environmental levels of
exposure. We Illustrate the predictiveness or
lack thereof of the Thorslund and Charnley model
for these examples.
1. Lung cancer associated with smoking
(component 1) and uranium mining (component
2).
POO * .57 x 10"4
POO > P10 » 5.87 x 10
POO + P01 « 2.27 x 10
-4
-4
P10/POO
P01/POO
9.30
2.98.
The additional component risks are large compared
to background. The joint risk estimated by the
Thorslund and Charnley model 1s
104 P
(U,V) * .57 + (5.87 - .57) + (2.27 - .57)
+ (5.87 - .57)(2.27 - .57)/.57
» .57 + 5.3 + 1.7 + 15.81 * 23.38.
The observed value 1s 22.7. In this example the
component additional risks are large relative to
background, the product term dominates, and the
components appear to be Interactive. The
Thorslund and Charnley model is predictive at the
environmental level of exposure but componentwise
additivlty does not hold there.
2. Lung cancer associated with smoking
(component 1) and asbestos work (component
2).
POO
POO + P10
POO + P01
1.13 x 10
12.3 x 10
5.84 x 10
-4
-4
P10/POO « 9.88
P01/POO - 4.17.
The additional component risks are large relative
to background. The Joint risk estimated by the
Thorslund and Charnley model 1s
104P(U,V) • 1.13 + (12.3 - 1.13) +(5.84 - 1.13)
+ (12.3 - 1.13)(5.84 - 1.13)/1.13
- 1.13 + 11.17 + 4.71 + 46.56
« 63.57.
The observed value 1s 60.2. In this example, as
In the first, the component additional risks are
large relative to background, the product term
dominates, and the components appear to be
Interactive. The Thorslund and Charnley model Is
predictive at the environmental level of exposure
but componentwise additivlty does not hold there.
3. Lung cancer associated with smoking
(component 1) and asbestos mining
(component 2)
ROO - 1
ROO + RIO • 12
ROO + Rol • 1.6.
The additional relative risk for smoking 1s large
whereas that for asbestos mining 1s not.
R(U,V) • 1 + 11 + 0.6 + 6.6 • 19.2.
The observed value 1s 19.0. In this example the
component 1 additional relative risk is large,
the product term 1s large relative to the
additional effect for component 2, and the
components appear to be interactive. The
Thorslund and Charnley model is predictive at the
environmental level of exposure but componentwise
additivlty does not hold there.
4. Abnormal sputum cytology associated with
smoking (component 1) and uranium mining
(component 2)
POO * .04
POO + P10 * .11
POO + P01 - .08
P(U,V) = .04 + .07
- .22.
+ .04
P10/P11 * 1.75
P01/P11 « 1.0.
(.07)(.04)/.04
The observed value is .22. In this examole the
component additional risks are comparable or
moderately large relative to background. The
Thorslund and Charnley model is predictive at the
environmental level of exposure but componentwise
additivlty does not hold there.
5. Oral cancer associated with smoking
(component 1) and alcohol use (component 2)
ROO - 1
ROO + RIO
ROO + R01
1.53
1.23,
The additional componentwise relative risks are
small relative to background.
R(U,V) - 1 + .53 + .23 + (.53)(.23) = 1.88.
The observed value 1s 5.71. In this example the
Thorslund and Charnley model predicts essentially
componentwise additivlty; 1t 1s not predictive at
the environmental level of exposure.
6. Renal cancer associated with smoking
(component 1) and exposure to cadmium
(component 2)
ROO * 1
ROO + RIO = 1
ROO * R01 = .8.
The additional component relative risks-are
essentially zero. Thus, R(U,V) 1s at most 1.
The observed joint relative risk 1s 4.4. In this
example the Thorslund and Charnley model predicts
-------
:':^^ns^
componentwise addHlvHy; 1t 1s not predictive at
the environmental level of exposure.
The performance of the Thorslund and Charnley
model with Relf's examples has a number of
Implications.
1. The Model predicts some observed component
Interactions at environmental levels.
2. The model does not predict all observed
component Interactions at environmental
levels.
3. Environmental exposure levels In a number
of the examples were sufficiently high for
the product term 1n the model's expression
for risk to dominate. Thus, the Thorslund
and Charnley model 1s not synonymous with
componentwise addltivity of risks at
environmental'exposure levels.
4. What constitutes "low" levels of exposure
and "high" levels of exposure for the
purposes of the model 1s based on risk
levels relative to background. Exposure
levels that might be quite low on an
absolute basis could still be "high" with
respect to componentwise addltivity 1n the
Thorslund and Charnley model.
5. Irrespective of whether or not the model
predicts component addltivity, Inferences
concerning the Joint effects of multiple
components can be based on Individual
component data alone. Component data are
the most readily available for risk
assessment purposes.
Conclusions
The USEPA Guidelines for the Health Risk
Assessment of Chemical Mixtures (1985), page 12
state "...When little or no quantitative
Information 1s available on the potential
interactions among the components, additive
models are recommended for systemic
toxicants...". This paper carries the above
recommendation a step further; the model accounts
for linear by linear Interactions empirically,
based on component data. This provides a good,
empirical modeling approach 1n the absence of
specialized mechanistic Information. The model
does not always predict componentwise addltivity
at low, environmental levels of exposure. It
predicts some, but not all, observed
environmental Interactions among mixture
components.
What level of subdivision of the mixture into
components should be used when carrying out the
risk calculations? If the composite, tested as a
whole, 1s not carcinogenic at the laboratory dose
levels, can testing be stopped without
considering componentwise tests? I believe that
the answer Is no! The USEPA Mixtures Guidelines
(1985), page 11 state '...Even If a risk
assessment can be made using data on the nlxture
of concern or a reasonably similar Mixture, 11
may be desirable to conduct a risk assessment
based on toxlclty data on the components In the
mixture...1n a chronic (high dose) study of such
a mixture (containing carcinogens and toxicants),
the presence of the (acute) toxicant could mask
the activity of the carcinogen...the toxicant
could induce mortality (at high doses) so that at
the maximum tolerated dose of the mixture, no
carcinogenic effect could be observed...".
However, at low, environmental levels of exposure
the acute toxicant might have no effect and so
the carcinogenic comoonent might be active.
"...The mixture approach should be modified to
allow the risk assessor to evaluate the potential
for masking, of one effect by another, on a case-
by-case basis".
Thus, a sensible empirical approach to
carrying out risk assessments on mixtures in the
absence of specific mechanistic information
concerning componentwise interactions, would be
to carry out dose response estimation and risk
calculations based on componentwise testing at a
number of different levels of decomposition of
the mixture, ranging from the entire composite to
very homogeneous constituents. At each level of
decomposition the componentwise risks would be
combined based on the -Thorslund and Charnley
model to obtain composite risk estimates. Large
discrepancies 1n the composite risk estimates at
differing levels of decomposition would indicate
the presence of synergistic or antagonistic
component Interactions.
In conclusion, I found this paper to be very
interesting, thought provoking, and well written.
It raises as many or more questions about
methodology for risk assessment on mixtures as it
resolves.
References
(1) Relf, A.E., Synerglsm 1n Carclnogenesis,
Journal of the National Cancer Institute,
Vol. 73, No. 1, 1984, pp 25-39.
(2) Thorslund, T.W. and Charnley, G., Use of
the Multistage Model to Predict the
Carcinogenic Response Associated With the
Time-Dependent Exposures to Multiple
Agents, Proceedings of the ASA/EPA
Conference on Current Assessment of
Combined Toxicant Effects. 1986.
(3) USEPA, Guidelines for the Health Risk
Assessment of Chemical Mixtures. Final
Report ECAO-CIN-434, 1985.
-------
^j&s
*
ASSESSMENT OF INTERACTION IN LONG-TERM EXPERIMENTS
S. G. Machado, Science Applications International Corporation
1. IKTRDDUCTIOH
This paper will address th« problem of uses-
sing interaction between carcinogens or toxic
substances in long-tern factorlally designed
animal experiments. The general context. Is that
of long-term screening tests for carcinogens, for
which the analysis is based on Cox regression
methods, See, for instance, Peto et al. (1980).
The designs considered are 2x2 and 2x2x2.
The method easily generalizes to other factorial
designs. The problem came to the author's atten-
tion via a request from Dr. C.J. Shellabarger
of Brookhaven National Laboratory who had com-
pleted a 2 x 2 x 2 experiment to examine inter-
actions between radiation and chemical carcino-
gens in the induction of manraary tumors in rats,
and was not sure how to analyze his data. He
had previously conducted 2x2 experiments and
to add a third treatment seemed a natural next
step.
In the statistical and epidemiological litera-
ture, there has been a lot of discussion in
recent years about what is meant by interaction.
Distinctions have been made between statistical
and biological interaction, and interaction in
the public health sense. As statisticians are
well aware, presence of interaction in a linear
model depends on the scale of measurement being
used. For instance, for a two-way layout with
one observation per cell, interaction can be "got
rid of" by a suitable power transformation of the
data. To reduce confusion, in an area which is
complicated enough, it is important for the
statistician to define what is meant by inter-
action at the outset of a study, and what is
meant by "synergism" and "antagonism," since
these terms do not mean the same things to all
scientists.
In this paper, the kind of Interaction
considered, between agents A and B, is that
which occurs if the effect of A and B taken
together is unexpectedly larger or smaller than
that of the sum of the effects of A and B taken
separately. Synergism Is said to occur if the
joint effect is larger than expected, and, con-
versely, antagonism occurs if the joint effect
is smaller than expected. The situation in
which only A produces the effect of interest,
but the presence of B modifies the effect of A,
is not considered. A and B are presumed to
have the same site of action.
The underlying model for no interaction
considered here is Finney's definition of simple
independent action of different agents and the
background (1971). This is equivalent to
Hewlett and Plackett's model of "dissimilar
nonlnteractive action."
For long-term experiments, under the propor-
tional hazards assumption, the model results in
a linear relationship between the hazard func-
tions rather than the multiplicative one commonly
assumed for interaction (see Wahrendorf et al.,
1981). Other researchers have looked at additive
as well as multiplicative models for no inter-
action, for instance, Thomas (1981) in the
context of general relative risk models-, and
Prentice et al. (1983) for the analysis of an
extensive cohort study.
The work for this paper was done with the
assistance of Dr. Kent Bailey, of the National
Heart, Lung and Blood Institute, and is essen-
tially a continuation of that of Wahrendorf et
al. The contribution of Korn and Liu (1983) who
took a non-parametric approach, i.e., without
making the proportional hazards assumption, will
be briefly mentioned.
2. 2x2 FACTORIAL EXPERIMENTS
The hypothesis to be tested Is that of inde-
pendence of action, i.e., of tumor inducing
potential, between carcinogens ?iven in combina-
tion. Suppose, ir. a 2 x 2 experiment with
treatments A and 3, that HQO animals receive no
treatment and n^Q, HQ^, r\n animals receive,
respectively, doses d^ of A, dg of B and
(d^ •*• d-g). The animals are observed throughout
the experiment for occurrence of tumors of
interest; times of tumor appearance or of deaths
from unrelated causes are noted. Let qij(t),
i,J-0,l, be the probability that an animal in
the group (i,j) remains tumor-free up to time t.
Let QIJ » qij(T) where T is any time after the
last event. Let a^j be the number of aniaais
with tumors in grouo (1,1) at time T. Finney's
hypothesis of simple independent action of A and
B is:
Ho: QiiQoo " QioQoi
Synergism corresponds to the left hand side
being much less than the right hand side of this
expression; conversely for antagonism.
Various methods have been proposed for test-
Ing this hypothesis, see Wahrendorf et al., Korn
and Liu, or Hogan et al. (1978). Perhaps the
simplest conceptually is the likelihood ratio
test. The likelihood is proportional to:
mij nij ~™i j
Hijd - Qij) QIJ
The log-likelihood is first maximized with
^Qlj) as four independent parameters, i.e.,
Qij • (nij-mij)/nij , and then with the {Qij }
constrained by the null hypothesis.
Taking time into account, Finney's hypothesis
of independent action of A and B becomes:
HQ: log ([qii(t)qoo(«)]/lqiO
-------
Synerglsm corresponds co the expression on the
left of (1) being greater than zero and, con-
versely, antagonism corresponds to the expression
being less than zero.
If che proportional hazards assumption is
•«4e. aiMly that Aij(t) may be expressed as
A00(t)fij where fj.j does not depend on t,
then the null hypothesis becomes, without loss
of generality:
HQ: 1 + fil - «10 - f01 • ° .
the arbitrary scale factor having been absorbed
into the arbitrary function AQO^i' T^6
alternative hypothesis allows for all three
parameters to be free. Let f - (foo if 10 >f01t
fll)'. For testing HQ it is convenient to
express f in terms of parameters (6) . Let
Si SV4
Tv^CS) • (l,e ...,e )' for arbitrary H>-1
and let W be any 1x3 aatrix of constants with
colucr.s orthogonal to the interaction contrast
vector (1,-1,-1,1)' • VAB, say. There are many
choices for W; a natural choice is to define W
as the first three columns of the design matrix
Under HQ, f is modelled as f - WT2(S), and
under the alternative hypothesis, f » 13(8).
The null hypothesis HQ is tested by the likeli-
hood ratio statistic, X - 2(Lg-Lc), where LS, LC
are, respectively, the maximized log-likelihood
functions under the saturated and constrained
models; X has approximately Xi distribution
under the null hypothesis. Technical details for
the likelihood maximization are described in
Machado and Bailey (1985).
3. EXAMPLE 1
The data for this example is from Table 2 of
Kom and Liu (1983). Female rats were treated
with two chemical carcinogens, labelled NTA and
MNNG. The endpoint of interest was death from
any cause. All rats alive at the end of the
experiment, as well as 4 accidently killed early
on, are considered censored observations. The
results of the analysis were:
Saturated
Model
Lc - -291.481
Constrained
Model
/\
- -294.588
- /0.25
11.56
f - -5.31
vAB'f - 0
The likelihood ratio test, X - 6.21 (a -
0.013), indicating significant departure from the
null hypothesis; thetinteraction Is antagonistic,
fro* the sign of vAB*f. This result corresponds
to those of Korn and Liu.
For comparison, the time-Independent likeli-
hood ratio test was 2(Ls - LC) " 4.32; this
statistic has approximately Xj. distribution,
thus -nis group may be excluded
from the analysis and f_ - ( f ^Q ,IQ^ , f^) iay
be modelled by VJT(p) with
W -
This represents the additive model subject to
f(30 * 0. If the parameters are estimated as
In Machado and Bailey, the log-likelihood is
the log-likelihood for the additive model (1)
for all four groups. The saturated model is
fitted similarly by omitting the control group
and modelling (f 1Q ,fQ1 ,f u) by T2( P).
5. EXAMPLE 2.
This example was described in Machado and
Bailey. The data are from a nine-month study
to investigate possible interaction between
the known carcinogens dlethylstilbestrol (DES)
and dimethylbenzanthracene (DMBA) in the
Induction of mammary adenocarcinomas In female
AC1 rats (Shellabarger et al., 1980). The
results of the test for interaction are:
Saturated
Model
LS - -152.46
0 » |-0.52\
\ 1.471
A.
Constrained
Model
LC - -156.848
• - -0.68
0.60 I
\4.33/
f -
o.5
.5
The test statistic X - 8.77 (a- 0.004),
indicating very significant departure from
the null^hypothesls. Since the contrast,
fll-?10-foii ls greater than 0, the Inter-
action is synergistlc.
The likelihood ratio test from the time-
independent test is 6.61 (*- 0.01), again
indicating significant interaction.
-------
y^^
6. PROPORTIONAL HAZARDS ASSUMPTION.
The proportional hazards assumption should
b« chtcked since gross departures from propor-
tionality may well affect the behavior of
the interaction teats in an adverse way.
talbfleisch and Prentice (I960, ch. 4) recommend
using "log-minus-log" plots: plots for all the
treatment groups of log(-log(q(t)) versus log(t),
where q(t) is any estimate of qj.j(t), will show
constant separation over time if there is pro-
portionality. For small to moderate sized
samples, it may be difficult to discern from the
plots whether there actually is constant separa-
tion over time. In this case the uniformity of
the fit of the saturated and constrained models
and of the behavior of the interaction statistics
over time may be checked by estimating sets of
parameters for different partitions of the time
axis. Most likely, divisions into early versus
late, or early, middle and late tiae periods will
be sufficient.
Suppose T is any time beyond the time to the
last event and let a time t be chosen so that
the time axis is partitioned into (0,t], (t,T].
Let Ls(l), Ls(2) be the maximized log-likelihoods
under the saturated model, respectively, for the
time periods (0,t) (events after t considered
censored) and (t,T] (individuals with either
events or censoring times before t excluded from
the analysis); let Lc(l), Lc(2) be similarly
defined maximized log-likelihoods for the con-
strained model. Then a test for the uniformity
of the saturated model over time is 2(Ls(D +
1.5(2) - Lg) which has approximate chi-square
distribution with degrees of freedom 3 for the
2x2 case. A test for the uniformity of the fit
of the constrained model over time is 2(L<;(1) +
L(;(2) - LC) which has approximate chi-square
distribution with degrees of freedom the number
of parameters in the model, e.g., 2 in the 2x2
case. If there appears to be no lack of unifor-
mity of fit of the saturated or constrained
models and no evidence of any interaction, then
one would be comfortable in accepting the null
hypothesis. If there seems to be evidence of
interaction and the Interaction is of the same
type in each time period, and also if there is
uniformity of fit of the saturated model, then
the overall test of interaction under the pro-
portional hazards assumption can be used. If
there is evidence of nonproportionality, the two
time periods could be considered separately with
respect to the presence or absence of inter-
action. It is worth checking the consistency of
the conclusions of such an analysis when different
values of t are chosen.
If the proportional hazards assumption does not
appear to hold, with different partitions of the
time axis, then the non-parametric methods of
Korn and Liu (1983) may be more appropriate.
7. EXAMPLES
Figure 1 shows the "log-minus-log" plot for the
data of Korn and Liu discussed in Example 1.
There is no reason to suspect departure from pro-
protionality of the hazard function.
Figure 2 shows the "log-minus-log" plot for
the data of Example 2. The plot indicates some
departure from proportionality since the curve
for the group receiving both DES and DKBA seems
steeper than those of the groups receiving a
•ingle treatment. The time axis was partition-
ed into two periods: (0.136) and (137,266),
day 136 being approximately the half-way point
in time and in numbers of events. The maxi-
mized log-likelihoods and estimated parameters
for the saturated model were, for the early
time period: LSU) - -80.63, Lc0.10) indicating no strong
evidence for lack of uniformity; the estimated
3 coefficients are not very similar but are far
from significantly different. The xj tests
for Interaction for the early and late tine
periods are 5.45 (a - 0.020) and 3.56
(a " 0.059), respectively; moreover, the
interaction contrasts are 2.35 and 3.32 and
thus there is significant synergism for both
time periods. Similar results were obtained
for various t between 129 and 190, Thus it
appears that there was a synergistlc inter-
action between DES and DMBA In this experiment.
8. KORN AND LIU'S 2 STATISTIC
Korn and Liu proposed a statistic for
continuous time data which does not rely on the
proportional hazards assumption. They made the
reasonable suggestion that the model of inde-
pendent action with no further assumptions is a
good starting place for an analysis.
Restricting attention to the 2x2 case,
suppose events occur at time ti, t2,..., and
suppose that there are no tied events. Let
where nij(t^) is the number of animals'in
group (i,j) exposed at time c^-0, ru-+(tk) -
zijnij (ck)> and the failure occurred in Kroup
(i,j). The statistic for testing Finney's
hypothesis of independent action is:
Z Zk
(I
which has approximately N(0,l) distribution.
The terms in the numerator, {Zfc}, have
conditional expectation zero under the null
model, and In this, are unique up to a multi-
plicative factor.
If there are ties in the data, Korn and Liu
suggest breaking them at random. Note that
with the test discussed in this paper, it is
possible to use the general maximum likeli-
hood solution to the proportional hazards
model, and thus ties do not pose a problem
(see Machado and Bailey).
Korn and Liu's statistic was calculated for
the data of Examples 1 and 2:
-------
Example 1.
Z • 2.45 (o • 0.014) compared with /X •
/6.21 • 2.49 (o - 0.013). Mote that In
their paper, they obtained Z - 2.48, a minor
difference, but due to arbitrariness in dealing
with ties. For this example, the likelihood
ratio test and Z are very close.
Example 2.
With the data ordered by treatment group:
Controls, DES, DMBA, DES plus DMBA, Z - -1.87
(a- .06); with the data ordered in reverse,
i.e., DES plus DMBA, DMBA, DES, Controls,
Z • -1.645 (a- 0.10). There are a lot of ties
in the data, which give rise to the difference
between these two values of Z. These values are
rather different from /8.77 - 2.96 (a » 0.004)
from the time-dependent likelihood ratio test, and
/6.61 • 2.57 (a - 0.01) of the time-independent
test. It is difficult to see why the Z values
should indicate less evidence of the synergism
between DES and DMBA.
Once a consistent approach to dealing with
ties is found, the Z statistic should prove
useful, since it is reasonably simple to
compute, especially for situations in which one
fee.ls uneasy about assuming proportionality of
hazards.
9. 2*2*2 FACTORIAL EXPERIMENTS
Let the three treatments of interest be A,
B and C and suppose that there are njifc animals
in the group (i,J,k) receiving a total treatment
dose of (idA + jdB + kdc), for l,J,k-0,l. Let
IllVt^)' Hjk(c) ke defined in an analogous
way to qij(t), ^ij(t) of Section 2. Further,
under the proportional hazards assumption, let
Xljfc(t) " ^OOO^t^ijk. »here fijfc is Inde-
pendent of t. Let q(t) be the vector of the
{qijkXt)} -with the subscripts in the order
(000,100,010,110,001,101,011,111) and let f be
the vector of {fijk) with the subscripts
in the same order. Let the columns of the
design matrix
(i -11 ® i: 11 ® (i -i
be labelled in order, VQ, VA, VB, vy^j, vc, VAC ,
VBC> VABC' Then the null hypothesis of inde-
pendence of action of the three treatments has
four parts, corresponding, respectively to the
interactions between A and B, A and C, B and C,
and A, B and C.:
' HO: VAB'log(q) ' 0 , (11) vAC'log(q) - 0,
(iii) vjc'logU) - 0, (iv) vABC'log(q) - 0
Under the proportional hazards assumption, as
in the previous section, HQ becomes:
(i) VAu'f ' 0
(iii) vBC'f ' 0
(11) VAc'f - 0
(lv) v^c'f - 0
with the saturated model, f • WT7(B); Che
resulting likelihood ratio statistic has
approximately x* distribution. One choice
for W is to take as its columns VQ, VA, vg, VQ.
Sequential tests for single Interactions are
made by modelling the specific constraints by
suitable choice of V. for example, to test for
the three-way Interaction, model f by W^CB),
where Wj Is 8 x 7, orthogonal to ?ABC» *n(* Bake
a one degree of freedom comparison with the
saturated model. Further, to then test for the
AB interaction, model f by W2T5(6), where
V/2 is 8x6, orthogonal to v^g and Vp&c, and
compare with the model WjTgCS). Leaving out
one constraint at a time leads to a series of
one-degree of freedom comparisons in the usual
way.
10. EXAMPLE 3
The data for this 2x2x2 exatnole are frow
a one-year experiment to assess possible inter-
action between DKBA, procarbazine (PCZ) and
x-irradiation (X-ray) in the induction of mam-
mary adenocarcinomas or fibroadenomas in feniale
Sprague-Dawley rats. The experiment was con-
ducted by Dr. C.J. Shellabarger and colleagues
at Brookhaven National Laboratory who kindly
made the data available. The rats were treated
at about 3 months of age and examined weekly
for the appearance of mammary tumors. Summary
information on nuobers of rats with one or -nore
tumors is in Table 1.
Table 1. Summary information on numbers of
female rats treated with DMBA, PCZ
and/or X-ray which developed mammary
tumors.
Treatment group Number
exposed
Control 35
DMBA 37
PCZ 37
DMBA & PCZ 37
X-ray 37
DMBA & X-ray 37
PCZ & X-ray 36
DMBA, PCZ & X-ray 37
Number with at
least one tumor
2
14
8
20
11
20
14
25
A joint, test of the four parts of HQ is made
by comparing the constrained model f • WT3< B),
where W is an 8 x 4 matrix of constants with
columns orthogonal to v^g,
The maximized log-likelihoods were:
LS - 510.981, LC • -511.422 resulting in
test statistic for overall interaction, Xi "
0.822, which is far from significance. There
were no two-way or three-way interactions
between DMBA, PCZ and X-ray since the single
degree of freedom chi-square tests for Indivi-
dual interactions are all bounded by such a
small number. For comparison, the likelihood
ratio statistic from the time-independent test
is 0.682, also very small. The estimates of
the multipliers {fijfe} from the saturated
and constrained models are very similar:
?- (1,2.19,1.47,2.66,1.90,2.85,2.18,3.05)' and
f - (1,2.42,1.53,2.70,1.96,2.85,2.37,3.04)' .
"Log-mlnus-log" plots showed close to constant
separation between all of the curves and thus
Is there no reason to doubt the proportionality
-------
• -• •• . 1-•>•••'.%,. - r«-.,,»^v^*- ,kV. ^-x^.,,
^
of the hatard function*. Thus the three treat-
ments act Independently In the Induction of one
or acre mammary tumors in this species of rat.
For this data, the time to the appearance
of second tumors was also recorded. This is a
much leȤ understood measure of carcinogenesis,
and the analysis is summarized here only for
Illustration of the method. Table 2 gives the
numbers of animals in each treatment group which
developed 2 or more mammary tumors.
Table 2. Summary information on numbers of female
rats treated with DMBA, PCZ, and/or
X-ray which developed 2 or more mammary
tumors.
Treatment group Number
exposed
Control 35
DMBA 37
PCZ 37
DMBA & PCZ 37
X-ray 37
DMBA & X-ray 37
PCZ and X-ray 36
DMBA, PCZ 4 X-ray 37
Number with 2
or more tumors
0
5
1
15
1
10
3
19
The likelihood ratio test for, no two-way or
three-way interactions was XA" " 1°-48 (<* '
0.035), indicating the presence of some inter-
action. The test for no DMBA and X-ray, or PCZ
and X-ray, or DMBA, PCZ and X-ray interactions
was X3 • 2.77 (a > 0.1), which is far from
significance.
The xi test for the DMBA and PCZ interaction
was 7.71 (a - 0.006), which is highly signifi-
cant. Examination of the statistics showed this
to be due to synergiso betwen DMBA and PCZ, in
the induction of multiple mammary tumors.
Although the biological implications of this are
not clear, this example shows that the test can
identify which pair of agents contributed to the
overall departure from the null model.
11. REFERENCES
Finney, D. J. (1971). Problt analysis, 3rd ed.
Cambridge: Cambridge University Press.
Hogan, M.D., Kupper, L.L., Most, B.M., Baseman,
J.K. (1978). Alternatives to Rothman's approach
to assessing synerglsm (or antagonism) In cohort
studies. American Journal of Epidemiology 108,
60-67.
Kalbfleisch, J. 0. and Prentice, R. L. (1980).
The statistical analysis of failure time data.
New TorVc: Wiley.
Korn, E. L. and Liu, P. (1983). Interactive
effects of mixtures of stimuli in life table
analysis. Biometrika 70, 103-10.
Machado, S.G. and Bailey, K.R. (1985).
Assessment of interaction between carcinogens
in long-term factorially designed animal
experiments. Biometrics 41, 539-545.
Peto, R., Pike, M.C., Day, N.E., Gray, R.G.,
Lee, P.N., Parish, S., Peto, J., Richards, S.,
Wanrendorf, J. (1980). Guidelines for siaole,
sensitive sisnificance tests for carcinozenic
effects in long-tera animal experiments. Annex
to Long-term and Short-term Screening Assays
for Carcinogens: A Critical Appraisal. Inter-
national Agency for Research on Cancer. Lyon.
Prentice, R. L., Yoshimoto, f. and Mason,
M. W. (1983). Relationship of cigarette
smoking and radiation exposure to cancer
mortality in Hiroshima and Nagasaki. Journal
of the National Cancer Institute 70, 611-22.
Shellabarger, C. J., McKnight, 3., Scone,
J. P. and Holt?mann, S. (1980). Interaction
of Dimethylbenzanthracene and Diethylstil-
bestrol on mammary adenocarcinoma formation in
female ACI rats. Cancer Research 40, 1808-11.
Thomas, D. C. (1981). General relative-risk
models for survival time and matched case-
control analysis. Biometrics 37, 673-86.
Wahrendorf, J., Zentgraf, R. and Brown, C. C.
(1981). Optimal designs for the analysis of
interactive effects of two carcinogens or other
toxicants. Biometrics 37, 45-54.
-------
&&&£9^i*^i&&^&?M&^^
UW
-0.5 •
-1.0 *
-1.5
-20-
-2.5
-3.0 •
•3.5
1t Concroli
2: UTA
3: MKNG
*: NTA 4 HNNC
FIGURE 1
FLOT OF loi
KOBH-LIU DATA
33 4
4
3 4
3 4
3 4
3 422
3 4 2
43 2
1 I
i 2
2 4
3
-4.0
•4.5 •
1
5.5
UOC I
I .0 •
0.5
a.e
-o.s
•i.o
•i.s
-2.0
-2.5
-3.0
-3.5
5.6 5.7 SB 5.9 6.0 6.1 6.2 63 64 65
IT
FIGURE 2
PLOT OF lo»{-lo»(q(t)) v.. log(t)
DES, DKSA EXPEXIMtNT
2: DES * *
3: DHBA 4
4: DES t DKBA *
4 2
222
2 2 2 22 22 2
33 333
3
3 3
3 3
3 3
3 33
6 6
4.0 4.2 4.4 4.6 4.S S.O 5.2 5.4 5.6
IT
S.O
-------
DISCUSSION
Fro* Machado '• presentation we have seen that
quantities
Chao W. Chen, U.S. Environmental Protection Agency
is equivalent to the null hypothesis
HQ: bu • 0.
olay a key role In the hypothesis testing of no
interaction when time-to-event data are avail-
able! Th« null hypothesis of no interaction, for
the case of a 2x2 design, is
for every c. For the case of a 2x2x2 design, the
null hypothesis of independent action of the
three treatments has four parts corresponGisg ,o
the three two-way and one three-way interactions.
Given the above background, my discussion
will be on the following three issues:
1 Application of the above null hypothesis
' to test the multiplicative effect of syn-
ergism under the theory of the Armitage-
Doll multistage model. Under the multi-
stage model, if each of the two (or more)
carcinogens affects a single hut different
stage of the carcinogenesis process, a
synergistic effect (in a multiplicative
sense) will result.
2. The implication of the alternative null
hypothesis of no Interaction,
H02: TlO» TQI, and T^ be random variables
representing, respectively, time to cancer death
of an animal exposed to dose rate 0, dA, dg and
(dA+d]j) under the condition of no competing risk.
Let MJ_J • min(Tij , L) where L is the time when
the study terminated. It follows that the expec-
ted time to cancer death (latent period) is given
by
E(Mi1) • / qt1(t)dt
0
and the life-shortening due to the exposure is
RiJ * E(Mo0-Mtj)
L
L 0
Therefore, the null hypothesis of no interaction
can be defined as
HQ: RH - RIO + ROI
which is equivalent to the null hypothesis
L
HO: / l * IQOM - qiO
-------
'''( '**» -»•]'.,
^^^^^
vhcr*
tit •••• tn **• the time to Cancer death,
to • 0, and
q\j • Kaplan-Meier estimate of qj_ j .
Th« estimate of standard deviation Is given by
u - »„<«.,! -
The statistic
Z - (eu
- e10 - e01)
(311 * 900 + 310 * 301}
is asymptotically distributed as a standard nor-
mal under HQ.
3. Implication of the Hull Hypothesis used by
Machado in a 2x2x2 Design
The null hypothesis used by Machado is
HQ: V'f - 0
ir are colunn vec-
where V - V^, VAC, VBC, or
tors given below:
VAB VAC
Similarly,
and
- o
Mow, synergistic and antagonistic effects should
be as follows:
EABC • E(A,B,C) - E(A) - E(B) - E(C)
" (PHI * POOO> - (PIOO - POOO) "
(POIO ~ POOO) ~ (POOI - POOO)
" Pill ~ PIOO " POIO ~ P001 * 2POOO
This shows that the null hypothesis used by Ma-
chado is stronger than the test of no synergetic
or antagonistic effects as defined by S^gc- If
there is no pairvise interaction [i.e.," E(AB)C»0
• 0, etc.], the null hypothesis HQ of Machaco is
equivalent to the null hypothesis of E^c " 0-
However, in general, E^c - 0 does not imply HQ
to be true.
Further research is needed in testing the null
hypothesis of no synergistic or antagonistic ef-
fects on 2x2x2 design, without assuming that the
pairvise interactions are zero. It seeas intul-
ively true that if all pairvise interactions are
positive, there must be a synergistic effect. On
the other hand, if all the pairwise interactions
are negative, there must be a synergistic effect.
'ABC
o
A
B
AB
C
AC
BC
ABC
1
-1
-1
1
1
-1
-1
1
1
1
-1
-1
-1
-1
1
1
Pijk>
or
J. k - 0, 1
as used by Machado.
Let
denote
The null hypothesis HQ corresponds to four
parts :
HABC " Pill ~ PllO - P011 " P101 * P100 +
P010 * P001 * POOO
' PlOl ~ P011 * P001> ~
(PI 10 ~ PIOO • POIO * POOO)
where (EAB)C«I and (ExB^C-0 *re defined by the
last equality of the equation and represent,
respectively, the effect due to treatment A and
B when C is held at level 1 or 0.
HAB " (Pill * P011 ~ PlOl * P001> *
-------
&fe£^^
CONCENTRATION AND RESPONSE ADDITION OF MIXTURES OF TOXICANTS
USING LETHALITY, GROWTH AND ORGAN SYSTEM STUDIES
Lavern Weber, Perry Anderson, Carl Muska, Elizabeth Yinger and Dennis Shelton
Oregon State University
Dose response relationships are the most
single unifying concept to the nany branches of
pharmacology and toxicology. Quantative
methodology to describe dose response
relationships began with the work of Trevan
(1927) and Gaddum (1933). The theoretical basis
of joint toxicant action was first systematically
discussed by Bliss (1939). Bliss recognized
three types of joint action: (1) Independent
joint action - the chemicals act independently
and have different modes of action; (2) Similar
joint action - the chemicals produce similar but
i ndependent effects, one component can be
substituted at a constant proportion for the
other. Susceptibility to the chemical components
are completely correlated; (3) Synergistic (or
antagonistic) action - the effectiveness or tne
mixture cannot be assessed from the individual
chemicals. Bliss' approach was modified by
Finney (1942) to develop a logical relationship
between the mathematical expressions for the
different types of joint action.
Plackett and Hewlett (1948, 1952) and Hewlett
and Plackett (1952, 1959) proposed a two-way
classification scheme of Bliss' model in an
effort to provide a less restrictive form. The
following diagram is their scheme with four
distinct'types of action.
Non-
Interactive
Similar
Simple similar
Dissimilar
Independent
Interactive Complex similar Dependent
They defined toxicant mixtures as "similar" or
"dissimilar" according to whether the toxicants
acted upon the same of different biological
systems and as "interactive" or "non-interactive"
according to'whether one toxicant influenced the
"biological action" of the other toxicants.
"Simple similar" and "independent action" were
regarded as special cases in a continuum of
biological possibilities and the mathematical
models proposed for complex similar and dependent
were generalizations of the models proposed for
"simple similar" and "independent action"
respectively.
Their mathematical models, particularly for
the quantal responses to mixtures of
"Interactive" toxicants, are very complex and
require the knowledge of certain parameters which
are normally unattainable when evaluating the
effects of toxicant mixtures on whole organism
performances. However, Hewlett and Plackett's
models for "joint action" are useful for
elucidating the limitations of and the
assumptions required for the special cases of
"simple similar" and "independent joint action".
The present discussion only considers the special
cases of "noninteractive" toxicant mixtures.
The difficulty of understanding complex
mixtures and the Interactive role that Individual
toxicants play is not easily elucidated. In 1970
my laboratory began to investigate the toxicity
of mixtures of chemicals. In the following •
decade we utilized the concepts of early
Investigators such as Bliss (1939), Finney (1942)
and Hewlett and Plackett (1959) to study the
validity of their nodels for studying toxicant
Interactions. The results to be discussed
involved tests of the model using lethality
(Anderson and Weber 1977), growth (Kolkemeister
and Weber 1979; Muska and Weber 1977, Weber and
Muska 1977) and on an organ system (Shelton and
Weber 1981).
The regulatory agents at the beginning of our
work essentially followed the National Technical
Advisory Committee's recommendation that the sum
of the ratios of tne measured concentration of
the permissible level of each toxicant snould not
be greater than one. This basically follows the
concept of a "Toxic Unit". The "Toxic Unit"
method arbitrarily assigns a value of one to that
concentration which induces particular response,
such as LCc0. The concentration of each toxicant
in a mixture is then expressed as a fraction of
its corresponding LCrQ value. The fractions are
added and if the resulting quantity is equal to
the toxic unit (1) than a 50% response is
predicted for the mixture. The basic assumption
of the "toxic unit" is that each toxicant
contributes to a common effect in proportion to
its relative potency. In Bliss' model this wouia
be "similar joint action" or in Hewlett and
Plackett's it would be "simple similar".
A multitude of terms have been suggested to
describe the various types oi-combined toxicant
effects. Ariens (1972) and Fedeli et al. (1972)
reviewed the various terminologies that have been
used. As Sprague (1970) and Warren (1971) point
out, the nomenclature is confusing particularly
since certain terms have been defined in more
than one way by different authors. Furthermore,
terminology describing the mechanisms of toxicant
action is not appropriate for studies evaluating
the effects of toxicant mixtures on whole
organism performances without knowledge of the
action of the individual toxicants. To avoid
both ambiguities in terminology and assumptions
implying knowledge of sites and mechanisms of
toxicant action, Anderson and Weber (1977)
introduced the terms concentration and response
addition which are mathematically analogous to
the "simple similar" and "independent action"
defined by Plackett and Hewlett (1952).
Concentration addition is mathematically
defined as the additive effect determined by the
summation of the concentrations of the individual
constituents 1n a mixture after adjusting for
differences in their respective potencies. The
primary assumption governing this type of
addition is that the toxicants in a mixture act
upon similar biological systems and contribute to
a common response in proportion to their
respective potencies. Bliss (1939) and others
have assumed that if two toxicants act similarly
the variations in susceptibility of individual
organisms to the toxicants are completely
correlated. As a consequence, the dose response
curves for the components and the mixture are
parallel. This has been observed for some
-------
vf^-mtt-
*^ . ^:.-.-.-^M'^l^'^^^^iAJ^l\^iK^ ri
toxicant mixtures; however, Plackett and Hewlett
(1952) presented examples of chemically related
insecticides which gave nonparallel lines. They
and other toxicologists (Ariens and Simonis,
1961) have stated, and we believe rightfully so,
that parallelism and hence complete correlation
of Individual susceptibilities 1s not a necessary
prerequisite for this type of addition.
In cases where the dose response curves for
the Individual toxicants in a mixture are
parallel, a dose response curve for the mixture
can be calculated based upon the assumption of
concentration addition. With the regression
equations for the individual toxicants in the
form of y » a + b log x (where y is the "»
response to each toxicant and x is its concen-
tration), the regression equation for a binary
mixture can be represented by (Finney, 1971):
b log
b log Z
:D
where,
y = * response to the mixture
aT = y intercept of_the first toxicant
b « common slope
IT. * proportion of the first toxicant in the
mixturi
HP - proportion of the second toxicant 1n
the mixture
p * potency of the second toxicant relative
to the first
Z = concentration of the mixture
This equation can readily be adapted to
represent mixtures containing more than two
toxicants. It should be noted that equation (1)
for concentration addition is similar in
principle to the toxic unit method used by Lloyd
(1961) and Brown 91968). Whereas the toxic unit
method measures the toxicity of mixtures only at
particular levels of response (LD.g, LC5Q, etc.),
equation (1) incorporates the entire do5e
response curve.
Response addition is the additive effect
determined by the summation of the responses of
the organism to each toxicant in a mixture. This
form of addition is based on the assumption that
the toxic constituents of a mixture act upon
different biological systems within the organism.
Each organism in a population 1s assumed to have
a tolerance for each of the toxicants in a
mixture and will only show a response to a
toxicant if the concentration exceeds Its
tolerance. Consequently the responses to a
binary mixture are additive only if the
concentrations of both toxicants are above their
respective tolerance thresholds. However, for
quanta1 responses the tolerances to the toxicants
in a mixture may vary from one Individual to
another in a population; therefore, the response
of the test animals depends also upon the
correlation between the susceptibilities of the
individual organisms to the discrete toxicants.
For example, in order to predict the proportion
of organisms killed by a binary mixture, it 1s
necessary to know not only the proportion that
would be killed by each toxicant alone but also
to what degree the susceptibility of organisms to
one toxicant 1s correlated with their
susceptibility to the other toxicant.
Plackett and Hewlett (1948) recognized this
statistical concept and developed mathematical
models that accounted for the correlation of
Individual tolerances ranging from total negative
to total positive correlation. If the
correlation is completely negative (r - -1) so
that the organisms most susceptible to one
toxicant (A) are least susceptible to the other
(B), then the proportion of Individuals
responding to the mixture (P ) can be represented
by;
pm m PA + PR 1f (P, " Ph * 1) 2a
m A B a b
where P. and Pg are the respective proportion of
organisms responding to the individual toxicants
A and B. With no correlation (r * 0) in
susceptibility the relationship is expressed by:
p = P
Pm KA
- PA)
(2b)
In the limiting case of complete and positive
correlation (r = 1), individuals very susceptible
to toxicant A in comparison with the peculation
will be correspondingly very susceptible to
toxicant B. In this situation the proportion of
animals responding the the mixture is ecual to
the response to the most toxic constituent in the
mixture. Mathematically this is represented by:
PM ' PA 1f PA * PB
PM-PB ifPB*PA
(2c)
For response addition, no significance can be
placed on the slope of the dose response curves
because the toxicants in a mixture are acting
primarily upon different biological systems with
varying degrees of susceptibility between
organisms. Even if the regression equations for
the constituents in a mixture are parallel for
toxicants acting in this manner, the dose
response curve for the mixture will not be linear
(Finney, 1971). This will be illustrated later
for two hypothetical toxicants whose dose
response curves are parallel. Although the
mathematical equations (2a, b, c) representing
response addition are relatively simple, the
statistical consequences of this type of adoition
are more complicated than those of concentration
addition (Finney, 1971).
Terms such as supra- and Infra-addition are
used to describe toxicant Interactions which are
greater or less than those predicted on the basis
of either concentration or response addition.
LETHALITY STUDIES: Anderson and Weber (1975)
Our first efforts were before we fully
recognized all the assumptions in the two models
we wished to use. We felt we could simply use
fish of one species and we began our work. Our
first lesson was that although we were
environmentally exposing the fish to toxicants,
the actual concentration to give a particular
response varied greatly with changes in size and
stock of fish (Anderson and Weber, 1975). In the
initial dose response curve we corrected for size
by an exponent function of weight. This approach
was developed by Bliss (1936). Bliss used the
following formula:
Y « a + b log M/Wh
31
-------
This expresses a linear function between
survival time and dose of different sizes of silk
worm larvae. M represents weight, Y the
dependent variable (death of fish in our case)
and M the aean dally toxicant concentration. The
Y Intercept "a* and the slope "b" of each dose
response was calculated. An h factor of a best
fitting regression and highest correlation
coefficient of the dose response curve was
determined using a computer program. The
toxicants we used and their corresponding h
factor 1s found in Table 1.
Slight changes in the normal distribution of a
species also was recognized as having a
significant effect on the slope of any
dose-response curve. We therefore attempted to
control all these factors by using an inbred
species of guppy. We avoided sex difference by
using only males.
Table 1. Toxicants and their corresponding h
factor.
Toxicant
n Factor
Copper chloride '0.72
Nickel chloride 0.67
Zinc chloride 0.3
Dieldrin 0.81
Potassium pentachlorophenate 0.72
MIXTURES: Anderson 4 Weber( 1977)
Our first attempts were with five mixtures:
copper.-nickel; dieldrin-pentachlorophenate-
copper-nickel; copper-zinc; pentachlorophenate-
cyanide; and dieldrin-pentachlorophenate.
Statistically there was an apparent parallelism
between the lethal response curves for copper and
CONCENTRATION ADDITION
. 6
-M
2
o
u
0,
i
>. 5
O
Copper
nickel. We assumed that as constituents of a
binary mixture, copper and nickel would
contribute to the mixture's toxldty In
proportion to their lethal potency. We tested
organisms to a series of binary mixtures of
copper and nickel. The linear function computed
for the observed results for the Mixture was
compared to the predicted linear regression by an
X' test for goodness of fit (Figure 1). The test
for goodness of fit between the observed and
predicted was significant at P«0.05. Our model
appeared to have predicted the strictly additive
action of Cu and N1.
The slopes of the response curves for dieldrin
(HEOD) and potassium pentachlorophenate (KPCR)
were found not to be parallel. Binary mixtures
of HEOO and KPCP were tested according to the
model of response addition. There was a good fit
(P<.05) to this model. (See Table 2)
An interesting temporal relationshio between
the lethal effects of pentacholorphenate ana
dieldrin supported (Bliss 1929} the "independent
joint action" or response addition hypothesis.
All mortality of fisn exposed to
pentachlorophenate occurred in 36 hours. The
effects of dieldrin after another 10 hours. The
predicted lethality of response addition for each
toxicant very closely aligned themselves to each
time period, that is, death from
pentachlorophenate before 36 hours and death from
dieldrin after 45 hours with the total equal that
predicted for response addition.
Mixtures of copper and zinc produced results
that did not fit either response or concentration
addition. The individual dose response curves
for copper and zinc were not parallel. We
initially tested the mixtures on the assumption
that they would be response additive. The
responses were greater than predicted.
Literature knowledge of the actions of mixtures
of copper and zinc suggested that they were
additive, a test for concentration addition was
made. The numbers dead were again greater than
Cu-Ni mixture
Predicted
-1.0
-0.9
-0.8
-0.7
0.9
1.0
1.1
1.2
1.3
1.4
log(M/Wn)
Figure 1. Lethal response curves for copper, nickel and their mixtures. The predicted
regression line is based on the relative,observed proportion of Cu (.006) and Mi (0.994)
and a relative potency (p) of 6.58 x 10" .
-------
Ttklt 2. Toxfclty study of »upp1tt oxpoud t» Mixtures of ttf Md HEOD
Assayed
level
of HCOO
1.0
4.45
(.3
6.4
4.8
6.9
Assayed
level
Of KP
•I/I
0.2*
0.40
0.31
0.40
0.29
0.41
Independent
variable..
log M/r"
forHOO
-2.44
-2.46
-2.46
-2.40
-2.46
-2.37
S Mortality
predicted
or HEOO
17
IS
27
27
16
35
Independent
variable,,
log IVW7Z
for KP
•0.713
-0.639
-0.685
-O.S8
-0.668
-0.594
* Mortality
predicted
for KP
11
34
17
Cl
24
54
S Mortality
predicted
for aliture
2f
44
39
72
36
70
Observed
S
,) Mortality
10
40
SO
60
70
80
Fron Anderson i Ueber, 1977
predicted. A ratio of observed to predicted
values represented a relative measure of the
increased effect or what we considered to be
super addition. The super addition was found to
be 2.5 times above that predicted on the
assumption of concentration addition.
The real challenge was to use a mixture of
four chemicals, two inorganic and two organic.
Nickel and copper were used as a pair that we had
shown to be concentration additive. Oieldrin and
pentachlorophenate were response additive.
Combining the nickel and copper as a single
(concentration additive) component, we treated
the mixture as three response additive components
(Table 3). Using the response additive approach
the predicted and observed results provided a
nice fit. In the case of pentachlorophenate and
cyanide they were tested and found to be response
additive.
We concluded that using the two forms of
addition, concentration and response, we were
able to describe four of the five combinations
adequately using lethality as an end point. One
of these mixtures contained four, two inorganic
and two organic, toxicants. In the case of the
one aberrant binary mixture, cooper and zinc, we
were able to clearly describe an interaction
which is super-additv/e.
HYPOTHETICAL QUANTAL DOSE RESPONSE RELATIONSHIPS:
Muska and Weber (1977)
Completion of these quanta! studies brought us
to a better understanding of the assumptions with
which we were working. To illustrate graphically
the relationship between concentration and
response addition, lyoothetical dose response
curves for two toxicants (A and B) are plotteo in
Figure 2 expressing percent response in probits
as a function of the logarithm of total
concentration. In this example the dose response
curves for the discrete toxicants are parallel
with A being 100 times more toxic than B. We
could have also chosen non-parallel curves;
however, for these cases equation (1) for
concentration is not appropriate. Hewlett and
Plackett (1959) have developed a more generalized
model (from which equation (1) can be deduced)
Table 3. Determination, using mean daily assayed concentrations, of the predicted mortality of fish
exposed to mixtures of HEOD, KPCP, Cu and Ni.
Predicted Mortality Proportion
Observed
Mortality
Proportion
Predicted
Numbers
Killed
Observed
Numbers
Killed
1 -
1 -
1 -
1 -
1 -
1 -
(1
(1
(1
(1
(1
(1
- .316){1 -
- .4)(l - .:
- .212)(1 -
- .268)(1 -
- .758)(1 -
-.655X1 -
.22X1 . - .057) =•
36)(1 - .136) - 0
.045)(1 - .023)
.184)(1 - 0.045)
.198)(1 - .084)
.277)(1 - 0.081)
0.50
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= 0
* 0.
- 0.
27
.43
82
89
0
0
0
0
0
0
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.60
.60
.60
.80
.90
5
6.
2.
4.
8.
8.
6
7
3
2
9
3
6
6
6
8
9
r * 5.57
d.f. « 4.0
-------
d
Si.
which does not depend on the assumption of
parallel dose response curves. (See Figure 2)
Dose response curves for mixtures of toxicant
A and B are obtained when the total concentration
1s varied and the ratio of the concentrations
for the Individual toxicants 1s kept constant.
Using the equations (1 and 2a, b, c) for
concentration (C.A.) and response addition (R.A),
dose response curves were calculated for
different mixtures containing fixed proportions
of toxicants A:B (1:10, 1:100, 1:1000). In
Figure 2, the responses to the mixtures are shown
graphically 1n relation to the dose response
curves of toxicants A and B.
Several observations can be made from the
relationships between the dose response curves in
Figure 2. As should be expected, the relative
toxicity of the mixture depends on the ratio of
its constituents. In Figure 2, a 1:10 mixture is
more toxic than the other mixtures depicted
because of the greater proportion of the more
toxic component - toxicant A. At certain ratios,
regardless of the correlation of susceptibility
(rj, the relative potencies of the mixtures
acting in either a concentration or a response
additive manner are very similar. This is
observed in Figure 2 for fixed proportions of
1:10 and 1:1000. Furthermore, for any one ratio
the relative potency of the dose response curves
for concentration and response addition (r » 1,
0, -1) depends on the level of response.
Focusing on the dose response curves for mixtures
in the ration of 1:100, it can be noted that at
low levels of response (i.e., at the probit of 2
which corresponds to approximately a 0%
response), the mixtures acting in a concentration
additive manner are considerably more toxic than
those acting by response addition regardless of
the degree of correlation (r). This Is due to a
fundamental difference 1n the two .types of
addition. At threshold or below threshold
concentrations of toxicants A and B, a mixture
acting 1n a concentration additive manner can
elicit a measurable effect because both toxicants
are acting upon similar biological systems.
Therefore, their concentrations can sum to
produce a concentration for the mixture which 1s
above the threshold level. However, the
responses to toxicants acting upon different
biological systems (response addition) are only
additive If each toxicant in a binary mixture 1s
present in concentrations above their respective
threshold levels. For similar reasons, as the
concentrations for the toxicants in a 1:100
mixture increase, the dose response curves for
response addition (except in the special limiting
case where r = 1) become progressively more toxic
relative to the dose response curve for
concentration addition. It is even possible that
a nign levels of res:cnse (in tnis example, for
resconses greater tf.jn 84% prooit of 6.0)
mixtures acting in a response adaitive manner
with negative correlation of susceptibility (r =
-1) can be more toxic than those acting on the
basis of concentration addition.
These factors (the type of interaction, the
ratio of the toxicants in a mixture, and the
level of response) must also be considered along
with the toxic properties of the individual
toxicants in assessing the relative toxicity of a
mixture. The failure to recognize these factors
can potentially lead to erroneous conclusions
concerning the-nature of the interaction of
multiple toxicants.
It is difficult to visualize the relationships
between the dose response curves in Figure 2
TOXICANT A
(r - 5 + 4x>
TOXICANT 3
(Y - I r4X)
-2.0
-1.5
-1.0
-0.5 0.0 0.5
LOG TOTAL CONCENTRATION (X)
1.0
1.5
Figure 2. Hypothetical dose response curves for toxicant A (1:0). toxicant B (0:1 I and their mixture
containing the fixed proportions (1:10, 1:100, 1:1000). See text for explanation.
-------
primarily due to the number of curves presented.
However, the relationships between the
hypothetical curve 1n Figure 2 can be readily
conceptualized with Isobole diagrams, a technique
Introduced by Loewe (19Z8, 1953). Isoboles are
lints of equivalent response. They are
constructed by plotting on a two-dimensional
diagram the concentrations of a binary mixture of
toxicants that produce a quantitatively defined
response, I.e. a 101, SOX or 90X lethal response.
It should be noted that an Isobole diagram can be
constructed for any level or response and the
relationship between the isoboles may vary
depending upon the response level selected.
The Isobole diagram for the SOX level of" ~
response of the hypothetical dose response curves
in Figure 2 is present in Figure 3. The x and y
axes in this diagram represent the concentrations
of toxicant B and A respectively. The radiating
dashed lines or mixing rays correspond to a
series of mixtures (A:B) of fixed proportions.
If the 50% response is produced by combinations
of two toxicants represented by points inside the
square area, the toxicants are additive.
Antagonistic interactions are represented by
combinations of concentrations falling outside
the square.
The Isoboles for concentration and response
addition are determined from the'concentrations
of the two toxicants which correspond to the
points of intersection between the 50% response
line (Figure 2) and the respective hypothetical
dose response curves. These concentrations are
plotted In Figure 3 on the appropriate mixing
ray. The lines connecting these points define
the course of the Isobole. Concentration
addition 1s represented by the diagonal Isobole.
For quantal data, response addition Is defined by
the curved Isoboles for complete negative (r *
-1) and for no correlation (r • 0) In
susceptibility. The upper and right boundaries
of the square correspond to the limiting case of
response addition with complete positive
correlation (r » 1).
QUANTITATIVE (GRADED) RESPONSE:
A consideration of the nature of the dose
response curves for quantal and graded responses
shows that the effects they express are quite
different. Quantal dose response curves exoress
the incidence of an all-or-none effect (usually
death) when varying concentrations are appliec to
a group of organisms. The curve is derives Dy
observing the number of organisms which respond
or fail to respond at various concentrations.
Consequently, the slopes of these curves
primarily express the individual variation of the
population to a particular toxicant. Graded dose
response curves characterize the relationship
between the concentration of a toxicant and the
magnitude of the effect under consideration. The
dose response curve can be derived by measuring
on a continuous scale the average response of a
group of organisms at each concentration.
1:0
IMO
1:50
I: 100
.10
.08
t- .06
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.04
.02
/ AOOITION (r • I) /
*+
1:200
2.0 4.0 6.0 8.0
CONCENTRATION OF TOXICANT 8
10.0
1:1000
0:1
Figure 3. Uobole diagram for quantal response data. Isoboles (or
concentration and respoose addition were determined from
hypothetical.dose response curves in Figure 1.
-------
•„».
As Clark (1937) and others have pointed out,
4t 1s possible to represent any graded response
as a quanta1 response provided that the response
of each Individual organism can be measured.
However, this procedure if adopted Is at the
expense of some "loss of Information" (Gaddum,
1953). • Quantal response data reveal only the
number of organisms that respond or fall to
respond at some particular concentration. On the
Other hand, graded response data not only tell us
whether or not a group of organisms respond but
also how much they respond.
The mathematical equations (2a,b,c) for the
response addition are not appropriate for graded
effects for two reasons. First, there 1s a
difference in the way the two types of data are
measured. For quanta! responses, the proportion
of organisms responding to any concentration is
determined by the ratio of number of organisms
showing the response to the total number
subjected to the concentration. For graded
responses, the mean response to each dose is
measured but in general the maximum possible
effect is not known, no proportional response can
be calculated. This is particularly true for
growth experiments where an organism's response
can potentially range from growth enhancement to
negative growth depending on the concentration of
a particular toxicant. Secondly, the statistical
concept of correlation between the suscep-
tibilities of the organisms to the discrete
toxicants in a mixture is not appropriate for
graded responses measured in the manner described
earlier. Graded response data represent the
1:0
average response of a group of organisms.
Therefore, the response of each Individual
organisms to the toxicants 1s not known. To be
sure, the tolerances of the Individuals In the
group will vary for the different toxicants In a
mixture; however, this factor will not alter the
relative toxlclty of the mixture because the
range of tolerances of the population Is
theoretically represented In the sample of
organisms from this population.
For graded response data, we have represented
the combined response to a mixture of toxicants
acting in a response additive manner as simply
the sum of the intensities of response which each
component toxicant produces when administered
alone. A similar relationship was defined by
Loewe (1953). Concentration addition can be
predicted for a toxicant mixture using equation
(1) if the component toxicants exhibit parallel
dose response curves. Figure 4 represents an
isobole diagram for a graded response. The
isoboles for concentration and response afioition
were determined with the appropriate mathematical
equations discussed.
The relatively simple types of isoboles
represented in Figures 3 and 4 should only be
expected for relatively simple in vitro systems
or in situations where there is a clear-cut
relationship between dose and effect. Given the
complexity and interdependency of physiological
systems, it is reasonable to suooose a priori
that the special types of additivity as
represented by strict concentration and response
addition will be approximated only occasionally
2.0 4.0 6,0 8.0 10.0
CONCENTRATION OF TOXICANT B
Figure 4. Uobole diagram {or graded rtiponie data.
0:1
-------
1n the responses of whole organisms to mixtures
of environmental toxicants. Furthermore, as
mentioned earlier, the relative toxicity of a
mixture depends on several factors which Include
the level of response (i.e., 10%, 50%, 90%
response), the ratio of toxicants in a mixture
(1.t. 1:10, 1:100, 1:1000), and the nature of the
response Itself. It should be noted that the
type of addition can only be described in
relation to the response under consideration.
With the same mixture of toxicants, different
types of toxicant interaction might be expected
for different responses (i.e. survival, growth,
reproduction). However, these special types of
toxicant interaction do provide a frame of
reference for evaluating the effects of toxicant
mixtures on whole organisms performances.
Isobole diagrams are useful for visualizing
the relationship between different types of
toxicant interactions ana for ael ineaf.ng the
various factors whicn can influence the relative
toxicity of multiple tox'cants. However, in
pracfce, isoboles a^e iif'icult to cerive
requiring a series of cose response curves for
the mixture at different ratios of the component
toxicants. Furthermore, there are no statistical
criteria which might be used to distinguish
between one form of interaction and another
(Plackett and Hewlett, 1952).
GROWTH STUDIES: Musxa and Weber (1977);
Koike^eister and Weber (1978)
Growth was selected as the graded response for
this study because it represents a performance of
the integrated activities of the whole organism
and as such is often a sensitive indicator of the
suitability of the environment (Warren, 1971).
Two of the ways environmental toxicants can
affect the growth of an organisms are: (1)
alter its ability to assimilate and convert food
material into body tissue, and/or (2) change its
rate of food consumption. To determine the
manner in which toxicants affect the growth of an
organism, both processes were investigated
separately.
Juvenile guppies were fed daily a restricted
ration of tubificid worms to determine the effect
of the toxicants on the gross growth efficiency
and relative growth rate (as defined by Warren,
1971) of the fish. The effect of the individual
toxicants and their mixture on food consumption
was investigated by feeding groups of fish an
unrestricted ration and measuring the amount of
worms consumed.
Parallel dose response (growth) curves were
found for copper and nickel. Concentration
addition was predicted as in the lethality
studies (Anderson and Weber, 1977). On the basis
of the mathematical model for concentration
addition, the predicted dose response curves were
calculated and statistically compared to the
regression equations experimentally determined
for the mixture. The results indicate that the
effects of the copper and nickel mixture on the
gross growth efficiency of the fish subjected to
both the restricted (Figure 5) and unrestricted
(Figure 6) feeding regimes. However, the dose
response curves for the mixture representing the
effects of the toxicants on the food consumption
of the fish was supra-additive relative.to the
dose response curve predicted on the basis of
concentration, Figure 7.
Dose response curves for dieldrin and nickel
were accessed. Theslopes of the dose response
curves for their individual effects on growth
proved to statistically parallel. We judged that
these compounds might Interact in a response
additive manner. Based on existing knowledge we
assumed they should act toxicologically by
different mechanisms of action. As we know the
parallelism of curves 1s only a suggestion, not
an absolute criterion for predicting either the
occurrence of concentration or for the negating
possible response addition. Regardless of the
growth parameters we looked at the dieldrin and
nickel studies were inconclusive. The reasons of
course could be many. The simple model we
proposed did not discriminate adequately to
classify the interaction of these two chemicals.
Mixtures of zinc and nickel were tested
(Koikemeiste1- and Weber, 1978). Our assumption
basea upon available data anc parallel growtr
dose response curves was that tney woula be
concentration adaitive. Mixtures proved to be
inf ra-concenfation additive.
In summary the graded results indicate that
the assumption of concentration addition
adequately predicts the effects of a
copper-nickel mixture on both the survival and
gross growth efficiency of guppies. The dose
response curves for the mixture representing the
effects of tne toxicants on the food consult-on
of the fisn was supra-aocitive relative to tie
dose response curve predicted on the basis of
concentration addition. An explanation for the
differences in these two responses to the mixture
was beyond the scope of the study. However, it
is reasonable to assume that the effects of tne
toxicants on the metabolic processes involved in
the conversion of food material into body tissue
are different from their effects on the
biological processes regulating the consumption
of food.
In our studies we found that the mathematical
model for'concentration addition predicted the
responses of guppies to both lethal and sub'ethal
concentrations of a copper anc nickel mixture.
However, it should not be inferred from these
results that the type of joint toxicity observed
when organisms are subjected to high, rapidly
lethal concentrations of mixtures will
necessarily occur in cases where animals are
subjected to low concentrations of the same
toxicants. Furthermore, the nature of toxicant
interaction can only be meaningfully described in
relation to the particular response under
consideration. For example, we found that
mixtures of copper and nickel were concentration
additive in experiments evaluating their effects
on the gross growth efficiency of the guppies;
however, in the food consumption studies, the
same mixture at similar concentrations produced a
more toxic response than was predicted on the
assumption of concentration addition.
Although each of our mixtures were not
accurately predicted, we must recognize that this
is a simplistic model. The complexities of
physiological systems from pharmokinetics to
actual receptor interactions certainly makes the
real world much more complex. The model does
allow a specific reference point to evaluate and
37
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80
% 70
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£ 60
M
NICKEL
COPPER
Cu
8
OBSERVED
o:
O
50
-6.5 -6.0
I
I
-5.5 -5.0 -4.5 0.5 1.0 1.5
LN TOTAL CONCENTRATION (mg/l
2.0
2.5
3.0
Figure 5. Doae respor.ae curves showing effects of copper, ruckei, ar.c their mixtures
(oDierved and predicted) on gross growth efficiency norma..zec to responses
of controls (restricted ration study).
o
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100
90
80
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Cu-Ni MIXTURE
O NICKEL
COPPER
1
1
-"6.0 -5.5 -5.0 -4.5 0.5 1.0 1.5 2.0
LN TOTAL CONCENTRATION (mg/l)
2.5
3.0
Figure 6. Dose response curves showing effects of copper, nickel, and their mixtures
(observed and predicted) on gross growth efficiency normalized to responses
of controls (unrestricted ration study).
38
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~ 100 r
5?
uj
90
80
a. 70
13
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Cu-Ni MIXTURE
\
NICKEL
COPPER
OBSERVED
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PREDICTED
-6.0 -5.5 -5.0 -4.5
0.5
1.0
1.5
2.0
2.5
3.0
LN TOTAL CONCENTRATION (mg/l)
Figure 7. Dote response curve* showing effects of copper, nickel and their mixtures
(observed and predicted) on food conmrr.pt ion rate normalized to responses
of controls {unrestricted ration study).
identify mixtures which deviate from the model
and the direction, infra or supra-additive, from
either concentration or response addition. To
insure the success of a species in nature, it is
necessary to evaluate the effects of potentially
hazardous toxicant mixtures on the performances
of whole organisms. This approach provides a
methodology for assessing the toxicity of
mixtures of environmental toxicants at this level
of biological organization.
ORGAN SYSTEMS: Shelton and Weber (1981)
Mortality (quantal response) and growth
(quantitative) respon-se were to this point used
to evaluate the concentration and response
additive models for mixtures. A third test of
the usefulness of this model was done using an
organ system level of toxicity. The decision was
made to test the model in a mammal (mice) rather
than a teleost. Liver damage was the specific
organ system response chosen. Plasma alanine
aminotransferase (ALT, formerly GPT) activity
has been shown to be a sensitive indicator of
liver damage in mice (Klaasan and Place, 1966)
and plasma elevation of ALT correlate well with
the severity of damage (Balazs et al., 1961).
The type of joint action observed for a binary
mixture can be influenced by the degree of
separation in the duration of onset of toxic
action for the respective toxicants in that
mixture, Turner and Bliss (1953). For that
reason, the temporal effects of the selected
hepatotoxicants used in the study on plasma ALT
were exanined. All experiments were perfomec
using male albino mice of the CF-1 strain reared
in our own breeding colony and housed at five per
cage. The animals weighed 25-35 g and were
maintained on laboratory pellet diet and wate*- ad
libitum. The animal room was maintained at a
12-hour light/dark cycle with an ambient
temperature of 70-72°F.
The toxicants were carbon tetrachloride
(CC1,), xcncchlorooenzene (MCE! and acetamnoznen
(ACEi). The CC1, and MCB were dissolved in corn
oil and ACET was dissolved in 0.9% N.aCl at <10°C.
The toxicants were diluted to deliver the proper
dosage in a final volume of 0.01 ml per gram of
animal weight. These compounds were administered
intraperitoneally between 11:00 a.m. and 1:00
p.m. each day.
Liver damage was assessed by measuring plasma
ALT activity. Relative plasma ALT elevations
were determined at 2, 4 8, 16, 24, 48 and 72
hours following the administration of each
toxicant. An optimum time interval was
determined and used in the toxicant mixture
study. The plasma ALT determination of Reitman
and Frankel (1957) was used and the results are
reported as international units (ID) per liter.
Single-component dose response curves were
initially developed for each hepatotoxicant.
Characteristics derived from these curves (i.e.,
slope, potency ration, TD50) are shown in Table
4. The TD5Q's were used to calculate the potency
ratios forjlhe toxicants. HCB and ACET were
found to be approximately equipotent in producing
liver damage whereas CC14 appeared about 35 times
-------
Tabl« 4. Dost response characteristics of selected h*patotox1cants on pi ISM lUnlnc anlnotraniftrase1 activity In Hi
lib'to "let.
m fc
""SO rV>te«£y,.
Toxicant
1.
2.
3.
Carton tttnchlorl*
(CC14)
Nonoehlorobcnzm* '
(«8)
tkttimlnophen
(ACH)
•9/kg
U.9
(14.2 . 19.9)
428
(395 • 466)
558
(485 - 643}
Mnl*/k9 ratio *
109.5 1.0
(92.5 . 129.6)
3807 34.8
(3505 - 4136)
3694 33.7
(3209 - 4252)
Slope
(±SO) t value4
6.57
(*!.»)
8.40 -0.45
(tl.24)
8.31 -0.77
Ul.15)
P value'
—
0.667
0.471
*A positive responie 1s defined as a plasma lUnlne anlnotransferase elevation *3 SO above the control meal (10 t 2 IU)
^Determined fro» the dose response regression eqoatlon. Parentheses Indicate 95X CI.
CTDCC(HCS or ACrn/TDcjiCC
CC
unole/kg comoar'son
T value determined when slope of dose response curve for KC3 or ACE* is corcsred to that of carbon tetracnlorlde.
'in eacn csse slopes were not significantly differs--, fror parallel at tt'e ' value (nd1catec.
Fror Shelton and Weee' (1981)
more toxic than either MCB or ACET."
Consequently, we decided to test the joint
hepatotoxic effects of the mixtures CC1. + MCB
and CC1. + ACET. The large potency ratio between
the constituents in the tested mixtures allowed
greated resolution in differentiating the
possible types of joint action resulting from
them. When the slopes of the MCB and ACET curves
were each compared to that of CCL. (t test), no
significant deviation from parallelism was
apparent (Table 4). It was assumed from these
findings that concentration addition would be the
most likely effect for the mixtures CC1. + MCB
and CC1. + ACET predicted in each case.
CC14 + MCS Mixture. A theoretical dose
response curve for the binary mixture of CC1, and
MCB at a molar oose ratio of 1:38 was predicted
using Finney's (1971) equation for concentration
addition. The development of this curve involved
utilization of data from the single component
dose response regression equations as well as a
common regression coefficient determined by
analysis of covariance. This curve is shown
plotted in Figure 8 along with the curves for
CC1., MCB, and the observed curve for the 1:38
mixture. The results show no difference between
the two curves at P > 0.975.
CC1* + ACET Mixture. The predictive equation
for the mixture of CC1, + ACET was developed for
a molar dose ratio of i:36.6 (CC1,.:ACET). This
curve is shown plotted in Figure 9 along with the
observe dose-response curve for the mixture as
well as those for the singly applied CCl. and
ACET. The test of comparison revealed that the
predicted and observed curves for the CC1. + ACET
mixture differ (P < 0.0005). The observed joint
effect for the mixture can thus be categorized as
infra-additive on the basis of concentration
addition.
To determine if response additivity might more
adequately describe the observed joint effect for
the CC1. + ACET mixture, the observe points were
statistically compared to those predicted on the
basis of response additivity. The findings show
that the observed and predicted curves again
differ (X = 40.6; P <0.0005).
The results of the organ system investigation
suggest that the toxicity of the mixtures can be
predicted and classified by examining the
single-constituent toxicities. The joint effects
observed for the CC14 + MCB mixture we"6 clearly
predicted by the equation for corcent'afon
addition. It is evident that the res:cnse :* a
given aose of a CCld + MCB mixture is not merely
the surr, of the toxic effects of the CC1. and MCB
given singly. Instead, the addition c* the
effects follows a log-linear relationship wth
respect to the total concentration of ooth CC1.
and MCB in the mixture.
The interpretation of the joint effects of the
CC14 -i- ACET mixture is more difficult. There is
an apparent antagonism exhibited with a resultant
infra-additivity. Since present knowledge of the
toxic mechanisms for both MCB and ACET does net
present any striking differences between the two,
any observed differences in joint action, when
ccmoined witn CCl^, is largely unexplained. It
has been inferred that acetaminopnen ~ay dar.age
the hepatic endoplasmic reticulum (Thoreirsson et
al., 1973). If this is the case, then this could
affect the activation of CC1., with resulting
infra-additivity..
CONCLUSIONS
When we began this work we hoped to use
pharmacological models already developed and
apply them to problems of environmental
toxicology. The desire was to have a model that
had applicability to environmental problems and
was rich enough in its information to lead us
into an understanding of the chemicals with which
we had concern. The most careful analysis of the
mixtures would involve a factorially designed
experiment. Using multiple toxicants and among
doses a factorial design would become impossible.
So the desire was to use existing knowledge and
utilize the model to expand our knowledge about
the toxicants. It was also our wish to have the
model serve truly multiple mixtures and not just
binary mixtures." We did successfully use it in a
mixture of four toxicants, two metals and two
-------
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O MONOCHLOROBENZENE
» CCI4:MCB (observed)
— CCI^MCB (prtdiclcd)
10
10 10"
DOSE (^mole/Kg)
10
Figure 8. Dose response curves illustrating the effects of carbon tetrachloride (CC1.) , mono~
chlorobenzene (MCB) and the 1:38 mixture (CC1.:MCB) on the percent of animals
(expressed as probit) responding with significant plasma alanine amrnotransferase
elevations. Both the predicted and the observed curves for the mixture are shown.
Each point represents a treatment of a minimum of ten animals.
7 -
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O ACETAMINOPHEN
» CCI4: ACET (observed)
CC14:ACET (predicted)
10
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DOSE (>imole/Kq)
Figure 9.
Dose response curves illustrating the effects of carbon tetrachloride (CC1.), acetaminoph
(ACET) and the Ii36,6 mixture (CC^iACET) on the percent of animals (expressed as
probit) responding with significant plasma alanine aminotransferase elevations, Both the
predicted and the observed curves for the mixture are shown. Each point represents a
treatment of a minimum of ten animals,
en
41
-------
organic chemicals; on the other hand most of our
tests used only binary mixtures. The basic model
has been theoretically expanded upon, Christensen
and Chen, 1985. It has also been reduced to such
a simplistic form that it lacks any richness
other jthan Its description of direction from
concentration addition, Marking, 1985.
Our own efforts using Plackett's and Hewett's
(1948) noninteractive scheme was not always on
the mark. The concentration (simple similar) and
response (independent) joint action has the
richness to describe possibilities of
correlations between susceptibility of animals,
interaction of infra or supra-addition compared
to the concentration and response addition. The
formulation of isobole diagrams plotting both
concentration and response addition defined
mixtures which would allow the greatest
statistical opportunity to differentiate between
the two noninteractive possibilities.
Our approac^ aooears to offer a method for
evaluating the effects of coramec toxicants. We
were successful in describing the types of
interaction for binary and of a mixture of four
toxicants in the case of lethality. The model
also was successful in describing interactive
effects of binary mixtures on growth and on an
organ, liver. Although it didn't describe all
Interactions accurately, it did provide insight
into possible questions which if answered might
help solve the complexities of the interaction.
The limitations of the model should not be
overlooked and one of the major limitations is
Inherent to all statistical explanations.
Statistically 1t 1s possible to state whether the
observed responses to the mixture agree with
those predicted within the limits of sampling
error. The statistical analysis can only provide
contradictory or permissive evidence, but not
indicative evidence (Hewlett and Plackett, 1950).
For example, an implication of the mathematical
model for concentration addition is that the
toxicants in a mixture act primarily upon similar
biological systems. Statistical agreement of the
observed dose response curves to the curves
predicted on the basis of concentration jccition
does not necessarily mean that tne toxicants act
upon similar biolcc'cal systems, but on"_,
they appear to oo sc.
Partial support provided by NIH Grant ES-00210
REFERENCES
Anderson, P. 0. and Weber, L. J. (1975) Toxic
response as a quantitative function of body
weight. Tox. Appl. Pharm. 3J_:471-483.
Anderson, P. D. and Weber, L. J. (1977) The
toxicity to aquatic populations of mixtures
containing certain heavy metals. Proc. Int.
Conf. Heavy Metals. 2, 933-953.
Ariens, E. J. and Simonis, A. M. (1961).
"Analysis of the action ofdrugs and drug
combinations", Quantitative Methods in
Pharmacology, H. de Jonge uditor),
North-Holland Publishing Company, Amsterdam,
p. 286-311.
Ariens, E. M. (1972) "Adverse drug
interactions—interactions of drugs on the
pharmacodynairric level", Proceedings of the
European Society for the Study of Drug
Toxicity, 13:137-163.
Balazs, T., Murray, T. K., McLaughlan, J. M., and
Grice, H. C. (1961) Hepatic tests in
toxicity studies on rats. Toxicol. Appl.
Pharmacol. 3:71-79.
Bliss, C. I. (1936) The size factor in the
action of arsenic upon silkworm larvae. J.
Exptl. Biol. 13:95-110.
Bliss, C. I. (1939) The toxicity of poisons
applied jointly. Ann. Appl. Biol. 26:585-615.
Brown, U. M. (1968) "The calculation of the
acute toxicity of mixtures of poisons to
rainbow trout", Water Research, 2(10):723-733.
Christensen, E. R. and Chen, C-Y. (198:} A
general noninteractive multiple toxic'ty model
including probit, logil -a-nd weibull
transformations. Biometrics 41:711-725.
Clark, A. J. (1937) "General Pharmacology",
Heffler's Handbuch der Experimentel'en
Pharmakologie, i*. Heuoner and J. Scp.uller
(Editors) /Verlag von Julius Springer, Berlin,
Volume 4.
Fedeli, L., Meneghim, L., Sangiovanni, V.,
Scrollini, F. and Gori , L.(1972)
"Quantitative evaluation of joint drug
action", Proceedings of the European Society
for the Study of Drug Toxicity. 13:231-245.
Finney, D. J. (1942) The analysis of toxicity
tests on mixtures of poisons. Ann. ADD!.
Biol. 29:82-94.
Finney, D. J. (1971) Probit Analysis, 3rd Ed.,
Cambridge Univ. Press, London and New York.
Gaddum, J. H. (1933) Reports on biological
standards. III. Methods of biological assay
depending on a quanta! response. Spec. Rep.
Ser., Med. Res. Coun., Lond., no. 183. His
Majesty's Stationary Office.
Gaddum, J. H. (1953) "Bioassays and
mathematics", Pharmacological Reviews.
5(1):87-134.
-------
Hewlett, P. S. and Plackett, R. L. (1950)
Statistical aspects of independent joint
actions of poisons, particularly insecticides.
II. Examination of data for agreement with
the hypothesis. Ann. Appl. Biol. 37:527-552.
Hewlett, P. S. and Plackett, R. L. (1952)
Similar joint action of insecticides. Nature.
169:198-199.
Hewlett, P. S. and Plackett, R. L. (1959) A
unified theory for quanta! responses to
mixtures of drugs: non-interactive action.
Biometrics 15:591-610.
Klaassen, C. D. and Plaa, G. L. (1966) Relative
effects of various chlorinated hydrocarbons on
liver and kidney function in mice. Toxicol.
Appl. Pharmacol. 9:139-151.
Koikerne1!ster, E. A. and Weber, L. J. (1978) An
effect of zinc anc mc
-------
DISCUSSION OF THE CONTRIBUTION OF L.J. WEBER AND ASSOCIATES OF
THE MARr HATFIELD SCIENCE CENTER AT OREGON STATE UNIVERSITY
Bertram D. Litt, EPA/OPP/HED
The paper by Or. Neber and his
associates reviews their work of the
past 12 years. They have made
significant contributions to the
literature on formal study of multiple
simutaneous exposures of fixed mixtures
of 2-4 compounds in fish and mice.
They have shown that there are
limited and unpredictable circum-
stances in which the dose/response
relationship observed fit traditional
matnematical models. More important,
tney have demonstrated that neither
structure—activity-relations hips (SAR)
nor parallelism of the allcmetric
responses of incividual chemicals or
pairs of chemicals provide sufficient
information to accurately predict the
activity patterns of simultaneous
exposure to three, four, or more chemi-
cals. This is an important finding
because modern man lives in an environ-
ment in which he is everywhere exposed
to sopnisticated combinations of chemi-
cal residues in the air he breathes,
the fooc he eats, and frequently even
the water he drinks. Weoer's paper has
shown that combination of toxicants can
result in either superadaitivity or
reduction in toxicity below that pre-
dicted by simple adjiitivity in teleosts
and mammalian experimental models.
This complexity precluded the use of
simple strategies for dealing with
complex mixtures on a routine basis.
At this particular time EPA is issuing
guidance recommending the use of the
additivity as the fallback position for
estimating cancer risk of mixtures when
adequate data on the mixture is not
available.
The work just summarized by Or. Weber
could be used as the first step for an
ordered strategy to evaluate both fixed
complex mixtures, such as pesticides
where the source mixture remains con-
stant, and varying mixtures, where
concentration and constituents of
pollutants vary with respect to time or
distance from the source of contami-
nation. The approach to both problems
may be unified by first studying the
morbidity and mortality effects of the
chemical mixture at the source concen-
tration at time tQ. A second study
would repeat the initial tQ effects as
part of a series of ocservations to
evaluate a; dirr.-nitior. of effects due
to temporal and/or spatial distance or
b) selective deactivation of the
chemical mixture.
Weber's work provides teleost and
rodent models which could be used to
perform rapid experiments suitable for
screening chemical mixtures for the
identification of components wnich
are reinforcing and tr.ose wnich show
antagonistic tcxicity enc-pcihts.
Secondly these studies should De usea
to identify LCso levels as the initial
step of evaluating the toxicity of the
mixture at the source concentration
and at lower concentrations of interest
in rodents.
Following the screening procedure,
the EPA Office of Pesticide Programs,
Section F Guidelines could be followed
for studying subchronic, chronic and/or
teratogenic effects using the source
concentration and at lower doses. The
selection of lower doses snould be
keyed to levels indicated by pnysiolo-
gical and environmental factors rather
than the considerations listed in the
guidelines for technical grade
chemicals.
-------
JOINT AQUATIC TOXIC1TY OF CHEMICAL MIXTURES AND STRUCTURE-TOXI CITY RELATIONSHIPS
Steven J. Broderius, U.S. EPA, ERL-Duluth
INTRODUCTION
Most studies evaluating the toxicitv of
environmental pollutants to various aquatic
organises and systems have involved exposures
to separate toxicants. Relatively few
investigations have defined the adverse
effects of Bixtures of two or more toxicants.
Effluents, leachates, and natural waters,
however, frequently contain several toxic or
potentially toxic substances. The zones of
'influence from point source pollution night
also overlap. As waste treatment technology
is advanced and implemented, nonpoint
pollution from sources such as agriculture and
atmospheric deposition will contribute to a
»reater degree to the overall pollutant load
received by aquatic ecosystems Therefore, in
assessing the effects of toxicants on aquatic
communities and to insure their success,
consideration should be given to the
likelihood that a wide variety of chemicals
might be present simultaneously and that joint
toxicity is quite likely the reason for
adverse impacts of pollutants on aquatic
environments.
Water quality criteria should insure that
the discharge levels of separate toxic
cnemicals and mixtures are not deleterious to
either the distribution or abundance of
important aquatic populations. The setting of
current water quality standards has been
developed from criteria based on "no-effect
levels" of single toxicants. Such a practice
may be inadequate to protect aquatic organisms
exposed to mixtures of chemical pollutants
(Spehar and Fiandt, 1986). This practice,
however, is becoming firaly established out of
necessity for lack of a better approach. A
tentative proposed approach to incorporate the
effects of joint toxicity has been to assume
strictly additive action for even diverse
toxicants Standards using this procedure,
however, have generally not been set because
formulating regulations on such a basis may be
premature, since other forms of less toxic
interaction are not uncommon
It would be desirable to be able to predict
or even estimate the probable toxic components
and response for an effluent, leachate, or a
water body solely from a knowledge of its
important individual toxic and relatively
non-toxic chemical constituents. If such a
predictive approach is valid, it would be
possible to determine the relative
contribution of each toxicant to the overall
toxicity. One could then take the appropriate
action necessary to effectively reduce the
toxicity of the waste water. Such an approach
would better enable regulatory agencies to
provide rationale for determining and
predicting the effects of chemical
combinations to valued aquatic organisms, and
defining high hazard situations where more
than one toxic substance is known to exist.
Defining the toxicity of mixtures is a major
problem at both the theoretical and practical
level. There has not been sufficient research
to establish whether there is any widely
applicable rationale and workable approach to
evaluate and possibly predict the joint action
of toxicants in the aquatic environment.
There are a few publications (i.e., Sprigue,
1970; Anderson and Weber, 1975; Marking. 1977;
Muska and Weber, 1977; EIFAC, 1980; Alabaster
and Lloyd, 1980; Calanari and Alabaster, 1980:
Konemann, 198lb; Hermens et al., 1985;.
Broderius and Kahl, 1985; Spehar and Fiandt,
1986) that summarise and' review much of the
information on combined effects of mixtures of
toxicants on aquatic organisms and approaches
jsed to evaluate these effects. It is
apparent from these articles that additional
work must be conducted to characterize the
joint action of mu.t.ple toxicants, especially
at sublethal levels This paper summarizes ar.
approach to explore basic principles wruch
govern the toxicol05.ca1 issues pertaining to
the joint action of multiple toxicants
TERMINOLOGY AND MODELS
Various terms and schemes for classifying
and naming effects of chemicals to describe
the response of test organisms to two or tfore
toxicants, as predicted from the separate
toxicity of the individual substances, have
'been recommended The different forms of
joint action have been graphically illustratec
and discussed by Sprague (1970), Muska and
Weber (1977), and Calaman and Alabaster
(1980).
The development of predictive methodology to
describe the joint action of multiple
toxicants has been approached in two distinct
ways (Marubini and Boranomi. 1970). The first
approach has been to describe responses
resulting from constituent interaction and to
try to give them a mathematical expression
based on statistical considerations The
second approach has been to postulate a
physical mechanism of interaction at receptor
sites, to derive theoretical response curves
on the basis of assumed primary mechanisms.
and to relate experimental and theoretical
results. It is the general belief that the
first approach is more suitable for a broad
and quantitative evaluation of the joint
toxicity of chemical mixtures to whole
organisms. Given the complexity and
interdependency of physiological systems,
however, it is reasonable to suppose that a
classification of the interactions between
environmental toxicants into various types of
responses for whole organisms will not always
be possible. The real value of designating
special types of toxicant interaction is that
they provide a frame of reference for the
systematic documentation and empirical
evaluation of multiple chemical effects.
Central to an analysis of joint action are
the- concepts of similarity and interaction.
These ideas were first proposed by Bliss
(1939) for two substances and later developed
45
-------
by PUckett and Hewlett (1948, 1952, 1967) »nd
Hewlett «nd PUckett (1959). Conridering
these general biological phenomena, the
different types of combined effects ctn be
identified from the relative toxicities of the
individual constituents. The types of joint
action are defined as similar or dissimilar
depending on whether the sites of primary
action to the organisms are the sane or
different, and as interactive or
non-interactive depending on whether one
toxicant does or does not influence the
biological action of another.
Interactive joint toxicity is not directly
predictable from the toxicity of the separate
components. Models describing quantal
responses to mixtures of interactive toxicants
are very complex and are not described by
simple formulas '.Hewlett and P'.ackett, 1359,
1964 Certain parameters required for the
.Tiodels are also normally unattainab.e when
evaluatin" the effect of a number of toncants
on wnoie organism responses Therefore.
virtually all investigators evaluating the
effects of toxicant mixtures on parameters
such as survival, growth, and reproduction of
aquatic organisms, only consider the special
cases of non-interactive joint action.
These concepts in conjunction with
concentration- response curves and isobole
diagrams of joint action have been used in an
approach to study the. lethal and suciethai
toxicity of mixt'ures to freshwater organisms.
The resulting models are named concentration
and response addition (Anderson and Weber,
1975), which correspond to the previous
terminology of simple similar and independent
joint action (Bliss, 1939), respectively
With concentration addition the toxicants
act independently but produce similar effects
so that one component can be expressed in
terms of the other after adjusting for
differences in their respective potencies.
Even sub-threshold levels for mixtures of many
toxicants can combine to produce a measurable
effect. Since the toxicants act upon the aame
or a very similar system of receptors within
an organism, the toxicants are completely
correlated so that no coefficient of
association need be determined. Therefore,
for homogeneous populations
concentration-response curves for individuals
exposed to separate toxic constituents and
corresponding mixtures of similar chemicals,
or ones which act similarly, are expected to
be parallel or similar in shape. Parallelism
of concentration-response curves and complete
correlation of individual susceptibilities,
however, are not a requirement for this type
of interaction. In cases where the
concentration-response curve for the
individual toxicants are parallel, Finney
(1971) and Anderson and Weber (1975) have
provided a procedure to predict a
concentration-response curve for the mixture
based upon the assumption of concentration
addition. The toxic unit model (Sprague,
1970), which measures the toxicity of mixtures
only at particular levels of response, can be
considered a simplification of the con-
centration addition model. This special case
of the general model assumes that a mixture
should be at a particular magnitude of toxic
response when the sum of the concentrations of
all toxicants expressed as fractions of each
toxicant's effect concentration equals unity.
A second model of joint action, response
addition, is predicted when each toxic
component of a mixture primarily acts upon
different vital biological systems within an
organism or affects differently the same
systems. Each toxicant neither enhances nor
interferes with one another and contributes to
a common response only if its concentration
reaches or exceeds a certain tolerance
threshold. Therefore, multiple toxicity
effects cannot be expected when each of a
mixture's components is below its respective
response threshold. The tolerance of
individuals exposed t: a mixture of toxicants
acting independently -ay or may not be
correlated Therefo-? tr.e resior.se c'jr'-e%
for each toxicar.t of ± mxture -ay or ma;. -;-
be parallel or similar .n sr.ape if the
response curves for ccnpcjnds in a mixture are
dissimilar or if the T.odes of toxic action are
known to be different for toxicants which have
similar response curves, then it is proposed
that the degree of response to the mixture can
be predicted by sumiring in various ways each
response produced by the separate toxicants.
The proportion of ind.viduals of a group that
are expected to rest:"d or the degree of
response for each individual organism exposea
to specific components and combinations
exerting response acc^tion depend upon the
responses to the inc.vidual compounds and the
correlation between tne susceptibilities of
the individual organisms to each toxicant
For mixtures of two chemicals this tolerance
correlation can vary from completely positive
to completely negative Three models have
been proposed (Hewlett and Plackett, 1959; for
correlation of individual tolerances of -I. 0,
and +1, For mixtures of many chemicals the
correlation coefficient ir) is expected to
vary from 0 to *1 i Xor.enann. 1981b. Response
addition is less likely to occur than other
types of action because an organism is a
coordinated system (Plackett and Hewlett,
1967). Nevertheless, response addition is
important theoretically for it leads to a
limiting mathematical model.
The application of concentration and
response additive models to mixture toxicity
data has not been extensive nor have the
models proven to be useful in all cases.
Also, when applying these classifications to
mixtures of more than two chemicals, problems
might arise because the joint action of the
different groups can fall under different
models as additional joint actions are
possible between the groups Therefore, a
mathematical description of the joint toxicity
of a mixture of greater than two compounds is
probably only possible for special situations
where non-interactive joint action seems to be
a prerequisite.
The more-than-strictly additive
(synergistic) and less-than-no addition
(antagonistic) joint actions are characterized
by a toxicity that is either greater or less
-------
than predicted from studies on the separate
toxicants. With these situations the
effectiveness of » mixture cannot be assessed
from that of the individual toxicants. The
response depends upon a knowledge of the
combined effect which is usually only
experimentally determined.
The different forms of Joint action can be
graphically illustrated by an itobole diagram
as presented in Figure 1. Isoboles are lines
of equal response and can be determined for
different mixtures of two toxicants where the
concentration of one toxicant for a
quantitatively defined response (i.e., 96-h
LC50) is plotted against the corresponding
concentration of the other toxicant. Mixtures
of toxicants A and B in different ratios are
identified by lines (mixing rays) radiating
from the origin of the isobole diagram. The
relationship between the isoboles may vary
depending upon the response level selected.
Combinations of the two toxicants represented
by points within the square area correspond to
responses that display joint addition. An
enhanced effect to that which Is strictly
additive, as represented by the diagonal
isobole, is more-than-strictly additive. A
lessened effect to that predicted for
summation is less-than-strictly additive, or
shows no addition. Response addition for two
toxicants with parallel concentration-
response curves is defined by the curved
isoboles for complete negative (r=-l) and for
no correlation (r=0) in susceptibility.
1:200
-I 4OO
2.0 4.0 6.0 8.0
TOXICANT B (mM)
10.0
Figure 1. tsobole diagram depicting various types of lethal responses for the
joint action of two toxicants displaying parallel concentration-
response curves. (From Muska and Weber, 1977).
-------
K&%£&£f;&3:^,::;: wvvms^i*^. i-.i;^-„• :^.
Combinations falling exactly on the upper and
right boundary of the square correspond to
ureas of no addition or the limiting case of
response addition with complete positive
correlation (r=l). Areas outside of the
square represent antagonistic responses
(less-than-no-addition) where one toxicant
counteracts or opposes the action of another
beyond that expected for the individual
toxicants. In a similar Banner to that
presented above, isobole surfaces can be
defined for three toxicants. This terminology
and classification scheme for the toncity of
two chemicals can, with certain modifications,
be extended to chemical mixtures containing
several toxicants.
EXPERIMENTAL APPROACH
A mechanistic approach incorporating
toxicant-receptor theory to assess jo . nt
action has not been pursued during our
research project because of the difficulty in
determining and lack of understanding of the
primary mechanisms by which toxicants eiert
their effects. Instead, the general approach
has been to study the relationships between
toxicant concentrations and whole organism
responses which can be observed and measured.
It is proposed that general elementary
principles and models describing responses
resulting from toxicants having simi.ar or
different modes-of-action can guide the design
of realistic and practical experiments that
will provide insight into joint action of
multiple toxicants. By designating special
types of toxicant interaction, a frame of-
reference for the systematic documentation and
quantitative evaluation of such effects for
chemical mixtures is provided. It should be
noted that the nature of each type of joint
action can only be described in relation to
the particular response being considered. The
special case of non-interactive joint action
has been investigated as a first and
predominant approach to evaluating the effects
of toxicant mixtures.
The specific forms of multiple toxicity that
are of particular concern from an
environmental point of view are characterized
by those with effects either greater than or
equal to that which would be expected if each
toxicant contributes to the overall effect
according to some function of its respective
potency. Therefore, experiments were designed
to differentiate between no addition,
less-than, more-than, and strictly additive
joint action.
The actual approach to studying the joint
action of chemical mixtures must be more
quantitative than qualitative. This may pose
complicated statistical questions related to
experimental design and analysis. To date
this issue has not been adequately addressed.
The experimental design should involve a wide
range of concentrations (sub-threshold to
effect levels for lethal and sublethal
endpoints) of the toxicants alone and if
possible at various proportions of chemicals
in mixtures. To accommodate this need, our
primary approach has been to conduct
experiments to define the joint acute toxicity
of binary mixtures as determined from isobole
diagrams. Additional work is planned with
sublethal endpoints.
Our initial experimentation has included the
testing of mixtures which are expected to
produce a concentration- addition response.
This type of joint action in which the
constituents act independently but similarity
is predicted when the quantal or graded
concentration-response curves for the separate
component toxicants and all mixtures are
parallel or similar in shape, or when the
primary mode of toxic action for the test
chemicals is expected to be similar. Response
addition, the joint action in which the
constituents act independently but diversely.
can be predicted if the quantal or graded
conce nt rat i on-re spc~.se curves for tr.e separate
component toxicants and all mixtures are
non-parallel : r are c ; 3 s i m i 1 a r in snape 7w,. s
type of joint act.or :s also predicted ;f
triere is a kr.swn difference in toxic action
between the constituents initially,
experiments were conducted with mixtures of
only two toxicants with multi-chemical
mixtures tested wher, confidence in
interpreting the sispler systems was obtained
or when a need for such information became
apparent
To allow for a nore comprehensive
interpretation anc extrapolation of limited
test results, a multiple toxicant study should
rely on fundamental relationships between
biological activity and selectivity, and the
chemical nature of toxicants Such an
approach, based on quantitative
structure-activity relationships (QSAR's)
where toxicity is predicted from models
incorporating molecular descriptors derived
from structure, has been proposed by Konemann
(I981b) and Hermens and Leeuwangh (1982).
With this approach it can be initially
presumed that chemicals causing a specific
effect by a primary and common mode-of-action
ii.e , narcosis, respiratory uncoupling.
acetocholinesterase inhibition, etc.) can be
modeled by a single high quality
structure-toxicity relationship. Each
different type of toxic action (selectivity)
should thus be characterized by a different
empirically derived QSAR, and concentration
addition would be expected for toxicants
within each relationship.
MATERIALS AND METHODS
Testing Conditions, Apparatus, and Procedure
The 96-h acute toxicity tests with 30-day
old laboratory cultured juvenile fathead
minnows (Pimepha1es prome1 as} were conducted
according to test conditions and with an
apparatus described by Brodenus and Kahl
(1985). The testing procedure was according
to ASTM (1980). Tests were initially
conducted with individual toxicants, and
subsequently expanded to test solutions
containing tip to 21 toxicants. Seven ratios
of two test chemicals were used to define the
binary isobolograms with four concentrations
-------
following »n 807. dilution factor »t each
•ixture ratio.
The values for the n-oct»nol/w»ter partition
coefficients (log P) wert taken from Hansch
and Leo (1979). Veith et al. (1979), and Veith
et al. (1985) or as calculated fro* the ClogP
version 3.2 computer program developed by the
Pomona College Medicinal Chemistry project
(Leo and Welninger. 1984; see Leo, 1985).
Data Analysis
Data were analyzed using several statistical
procedures. Estimates of the concentration of
toxicant most likely to cause 50% mortality
(LC5Q) and their 957. confidence limits were
determined from relationships fitted
mathematically by the trimmed Spearman-Karber
method ''Hamilton et al , 197"' Concentra-
tion-response slopes were determined by a
least squares linear regression program
The manner in which the comoined effects
of mixtures of two or more toxicants are
calculated by the quantitative tone unit,
additive index, and mixture toxicity index
approach have been outlined by Sprague (1970),
Marking (1977), and Koneraann (I981b).
respectively. The procedures used to analyze
results by concentration and/or response
addition models are according to those
proposed by Anderson and Weber (19751 A
statistical procedure to determine if binary
test data are better described by a straight
(strictly additive) or curved isobole has been
described by Broderius and Kahl (1985)
RESULTS AND DISCUSSION
Concentration-Response Curves
Acute lethality tests were conducted with
juvenile fathead minnows in order to define
the toiicity of individual chemicals alone and
in combination with certain other test
compounds. A plot was made of percentage
mortality in probit values as a function of
loj molar toxicant concentration (Log M) for
individual treatment levels from experiments
conducted with several chemicals and for each
of three suspected different modes of toxic
action. An example of one plot is presented
In Figure 2a. The slopes of the concentration
response curves for each separate mode appear
to be reasonably parallel and therefore can be
characterized by a single slope. Plots were
made of these data for the Narcosis I,
Narcosis II, and uncoupler of oxidative
phosphorylation model relationships, as
normalized according to the potency (Log M
96-h LC50) of that for 1-octanol, phenol, and
2,4-dinitrophenol. respectively. An example
of one normalized plot is presented in Figure
2b The slope for the normalized response for
each different mode is quite similar and
ranges from 12 8 to 15.1 for the Narcosis !I
and jncoupler chemicals respectively liable
1) Therefore, it is apparent that the slope
of acute lethality concentration-response
curves cajinot necessarily be used to separate
chemicals by their mode of toxic action.
1 sobo1e Pi agrams
Acute toiicity tests are also conducted in
order to define isobole diagrams for binary
mixtures. The test concentrations of two
toxicants are combined in various fixed ratios
to provide seven 96-h LC50 values that define
an isobologram Results from these tests.
representing three types of responses, are
presented in Figures 3-5. Mixtures of
1-octanol and 2-octanone display a strictly
additive type of joint action over the entire
mixture ratio range. This is apparent in
Figure 3 from a plot of the 96-h LC50 values
and 95" confidence limits for the binary
mixtures at 7 test ratios. A statistical
analysis of these- test data that establishes a
Table 1. Percentage mortality in probit values (Y) as a function of log molar
toxicant concentrations (X) for 96-h acute tests with juvenile fathead
minnows
Normalized concentration-response
relationship (Y=a+bX)
Mode of
toxic action
Narcosis I
Narcosis 11
Uncoupler
oxidative
phosphorylation
Reference chemical
1-Octanol
Phenol
2,4-Dinitro-
phenol
Intercept
59.1
±3.18
50.8
+4.26
87.1
±6.28
Slope r*
13.5 0.724
±0.792
12.8 0.562
±1.20
15.1 0.730
±1.52
N
113
60
36
-------
_ .
I0r-
Ol I 1 I I I I I I I I I I l I I I I 1 I
101-
8-
«••
15 .
o
B
41—
O
2
Y'59 I + 13 5X
t3.!8 ±0792
R-0.724
N-H3
i i I i i i i
-5
-4
-3
-2
Toxicant Concentration (Log M)
Fi»ure 2. (A) Percentage mortality in probit values as a function of log
toxicant concentration for treatment levels from Narcosis I test
chemicals. Up and down arrows represent 100 and 0 % mortality,
respectively. (B) Normalized plot of data in Part (A) as adjusted
according to the potency of 1-octanol. (From Broderius and Kahl,
1985).
-------
strictly additive joint toiicity was tlso
conducted (Broderius and Kahl, 1985).
Because of the difference in symptoms
associated with fish dying when exposed to
1-octanol and 2.4-pentanedione. a response
•dditi»e type of joint action would be
predicted for binary Mixture* of these
cheaicals. Test results, however, were
definitely not strictly additive but did show
joint action that was less than strictly
additive but apparently greater than response
addition with r=-l (Figure 4). Therefore,
results from this binary raisturc acute test
did not fit either the concentration or
response additive joint action models. A more
hazardous joint action than response addition
was observed.
The tests with binary aixtures of 1-octanol
and 2-chloroethanol provided interesting luc
explainable results. The 96-h LC50 for
1-octanol was unchanjed up to the LC50 level
for 2-chlorocthanol. The toiicity of
2-chloroethanol, however, was Markedly reduced
by the presence of octanol. It is proposed
that the presence of octanol inhibits the
metabolise of 2-chloroethanol to a nor* toxic
metabolite and thus results in a complex
isobole diagram. From the approximately 75
isobole diagram relationships thai we have
jenerated, the majority display a rcsvonse
exemplified by the first two digrams (figure
3 and 4). The complex type of joint action,
as exemplified by 1-octanol and
2-chloroethanol, was observed in oiily a few of
0.60r-
0.02 0.04 0.06 0.08 0. ft 0. 12 0~l 4
-Octanol (mM)
Figure 3. Isobole diagram depicting the 96-h LC50 values and confidence limits
for juvenile fathead minnows exposed to different mixtures of
1-octanol and. 2-octanone.
-------
the isobole type tests. These Utter tests
frequently included primary aromatic amines
(Aniline derivatives) us one of the test
chemicals. In only one instance has a
Markedly "ore than strictly additive type
joint action been observed in binary Mixtures
of industrial organic*.
OSAR and Joint Tnxicitr - Narcosis 1 Chfmu.-a 1 •<
If the results from joint tuxicity tests arc
to make an important contribution to aquatic
toxicology, a certain basic understandinj as
to how chemicals jointly act must be
provided. Tests must also be conducted in
such a manner that there is a predictive
nature to our findings. To address these
joals. our Mixture testing effort is related
to an acute toxicity data base that is being
systematically (enerated for a projran to
evaluate aquatic toxicity of organic chemicals
from a structure-activity approach. This data
base for juvenile fathead Minnows is being
developed at the U.S. Environmental Protection
Agency, Environmental Research Laboratory-
Duluth. Some of this data has been tabulated
by the Center for Lake Superior Environmental
Studies (CLSES 1984, 1985). A plot of our
°'8.0 0.02 0.04 0.06 0.08 0.
1-Octanol CtnM)
0.12 0.14
Figure 4. Isobole diagram depicting the 96-h LC50 values and confidence limits
for juvenile fathead minnows exposed to different mixtures of
1-octanol and 2,4-pentanedione (-.-«- predicted relationship
for response addition with r=-l).
-------
acute toxicity data base for approximately 600
industrial orj»nic chemicals is presented in
Figure 6. The solid square data points define
»n approximate water solubility line above
»hich there »re very few observed dat»
point*. This line, therefore, defines a xone
beyond which an acute response is not expected
in a four day test. It is apparent that the
data do not fall into siany obvious patterns
•hen the acute response is plotted only with
lot P- Virtually all of the test data fall
within a lo| P ran|e of about -1 to 8 and the
acute toiicity is in general directly related
to log P. Ve'ith et al. (1985) observed that
almost 507. of the 20,000 discrete organic
industrial chemicals currently in production
have log P value* less than 2.0. Therefore,
since our data base is representative of the
TSCA chemicals, the 96-h LC50 to juvenile
fathead minnows of nost industrial chemicals
is expected to be approximately 10 M or
greater. There also appears to be a base line
toxicity (Figure 8) below which a chemical can
not be less toxic. This is most apparent for
chemicals with a log P of less than about 4.0.
Because it is difficult to make any specific
conclusions from such a plot the data were
divided into smaller units and plotted
according to chemical class or subgroupings.
An example of one such unit was for the
t .4r-
0.
0.02
0.04 0.06 0.08
1-Octanol (mM)
j
0.12 0.14
Fijure 5. Isobole diagram depicting the 96-h LC50 values and confidence limits
for juvenile fathead minnows exposed to different mixtures of
1-octanol and 2-chloroethanol (-«-.- predicted relationship for
response addition with r=-l). Vertical arrows indicate greater than
v;. I ues.
-------
^
ketones (Figure 7). From this plot it is
apparent that the majority of the tested
Icetones conform to a response model line that
Veith et al. (1983) have characterized by a
•ode of toxic action called Narcosis I. This
procedure was repeated for 22 other chemical
groupings and it was observed that greater
than SOX of the industrial organic chemicals
that we have tested conform to this
non-reactive or baseline mode of acute toxic
action. Therefore, the majority of organic
industrial chemicals apparently do not have
specific structural features which allow them
to be biologically active by specific
mechanisms. This nonspecific or general
membrane perturbation mode of toxic action
called Narcosis results from the reversible
retardation of eytoplasmic activity as a
result of the absorption of foreign molecules
into biological membranes The environmental
concentration necessary to pro;Jce this
response is independent of Tc.ecular structure
and is linearly related to log P. This is
only true, however, if no metabolic
alterations result in more toxic metabolites
and steady state equilibrium is attained.
If test chemicals are conforming to a QSAR
that defines a suspected mode of toxic action,
then one Bight expect that chemicals defining
this Mode will be strictly additive in their
joint toxicity. To test this premise, isobole
diagrams were generated for binary mixtures of
1-octanol (e.g., Narcosis I reference
chemical) and a second chemical from each of
seven different chemical groupings that in
general conform to the Narcosis 1 model line.
The results of these tests, as normalized to
the potency of 1-octanol, are presented in
Figure 8 (Broderius and Kahl. 1985). It is
apparent that the iscsoles are in genera!
characterized Dy a :.agonal line that
describes a strictly additive type of joint
action This su;g» = ts tr.at trie fathead ,TM nr.ow
perceives these che- :a.s as having the same
2r-
-2
o
0
O -4
to
o
-C
s -6
-8
O _J
o
o
-2
-4
a
o
-6
-Q
L
0
-8
8.0
~to
Log P
Figure 6. Acute toxicity to the fathead minnow of approximately 600 industrial
organic chemicals is related to the octanol/water partition
coefficient (Log P). Water solubility of allcyl alcohols Indicated by
square data points.
-------
or a very similar »ode of toxic action.
k iecond type of experiment has been
conducted to document the joint toxicity of
Mixtures containing two or more Narcosis 1
toxicants. An attempt was »ade to prepare
tett concentrations of these mixtures on an
equal proportion basis, based on LC50
concentrations of the individual chemicals.
Usinf the mixture toxicity index (MT1) scale
(Konemann. 1981b), it was observed that the
joint action for the tested mixtures
containing 2 to 21 chemicals is in general
characterized by strict additivity (i.e., MT1
- 1). Therefore, a concentration addition
type of joint action has not only been
demonstrated for chemicals fron the same class
but also for chemicals from seven different
:iasses and in equitoxic nixfures containing
^r to 2'. chemicals (Brodenus and Kahl, 1985)
We have conducted acute toxicity tests with
severa: alky! alcohols, which produce a
c'. ass.oa! narcosis type of tone act:on The
acute toxicity of these alcohols has been
observed to increase »ith increasing log P and
decreasing water solubility. The relationship
is apparently linear for the homo logs tested,
with the acute response covarying with water
solubility at lof P values less than 4.0.
The allcyl alcohols apparently define a QSAR
series when log P is used as the only
independent variable. Veith et al. (1983)
have proposed a bilinear QSAR model for
physical narcosis that is based on a
relationship derived from about 65 common
industrial chemicals (e.g., alcohols, alkyl
halides, ethers, ketones, benzenes). These
data indicate that chemicals exerting a common
narcosis node of action, characterized by
membrane expansion, may be modeled jointly,
even though ethers, ketones and benzenes are
in general siijntiy more toxic tnan alcohols
The joint action of test chemicals associated
with the Narcosis 1 SAR were expected to be
characterized bv the concent rat.on addition
2r-
0-
-2 -
O)
O
O -A
\r>
o
.c
i
-------
model. Our results indicate thit this was true
for numerous binary and equitoiic mixtures of
up to 21 chemicals.
Konemann (I981a) conducted 7 or H day
equitoxic acute toxicity teits usini juppies
fPo>eiHa rettcnltti) and •ixturet containing-:1
up to 50 industrial chemicals. Henaens et al.
(1984) conducted 48-h acute toxicity tests
with pfpbnia magna and Mixtures containing the
same 50 chemicals as tested with guppies.
When these data are plotted against the
Narcosis I bilinear SAR node! line of Veith et
al. (1983) (Figure 9), a good log P and
biological activity dependent correlation is
noted among tJ1 three model lines. This
suggests that the sensitivity of different
fish species and daphnids to non-specific
anaestnetic-iike chemicals is similar since
the Narcosis I model relationships in Figure 9
are a.l quite similar Schult: and Moulton
',1384 have recently reported a similar
relationship with a different activity scale
between log ? and biological activity in
Tetrahvnena ovnformis for 43 aromatic
industri al chemica1s
The type of joint action that Konemann
(1981b) an-* Hermens et al. (1984) observed for
mixtures containing numerous lipophilic
organic compounds can generally be
characterized by concentration addition.
Their MTI values were reported to be 1.02 and
0.95, respectively. This was even true for an
equitoxic mixture containing 50 compounds at
0.02 of their respective LCSO values. This
apparent additivity for industrial chemicals
characterized by a narcosis type mode of
action should be of particular interest
because a proportionately large number of
chemicals from the TSCA inventory are likely
to cause lethality through narcosis (Veith et
al., 1983).
Numerous authors (Ferguson, 1939; Seeman.
19T2; Konemann. 1981a. and Hermens and
Leeuwangn. 1982) have suggested that phvs:
unspecific toxicitT can be minimally expe:
of .nost nycrophob i c organic cnemicals at •
concentrat,on. This is expected unless a
chemical is metaboUzed or its effect is
masked by overwhelming irreversible and mo:
toilc effects from specific structural
0.12 —
o.oo
0.00
0.02
0.04
0.06
0.08
0.10
l-Octanol(mM)
TOXICANT H
• l-Hexanol (fry)
O l-Hexanol (juveniles)
A 2-Octanone
a Dlisopropyl Ether
* Tetrachloroethylene
O 1.3-Dichlorobenzene
4 n-Octyl Cyanide
7 n,n-Dimethyl-P-Toluidine
0.12
Figure 8. A composite isobole diagram of 96-h LCSO values depicting the joint
toxic action for 1-octanol with seven other chemicals, each normalized
to the toxicity of 1-octanol. (From Broderius and Kahl, 1985).
-------
characteristics. In this case, a specific
interaction with a receptor may be responsible
for the effect. Therefore, the joint toxicity
of mixtures of hydrophobic organic chemicals
with various actions is •inimilly based on
concentration addition of their Biniaal
untpeciflc toxicitj. This contribution of a
compound In a nonionixable form can be
emulated fro. the Narcosis I QSAR (Kone.ann.
I981b- Veith, 1983; and Hernens et al..
1984) In mixtures with only a few compounds
with different specific and more toxic action
this unspecific toxicity mi|ht not markedly
contribute to the observed response. In a
mixture of numerous differently acting
compounds at equitoxic concentrations, the
specific tone effects mijht not be apparent
because the concentration of the individual
members will be so low. The fractional
unspecific toxicity from hydrophobicity,
however, will persist and this tdditive effect
may markedly contribute to the observed
response. Therefore, organic chemicals in any
concentration are expected to contribute to
the toxicity of a mixture with respect to the
non-specific common site of action.
OSAR and Joint Toiicitv - Narcosis 11 and
Uncoupler Chemicals
There is considerable evidence that
reversible narcosis might result from several
mechanisms. Veith et al., 1985 have suggested
that the comparatively non-specific narcosis
from membrane expansion might be separated by
a QSAR from narcosis by membrane depolar-
ization. This latter more sensitive
mechanism, which is observed at chemical
Or—
-J -2
C
O
C
0?
O
o
o
-4
o
o
'x
|2
-6
-8
B
-2
8
Log P
Figure 9. Acute toxicity to the guppy (0,7- or 14-day LC50) and Daphnia ma?na
(t, 48-h LC50) of 50 and 19 industrial chemicals, respectively, as
related to the octanol/water partition coefficient (Log P). QSAR
model lines for physical narcosis were determined by (A) Konemann,
1981b; (B) Veith et al., 1963; and (C) Hermens et al.. 1984. (From
Broderius and Kahl, 1985).
57
-------
• '•"•• •'•-.->•"" ' . v**.-y-.«•;• v-<• •.'•• ' "",'• " •- ' .. .' "•••-jV'x?-' "-"••
activities statistically lower than the
baseline narcosis (Narcosis I), is identified
by Veith et al., (1985) as Narcosis II. One
major class of chemicals thought to produce
narcosis by depolarizing membranes at chemical
actiritits lower than baseline narcosis is the
esters (Veith et al.. 1985). This group
includes the benzoates. adipates. phthalates,
simple salicylates, and alkyl acid esters. We
cannot, however, confirm that these esters are
acting by this second mode of toxic action.
In fact, we have observed that nany of the
nonoesters are approximately strictly addi'tive
with 1-octanol in their acute joint toxicity
and therefore presumably act by a similar
Narcosis I mode of toxic action. Several
diesters were observed to be less than
strictly additive with 1-octanol or phenol and
thus assumed to have a different mode of
action than either reference chemical.
Additional groups of c-emica's that we have
tested include the sub;:. fjted ana
halogenated phenols Tv.ese compounds can
generally be thought of as not chemically or
biologically reactive. However, depending
upon the substituents present on the molecule
the hydroxyl derivative night ionize to
various degrees at different test pH values.
The hydroxy substituent can also conjugate
with electron-withdrawing groups by resonance
through the aromatic ring of the molecule
(Hansch and Leo 1973) Therefore, it "as
anticipated that non-log ? related effects
might be important in determining their toxic
response and thus not mode led-by the Narcosis
! QSAP.
The results of our studies have suggested
that the toxicity of phenolic compounds can be
modeled by three QSAR's. We have observed
that those non-acidic substituted and
halogenated phenols with a log P of about 3 or
greater are strictly additive with 1-octanol
or phenol. Those phenolic compounds with high
log P values are highly hal ogenated' and/or
alkyl substituted and act chemically more like
hydrocarbons or halogenated hydrocarbons than
phenols. Those phenols with a log P of -3 or
less, however, are only strictly additive with
phenol and not with 1-octanol. Since phenol
is not strictly additive with 1-octanol we
feel that we have defined another mode of
tone action characterized by Veith et al .
(1985) as Narcosis I!. These polar chemicals
are slightly more active than the baseline
toxicity of non-ionic narcotic chemicals.
Multiple chemical mixtures consisting of 11
phenolic compounds characterized by a Narcosis
II mode of action have been observed to be
strictly additive in their joint acute
toxicity to the guppy (Konemann and Musch,
1981). Their test chemicals consisted of
phenolic compounds with log P values of both
greater and less than 3.
A third SAR grouping has been identified and
is characterized by acidic phenols. Chemicals
in this group have activities lower than that
of Narcosis 1 and II SARs and are structurally
characterized as having strong electron
withdrawing substituents adjacent to a
hydrogen bonding group. Their mode of toxic
action is thought to be that of uncoupling of
oxidative phosphorylation. In our experiments
we have designated 2,4-dinitrophenol (2,4-DNP)
as the reference uncoupling agent for this
mode of toxic action. Acute toxicity tests
have been conducted with 2,4-DNP and chemicals
such as HCN or rotenone which are known to
inhibit electron transport in the Mitochondria
of cells. These latter two chemicals have
activities lower than those of the oxidative
phosphorylation nncouplers (Figure 10) and are
therefore thought to have a different mode of
toxic action. When rotenone was tested in
combination with 2,4-DNP, a less than additive
but more than response additive type of joint
action was observed. When HCN and rotenone
were tested in combination, however, a nearly
strictly additive joint acute action was
observed These results are consistent with
the proposal that chemicals characterized by
different QSARs do indeed have different
primary modes of acute toxic action ar.c s-.c'iij
not interact ;n a concentration aci . t .-•.-•
manner. Those within a mode, however, snouid
be strictly additive in their joint action
It has been proposed that the QSARs for
Narcosis II and uncoupling of oxidative
phosphory1 ation might be improved through, in
addition to log P the use of molecular
decriptors such as. electronic and steric
factors which reflect the polarity of the
chemicals The use of pKa as an electronic
descriptor has seen ased extensively
Hermens and Leeuwangh 11962; proposed that
for mixtures with a relatively large number of
chemicals with diverse modes of action a
similar joint toxicity for the different
mixtures will result. Thus, mixtures
containing an equal number of chemicals will
have MTI values which are approximately the
same. This hypothesis was tested by Hermens
and Leeuwangh (1982) «ith five mixtures of
eight chemicals each, one mixture of 24
chemicals, and was demonstrated to be
approximately correct. The joint response of
the mixtures varied from partially additive to
concentration additive. It is not likely that
this unexpected high joint response resuitea
from simple similar action, because in some
mixtures it is most probable that the
chemicals actually had different modes of
action. Hermens and Leeuwangh (1982) proposed
that the most plausible explanation for their
experimental results for lethal tests is that
dependent action is the most likely type of
joint action to occur when dealing with
mixtures of numerous chemicals with diverse
modes of action. The fact that these mixtures
result in a nearly constant MTI value is most
interesting but yet unexplained. It is
important to determine how the size of a
mixture group would affect these results
Hermens and Leeuwangh (1982) and others have
adequately demonstrated that organic chemicals
with diverse modes of action and at
concentrations about 0.1 of the LC50 values
and lower do contribute to the joint toxicity
of mixtures. Therefore, no effect levels of
separate chemicals may have little meaning for
mixtures and probably should be established
for groups of chemicals.
-------
it.j.^.i»_A
Future Research
The direction of future research in
evtluttin{ the environmental hazards posed by
Multiple toxicants should include not only the
•cute response bat also important chronic
endpoints such as growth and reproduction.
The effects of an accumulated total body
burden of toxic chemicals on reproductive
success and embryo-larval fish survival and
growth should be investigated. In addition to
these traditional endpoints, future research
might include the effects of multiple
chemicals on cytotoxic responses such as
teratogenic and carcinogenic effects.
Most aquatic multiple toxicant tests have
been conducted mth daphnids, various
freshwater fishes, and a few other organisms
The incorporation of new test organisms and
endpoints such as the African Clawed Frog
i X e n o p u s I a e v i s 1 to study teratoger.ic effects
(Schultz and Duraont, 1984, and the rainbow
trout embryo for carcinogenic effects (BlacK
et al.. 1985) Bight be desirable. Tests using
endpoints other than those obtained from whole
organism responses may also be instructive.
These later tests may be of particular value
when it is suspected that mixtures are
displaying an interactive Joint action with
the metabolism of parent compounds playing a
major role in defining observed responses.
The type of tests that are needed in
multiple toxicant work include those that are
systematically conducted with individual
chemicals and various mixtures. One cannot
over-emphasize the importance of a good data
base on diverse chemicals. A specific test
that has proven most valuable is the binary
mixture test as conducted at several mixture
ratios. Such data allows one to define
isobole diagrams of joint action This
procedure has prove:, useful as a dis-
criminating too! ir, identifying pairs of
chemicals that have a suspectea similar or
different mode of ::iic action As testing
nas expanded into -..tipie che-,;ca
Or-
-2
-A
O
o
O -6
10
o
JC
s -8
-10
NARCOSIS i:
MODEL
-NARCOSIS I MODEL
2.4-01nftroph«no
HCN
UNCOUPLER MODEL
ELECTRON TRANSPORT
MODEL
-^
° Antlwycln A
_L
0.0
2.0 4.0
Log P
6.0
8.0
Figure 10. Acute toxicity to the fathead minnow as related to the octanol/water
partition coefficient (Log P) for chemicals thought to be uncouplers
of oxidative phosphorylation (•) or that inhibit electron transport
and thus the metabolism of oxygen (0).
-------
it has been the tradition*! approach to teat
equitoxic Mixtures. In future testing it
might be desirable to plan experiments
accordinf to a multifactorial design. With
this approach all combinations of sereral
diffcrtnt ieti of no-effect and effect level
treatments or measurements of all possible
joint interactions can be tested without
examining all possible combinations. The size
of such studies can thus be reduced by
assuming that certain interactions between the
concentrations and the responses are
nejli gible.
Our selection of test chemicals has been
{Uided by principles established using a QSAR
approach. This is done to optimize our
evaluation of how chemicals jointly act and to
broaden the application of test results We
nave attempted to test chemicals within and
between different QSAR's, assuming that we are
estaoiishing how chen. ca 1 s jointly act w,th
si-ilar and different modes of action
Reference chemicals have been usec to
represent various modes of toxic action
Future experiments will include those
chemicals that have a "more specific" mode of
tone action and which might display different
levels of electrophi1ic reactivity. We have
also separated our testing of organic
chemicals from that of metals. It would be
desirable to combine organic and inorganic
chemicals into mixt-jres when an understanding
is obtained of how each group acts separately.
The statistical analysis of our test data
has been minimal, We have used standard
statistical techniques as previously described
by Sprague (1970), Marking (1977), and
Konemann (I981b). More sophisticated
techniques as reported by Durkin (1981) or
Chnstensen and Chen (1985) might be more
instructive in defining the degree of joint
action and similarity among chemicals in
mixtures.
Various relationships have been derived
between toxicity and the octano1/water
part;t;on coefficient as the aotiinant
parameter. This has proven adequate to
describe the relationships for non-specific
organic toxicants but might be inadequate for
chemicals with more specific primary
aodes-of-act ion. An untested but potentially
powerful approach to predicting joint toxicity
of mixtures deals with N-space analysis where
the "likeness" of tested and untested
chemicals, and certain benchmark chemicals,
can be quantitatively described. With this
approach it would be assumed that if the
structural properties of a chemical can be
described with N factors and plotted in an
N-dimensional structure space, the chemical
and biological properties of a chemical should
be similar to its "nearest neighbors" for
which data are available. This approach might
allow one to cluster compounds that show a
similar mode of toxic action and thus display
a concentration-addition type of joint toxic
action. The type of joint action displayed by
chemicals in different clusters light be
characterized by a form of response addition.
It is also quite probable that the type of
joint action between chemicals in different
clusters is too complicated to be presented by
simple models and will r.sed to be empirically
def ined.
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6 209-21'
Hermens, J., H. Canton. P. Janssen, and R. De
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Hermens, J. and P. Leeuwangh. 1982. Joint
toxicity of mixtures of 8 and 24 chemicals
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unified theory for quantal responses to
mixtures of drugs: competitive action.
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Konemann, H. 198la. Quantitative
structure-activity relationships in fish
toxicity studies. Part 1: Relationship for
50 industrial pollutants. Toxicol. 19:
209-221.
Konemann, H. 1981b. Fish toxicity tests with
mixtures of more than two chemicals: A
proposal for a quantitative approach and
experimental results. Toxicol. 19:229-238.
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i^v'^^
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DISCUSSION
Q. P. Pmtil and C. Taillie, The Pennsylvania State University
1. DTTBODDCTION AND BACKGROUND
author deserves Commendation for t>\m
prepared for presentation at the ASA/SPA
on Currant AM element of Combined
Toxicant Effects to •joint audience of
participants from various related disciplines.
As he puts it, "defining the toxicity of
Mixtures is a aajor problem at both the
theoretical and practical level ... There has
not been sufficient research to establish
whether there is any widely applicable rationale
and approach for evaluating and possibly
predicting the joint action of toxicants in the
aquatic environment ... The types of tests that
are needed in Multiple toxicant work include
those that are systematically conducted with
individual chemicals and various Mixtures. One
cannot over—emphasize the importance of a good
data base on diverse chemicals. A specific test
that has proven roost valuable is the binary
Mixture test as conducted at several Mixture
ratios. Such data allows one to define isobole
diagrams of joint action. This procedure has
proven most useful as a discriminating tool ID
identifying pairs of chemicals that have a
suspected similar or different mode of toxic
action. As testing has expanded into multiple
chemical mixtures, it baa been the traditional
approach to test equitoxic Mixtures. In future
testing, it May be desirable to plan experiments
according to a multifactorial design — Our
selection of test chemicals has been guided by
principles established using a QSAR approach.
This is done to optimize our evaluation of how
cheaicals jointly act and to broaden the
application of teat results. We have attempted
to teat chemicals within and between different
QSAR'a assuming that we are establishing how
cheaicals jointly act with similar and different
aodes of action. Reference cheaicals have been
used to represent various modes of toxic action
has been minimal. We have utilized standard
statistical techniques ... More sophisticated
techniques may be more instructive in defining
the degree of joint action and similarity among
cheaicals in mixtures ... An untested but
potentially powerful approach to predicting
joint toxicity of mixtures deals with N-space
analysis where the 'likeness* of tested and
untested chemicals, and certain benchmark
cheaicals, can be quantitatively described.
With this approach, it would be assumed that if
the structural properties of a chemical can be
described with N factors and plotted in an
N-dimensional structure space, the chemical and
biological properties of a chemical should be
similar to its 'nearest neighbors' for which
data are available. This approach may allow one
to cluster compounds that show a similar mode of
toxic action and thus display a
concentration-addition type of joint toxic
action. The type of joint action displayed by
chemicals in different clusters May be
characterized by a form of response addition.
It is also quite probable that the type of joint
action between cheaicals in different clusters
is too complicated to be presented by siMple
Models and will need to be empirically
defined..."
The author should be complimented for his
effort in developing these complex problem areas
and in communicating them to the substantive
scientists, statistical sethodologists, and
managers. The paper covers a broad spectrum of
issues and approaches pertaining to aquatic
ecotoxicology. risk assessment, monitoring and
•angement with particular emphasis on matters
relating to the perceptive isobole diagrams and
the widely recognized QSAR techniques.
2. STATISTICAL CONSIDERATIONS
We initially propose to briefly discuss and
formulate MOM of the basic statistical aspects
of the approach leading to the isobole diagrams,
and aubsequently offar a few remarks pertaining
to their role and use for field situations.
Let X
lat the toxicants be denoted by A, B, C,
denote the tolerances of
an individual to the toxicants A, B, C, ...
respectively. Let BA, Eg, Eg, ... denote the
exposure/concentration levels of A, B, C, ... .
2.1 Tolerance Distribution: Assume that a
tolerance level can be associated with each
individual organism. Thus the organism shows a
response if the exposure level exceeds its
tolerance. The distribution of tolerance levels
across the population of individual organisms is
said to be the tolerance distribution.
2.2 Response Function: This is the expected
proportion of organisms that show a response at
a given exposure level. Note that in the case
of one toxicant, the response function is the
save as the cumulative distribution function of
the tolerance distribution. As we will shortly
see, this is not true for multiple toxicants.
While the response function is directly
observable, tolerances and tolerance
distributions are concepts that may be useful in
guiding one's thought processes. However,
situations arise where the tolerance concept may
be faulty. Whether a given organism exhibits a
response depends upon numerous environmental
factors. To the extent that these factors and
their interactions are not known or are not
predictable, the organism's zero-one tolerance
level needs to be replaced with a "fuzzy"
tolerance, i.e. there is a probability that the
organism responds at a specified exposure level.
The response function is then the average, taken
over all exposed organisms, of these
probabilities. The effect is to increase the
variance or, equivalently, to decrease the slope
of the probit diagram. The smaller slope is a
major point of differentiation between field and
laboratory investigations.
2.3 Joint Tolerance Distribution: For
simplicity, we consider only pairs of chemicals
and bivariate distributions. To each individual
is associated a pair (X^,Xg) of tolerances.
Notice that each component tolerance, XA or
Xg, determines whether the individual responds
to the chemical, A or B, when exposed to the
chemical separately. There are no combined
effects involved at this point. The
distribution of the pairs (X^.Xg) across all
organisms in the population is the bivariate
tolerance distribution. If A and B act upon
similar receptor sites, then the tolerances
(X&,XB) are expected to be positively
correlated. A correlation of zero is expected
if the sites are dissimilar. Negative
correlation, while possible, appears to be
unlikely.
2.4 Mode of Action: Unlike the univariate
.case, the bivariate tolerance distribution does
not determine the response function. To pass
from tolerance to response, an additional
concept is required, one that describes the
effect of the chemicals when they act in
63
-------
.ffe
•u «i. Jc".
imtioa with one toother. Ut (I^.lg) b«
the Joint concentration (exposure lavel) of the
tno chemicals. The Bode of action of A and B
should determine, in terms of the organisms'
tolerances (XA,XB), which organisms will show a
to (BA,BB). Formally then, the •£& fif
metioB can be defined aa a rule that
to aach Joint anpoaura level (B^iBg) •
ration in the two-dimensional plane (XA,Xj) of
possible tolerance value*, a jiven organism
shows a response to (BA,BB) if and only if ita
tolerance pair falls within this region, which
we call the response region.
Once the mode of action is specified, it is
easily seen that the bivariate response
function, evaluated at (BA,BB), is the integral
of the bivariate tolerance distribution over the
region associated with (E^,Eg). Both the joint
tolerance distribution and the node of joint
action are needed to determine the joint
response function. A central issue is whether
and to what extent it is possible to infer
properties of the tolerance distribution
and/or the node of action from observations
made upon the response function.
Joint
Tolerance
Distribution
The mode of joint action needs to
satisfy at least the following requirements
(where R is the response region associated with
(BA,BB)):
The point (E^.Eg) lies on the
boundary of R. This requirement
appears to rule out physical
interactions between the
chemicals.
(i)
(ii)
If
and
is in
then
R and if
S X.
is also
A-V
.B < XB. then (XA,XB)
in R. In words, if an organism
shows a response then so will all less
tolerant individuals.
(iii) If B^ < BA
and
< BD then the
response region associated with
(BA,Bg) is a subset of the response
region associated with (BA,Bg).
Figure 1 shows some hypothetical response
regions that meet these requirements.
2.5 Examples of Modes of Action: The mode of
action is called concentration addition when a
law of simple linear substitution applies. In
other words, it is possible to reduce the
concentration of B and produce identical
results by making a corresponding increase in
the concentration of A. The response region
has for ita boundary a straight line with
negative slope; the magnitude of the slope is
the relative potency of the two toxicants.
Notice that ail points along this straight line
\\ V
*A
(at)
Figure 2. Response regions (shaded) for three
different Bodes of action: (ii) concentration
addition, (iii) response addition. The mode of
action (i) has no standardized name but
represents a situation in which A and B act
upon different sites and these sites form a
parallel-system in the sense of reliability
theory.
determine the same response region and,
therefore, the sane value of the response
function. It follows that, in the case of
concentration addition, the iaobolea (contours
of the response function) are exactly the
boundaries of the response regions.
Concentration addition is often motivated by
supposing that the toxicants act upon the same
receptor sites, thereby implying a perfect
correlation in the tolerance distribution. We
see that a perfect correlation is not a
logically necessary condition for concentration
addition. In fact, there are infinitely many
tolerance distributions that assign the same
probabilities to the triangular response regions
and thereby determine the same response
function.
From a regulatory standpoint, it is the law
of substitution that is important and it is the
linearity of that law that makes for a simple
regulatory strategy. One can easily envision
situations involving nonlinear laws of
Substitution (Figure 2). Let us define a mode
of action to be self-similar if every point on
the boundary of a response region R has R as
its resoonse region. Concentration addition is
self-similar, as is any mode of action whose
response regions have boundaries defined by
single equations such as XA • XB = constant or
X? -f X5 = constant.
: of nonlinear law of
substitution.. Response regions have circular
area for their boundaries. All chemical
ne °f
64
-------
to iraanin with concentration addition, all
eelf-eiailar modes of action have the two
properties that (1) isoboles are the boundaries
of the response regions and (ii)'there are
infinitely many different Joint tolerance
distributions that yield the same response
function (in fact one can always find such a
joint tolerance distribution that is perfectly
correlated in the sense of concentrating its
probability MM on a ooe-diaensiooal subset of
the (IA.X.) plane).
A aaconrt mode of joint action la known aa
addition. This occurs when an organism
.a response to (BA,BB) if and only if it
would respond to BA acting alone or to Bg
meting alone. Response addition calls for the
simple regulatory strategy of setting separate
standards for each of the two toxicants. The
response region for response addition is shown
in the third diagram of Figure 1. The picture
reveals the aptness of the term "response
addition" since the total number of responses is
the sun of the responses to A and the
responses to B (after adjusting for double
counting).
Response addition is not a self- similar
mode of action; for example, the points (B'^.Bg)
and (BA>Bg) in Figure 1 determine different
response regions. The shapes of the isoboles
depend upon the joint tolerance distribution.
By contrast, for a self-similar mode of action,
we need the tolerance distribution to determine
the levels (LC50, LC80, etc.) but not the shapes
of the isoboles. Also, in the case of response
addition, the joint tolerance distribution is
uniquely determined by the response function.
Indeed, from Figure 1, the response function
evaluated at (E.,BB) is 1 - F(BA,E,,) where F
AD AD
is the survivor function of the tolerance
distribution.
3. STATISTICAL ISSUES IN THE APPROACH OF
BRODBRIUS
This section hopes to identify a few
statistical issues that seen to be implicit in
the approach that Broderius has presented. This
is not an exhaustive list, but only indicative
and preliminary.
3.1 Isoboles and the Nature of the Joint
Action: Isoboles are the appropriately chosen
contours of the response function. They depend
upon both the mode of joint action and the joint
tolerance distribution. Thus, it is impossible
to infer the nature of the joint action from the
examination of the isoboles alone. It is
necessary to know or to assume a model for the
joint tolerance distribution. Broderius appears
to assume a joint probit model. But different
models could yield different conclusions
regarding the nature of the joint action.
3.2 fcoboles and Levels of Isoboles: Broderius
restricts attention to LC50 isoboles. Would the
conclusions be qualitatively the same or
different if other levels were employed? It
should be helpful to investigate these problems
both in theory and practice.
3.3 Biological Homogeneity in Broderius
Approach and Field Heterogeneity. The
laboratory work described by Broderius
maintains a high degree of biological
homogeneity. This results in'the steep slops*
in his probit diagrams and nearly degenerate
tolerance distributions. Bven within the
framework of probit model, the isoboles
corresponding to response addition are heavily
dependent upon the slopes. It is not apparent
that conclusions about modes of joint actions
that are derived from laboratory studies under
regimes of strict biological control could be
extrapolated to field conditions, where
biological aa well aa environmental
heterogeneity prevails.
3.4 the Issue of Synchronous and
Asynchronous Exposures: Fish are mobile,
sometimes highly so, and are exposed to a
variety of toxicants during their lifetimes.
Would the results from Brooerius study, which
assume synchronous exposure, carry over to the
asynchronous exposure that is common under field
conditions?
4. CONCLUDING REMARKS
Steve Broderius has presented a very
interesting and illuminating paper on a problem
of current practical concern in aquatic
ecotoxicology. It reminds us of three workshops.
on aquatic toxicology and risk assessment held
in the recent past.
The Northeast Fisheries Center of the
NOAA/NMFS organized a workshop in 1983. Issues
involved definition of water management zones,
grouping of chemicals and endpoints with a view
to be able to consider representative chemicals
and representative endpoints, and formulation of
indicators and field based statistical indices
leading to a crystal cube for coastal and
estuarine degradation.
The BPRI workshop had emphasis on
multivariate bioassay, ecological risk
assessment, and relevant experimental designs.
The NOAA Chesapeake Bay Stock Assessment
Committee has had its thrust on partitioning
fish mortality due to pollution (multiple
chemicals included), environment, habitat, and
fishing that has involved multivariete multiple
time aeries and categorical regression related
tools.
Broderius' paper develops a promising
approach to the contemporary issue of aultiple
toxicants and raises several challenging and
fascinating technical problems such as:
statistical graphics of combined effects,
multivariate tolerance distributions, binary
mixtures and multivariate results, synergism
concepts for the 'whole' being 'more than the
'sum', QSAR related chemical species grouping
methods reminding one of ecological 'guilds' and
functional groups, and so on.
The multiple toxicants 'ball' is not just
in a statistical court. It is in every other
relevant court at the same time. It will take a
timely interdisciplinary effort involving
simultaneous (and not sequential) collaboration
of various substantive players. We wish to
congratulate Steve Broderius for this
interaction at this ASA/EPA Conference.
Acknowledgements: The authors would
like to acknowledge the partial support for
this work received through a NOAA research
grant to the Center for Statistical Ecology and
Environmental Statistics, Department of
Statistics, The Pennsylvania State University.
under the auspices of the Northeast Fisheries
Center of the National Marine Fisheries
Service, Woods Hole, Massachusetts.
65
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DEVELOPMENT OF MODELS FOR COMBINED TOXICANT EFFECTS
Erik R. Chrlstensen, University of Wisconsin—Milwaukee
ABSTRACT
Adequate unlvarlate dose-response functions
•re necessary 1n order to develop a satisfactory
•ultlpl* toxldty model. We Investigate here the
use of unlvarlate Welbull and problt distribu-
tions with literature data for the quanta! re-
sponse of fathead minnows (Pimephales promelas)
to 27 different organic chemicals. We also
examine fits of the Welbull, proMt. and loglt
models to literature data for the growth rate
and yield of the diatom Navicula Incerta Inhi-
bited by Cd. Cu, Pb. or In. The Weibull model
appears to provide a superior fit for both fish
and algae, thus supporting a previously
developed mechanistic-probabilistic basis in
terms of chemical -eactions between toxicant
molecules and receptors of the organisms.
The application of a general multiple
toxldty model is demonstrated using published
experimental results regarding the action of
binary combinations of N1, Cu, potassium penta-
chlorophenate, dieldrin, and potassium cyanide
on male guppies (Poecilia reticulata). We also
analyze results of our own experiments regard-
ing the combined effects of Ni2+ and Zn2+
on the growth rate based on cell volume of the
green alga Selenastrum capricornutum. Host of
the multiple toxicity data are fitted well by
the model.
INTRODUCTION
Aquatic Ecotoxicology is becoming a topic of
major concern (1,2). It deals with the re-
sponse of aquatic organisms to toxicants such
as heavy metals and organics, both in natural
waters and water and wastewater treatment
plants. One important goal is to protect aqua-
tic organisms against adverse effects from
pollutants.
Several factors complicate the evaluation -of
the toxic response of aquatic organisms to
specified concentrations of pollutants. For
example, the chemical form of heavy metals 1s
Important. It 1s well known that the ionic form
of metals such as Cd, Pb, Ni, or Cu is generally
more toxic than the complexed forms (3). For
organics, e.g., polychlorinated biphenyls
(PCB's) or polycycllc aromatic hydrocarbons
(PAH's), the octanol-water partition coefficient
1s of Interest. This 1s because there 1s often
a correlation between this coefficient, the
UpophiHty. i.e., the solubility in fat, and
the toxicity (4). Other factors include vola-
tilization to the atmosphere and partitioning
to particulate matter. Considerations related
to the organisms are exposure time, biomagnifl-
cation, age, and species composition.
The response obtained within a given time of
exposure, e.g., 96h, has been studied for
•any different compounds and a variety of
organism such as fish and algae (2.5). How-
ever, In most cases, only one toxicant has been
considered In any given experiment. This 1s
obviously a simplification since actual aquatic
systems usually have more than one dominant
toxic compound. The objective of the present
work 1s to Introduce a multiple toxicity
dose-response model and apply it to fish and
algae. Unlvarlate dose-response models for
these organisms will also be examined.
CLASSIFICATION OF 8IOASSAYS
The response of aquatic organisms to toxi-
cants can be evaluated from bioassays conducted
in the laboratory or in the field, or in sorre
cases, from the observation of actual ecosys-
tems. Possible forms for laboratory bioassays
are shown in Table 1 (6). For most macroorgan-
1sms, or mixed cultures of microorganisms
(Groups I and II), there is a tolerance distri-
bution for individual organisms. This means
that some organisms with high tolerance will
survive at high concentrations or long exposure
times while others with low tolerance will not.
In contrast, organisms from a pure culture of
microorganisms (Groups III and IV) originate
from a single clone and, therefore, have the
same genetic material. Thus, there is no
tolerance distribution for Individuals which
will respond 1n the same way to the toxicant.
The response can be quanta! or continuous.
An example of a quanta! response is death for
Group I organisms. A continuous response can,
for example, be growth rate based on biomass
(Groups II. IV). For Group I organisms, the
response is the fraction of all individuals
that are affected, e.g., by death. Similarly,
for Group III organisms, we may consider the
response to be the fraction of subsequent cell
divisions that are blocked. This is the same
as the reduction In relative growth rate based
on cell number. This Interpretation 1s extended
to apply also to Group IV organisms.
DOSE-RESPONSE MODELS FOR ONE TOXIC SUBSTANCE
Dose-response models for a single toxicant,
assuming a fixed time of exposure, e.g., 96h.
are shown 1n Table 2. Of these, the problt
model (7) Is perhaps the most well known. It
1s based on a normal distribution of the re-
sponse as a function of log(z) were z is a
toxicant concentration. Other useful linear
expressions are the logit transformation (8),
and the Welbull transformation (9).
The probit, loglt, and Weibull models must
be considered mainly empirical although some
-------
TABLE 1. Populations of Organisms Considered In Bloassays
6enet1c
Characterization
TYPE OF RESPONSE
Quanta! Response
Continuous Response
Tolerance Distribution
for Individual Organisms
All Organisms from a Single
Clone
(No tolerance distribution
for individual organisms)
Broup I
Nacroorganlsms
Response: death of an organism
Classic problt analysis
Binomial statistics
Group III
Pure culture of microorganisms
Special case: Synchronous
growth
Response: growth rate based on
cell number
Srouo II
Nacroorganlsms
Nixed cultures of microorganisms
Response: growth rate, C-14
uptake, respiration
Group IV
Pure culture of microorganisms
General case
Response: growth rate, C-14
uptake, respiration
TABLE 2. Comparison of the Weibull Transforma-
tion with the Probit and Loglt Trans-
formations
Type
Transformation*
Probability of
Response or
Relative Inhibition
Weibull u * In k + n In z P»l- exp(- e )
Probit Y « a + B log z P « kl+erf(^))
Logit I = 6 + $ In z P » 1/(1 -t- e'1)
*z is a toxicant concentration
k, ti,.«, B, 6, $ are constants; A « In k
theoretical basis has been claimed. The problt
model 1s based on the often found log-normal
distribution In biological systems. The legit
model is valid for certain types of autocataly-
sls and enzyme kinetics (Group III and IV or-
ganisms) (10, 11). The parameter * 1s the
number of toxicant molecules per receptor. It
appears that the Weibull model may have a simi-
lar Interpretation so that n would be the
number of toxicant molecules reacting per re-
ceptor molecule (12, 13). In addition, the
Weibull model 1s related to the multistage
model in carcinogenesis and 1s Identical to the
single-hit model for n - 1 (14).
Applications
F1sh. To Illustrate differences between the
problt and Weibull models, we shall consider
the experimental results of Broderlus and Kahl
(15) on the mortality of fathead minnows
(Plmephales promelas) in the presence of each
of 27 different organic chemicals. A plot of
the results obtained by these authors is shown
1n F1g. 1, where the toxldties have been nor-
malized (M 96h LCSO) to the potency of
1-octanol. The normalized experimental results
and the problt line (o = 59.1, B - 13.5) are
as reported by Broderius and Kahl. In addition,
we have included a Weibull curve (A = 53.16,
n « 5.81) fitted to the experimental points.
10r
8 -
£
CO
o
cc
^ 6 -
<
cc
o
PROBIT
WEIBULL
4 -
-3
-2
-1
TOXICANT CONCENTRATION (Log M)
F1g. 1. Mortality vs. toxicant concentration
for 27 different organic chemicals.
The mortalities are normalized (96h
LC50) to that of 1-octanol. Experi-
mental points and the problt line are
from Broderlus and Kahl (15). In
addition, we have Included a Weibull
function with parameters A = 53.16 and
n - 5.81 that have been adjusted to
fit the experimental data.
Because the normalization was made with
respect to the LCSO-values only, and not the
slopes, 1t 1s not entirely appropriate to use a
statistical criterion such as ch1-square to
compare the goodness of fit of the two models.
67
-------
Howtvtr. since the slopes of the 27 'dost-
rtsponse curves were fairly similar, and the
Mortalities were fairly evenly distributed
between 0 and 100%. a comparison may still be
wild. From Fig. 1 It 1s seen that the test
«ata tMd to follow the curved Helbull function
ratlttr than the straight problt line. Similar
observations on other bloassay data were made
previously (9).
The problt and Welbull models give compar-
able response rates for problt values between 4
and 6, but highly diverging values at the ex-
tremes. The mortalities from the Welbull func-
tion Is the highest In both ends. This 1s
Important 1n the case where response functions
obtained by fitting to Intermediate test mor-
talities (e.g., between 10 and 90S) are used
for extrapolation to high or low concentrations.
As may be seen from Table 3, the difference
between the mortalities from the two models 1s
rather trivial for values of log H between -4.1
and -3.9. However, at log H = -3.8, the probit
model predicts that 255 out of 105 organisms
will survive, while the corresponding number for
the Weibull function is only 5. Similarly, at
log M * -4.3, the probit model Implies that al-
most no organisms are affected (only 4), whereas
a total of 1230 are killed according to the
Weibull model.
TABLE 3. Number of Fish Killed (fathead minnows,
Pimeohales promelas) out of an Initial
Population of10s as Predicted from
the Probit and Weibull Models. The
parameters of the problt model (a =
59.1; 8 « 13.5) are from Broderius and
Kahl (15) * and those of the Welbull
model (A - 53.16; n - 5.81) have
been adjusted to fit the experimental
data of these authors.
Toxicant
Concentration
(log M)
-3.6
-3.7
-3.8*
-3.9
-4.0*
-4.1
-4.2
-4.3*
-4.4
-4.5
-4.6
-4.7
-4.8
-4.9
-5.0
Model
Probit
100.000
99,998
99,745
92,645
53,983
10,565
466
4
0
0
0 -
0
0
0
0
Weibull
100.000
100,000
99,995
92,681
49,534
16,463
4.608
1.230
324
85
22
6
2
0
0
Corresponding to broken vertical lines 1n F1g. 1
Algae. The models for one toxic substance
listed In Table 2 have been applied to the
growth of the diatom Mavlcula Inqerta exposed
to Cd, Cu Pb, and Zn. The raw data are from
RachUn, Jensen, and Warkentine (16).
The results for Mavlcula Incerta are given
1n Tables 4 and F1g. 2. From Table 4 It 1s seen
that tlit Welbull model provides the better fit
compared to the problt and loglt models when the
number of degrees of freedom art two or more.
The slope * appears to assume the value 0.5
for Cu, Pb. and Zn when growth rate 1s used as
a parameter. The Interpretation of n may be
the number of .toxicant molecules per receptor
of the organisms, and the Implication 1n the
present case 1s, therefore, that each of the
metals Cu, Pb, and Zn combines with two recep-
tors.
A NONINTERACTIVE MULTIPLE TOXICITY MODEL
We have expanded Hewlett and Plackett's P7)
bivariate normal model to include any mono-
tone tolerance distribution for individual
toxicants, such as a logit or Weibull distribu-
tion, and n toxicants (12). Let us consider a
general blvariate model. Besides the parameters
characterizing the Individual dose-response
curves (Table 2), there are two additional para-
meters: a similarity parameter x and a corre-
lation p of mortality tolerances (Group I
organisms, e.g., fish) or cell division toler-
ances (Group III or IV organisms, e.g., algae).
The similarity parameter x indicates
whether the toxicants act on similar (x « 1),
different (X = 0), or partially similar bio-
logical systems (0 < X < 1). The other para-
meter p is a measure of the degree of corre-
lation of the susceptibility of the organisms
(Group I) to the two toxicants. For full cor-
relation (p » 1), organisms that are very
susceptible to one toxicant are also very sus-
ceptible to the other. In the case of full
negative, correlation (p - -1), there is an
Inverse relationship between the susceptibi-
lities, e.g., organisms that are very suscepti-
ble to one toxicant are least affected by the
other. Zero correlation (p = 0) means that
there is no relationship between the suscepti-
bilities of the organisms to the two toxicants,
and all other values (-1 < p < 1) represent
intermediate cases. For microorganisms, it is
hypothesized that p should be one because all
organisms are from the same clone and are in the
same (Group III) or nearly the same (Group IV)
physiological state.
The case of (x - 1; p - 1) 1s charac-
terized by the term concentration addition
(C.A.), and the case of (X - 0; p «= 0) by
the term response multiplication (R.M.). Com-
puter programs to estimate the parameters of
the unlvariate distributions in Table 2 are
available (18). Also, the general noninter-
active multiple toxicity model has been formu-
lated into a computer program MULTOX which may
be obtained from the same source (19).
Applications
F1sh. We shall here analyze the results
obtained by Anderson and Weber (20). They
68
-------
TABLE 4. Fit of the Helbull, Problt. and loo.1t Distribution to Growth tat* for the Diatom Navlcula
Incerta. The Raw Data are from Rathlln. Jensen, and Harkentlne (16). Concentrations are 1n
ttolbull
Para-
meter
Growth
Rate
Yield
Toxicant df*
Cd 1
Cu 2
Pb 3
Zn 6
Cd 1
Cu 2
Pb 2
Zn 6
A «
-2.13 0.895
±0.051
-2.59 0.561
±0.079
-2.26 0.561
±0.092
-1.75 0.431
±0.104
-1.'31 0.797
±0.088
-1.72 0.554
±0.084
-2.07 0.650
±0.098
-2.59 0.958
±0.109
X2
0.00031
0.0019
0.0071
0.0345
0.0021
0.0062
0.0031
0.0197
Problt
• B
3.71 1.53
±0.03
3.49 0.831
±0.127
3.74 0.807
±0.154
4.01 0.665
±0.166
4.21 1.66
±0.003
3.94 1.03
±0.16
3.83 1.01
±0.15
3.32 1.69
±0.21
X2
0.000044
0.0026
0.0104
0.0366
8.2xlO-7
0.0084
0.0040
0.027
Loatt
• *
-2.18 1.12
±0.004
-2.61 0.641
±0.093
-2.19 0.625
±0.116
-1.66 0.495
±0.123
-1.31 1.18
±0.01
-1.77 0.745
±0.114
-1.99 0.755
±0.120
-2.91 1.27
±0.15
X2
3.1X10-8
0.0021
0.0089
0.0356
0.000020
0.0075
0.0038
0.0206
•Degrees of Freedom
-3-2-10123456
LOG CONCENTRATION (ZINC, mg/l)
-3-2-10 1 234 56
LOG CONCENTRATION (ZINC, mg/l)
F1g. 2. Fit of the Welbull, probH and loglt models to growth parameters for Navlcula Incerta:
(a) relative growth rate, and (b) relative yield, both based on cell number. The raw data
are from RachHn, Jensen, and Warkentlne (16).
considered only R.M. and C.A. with parallel
dose-response curves. I.e., Identical B-values
(Table 2), while we shall allow any correlation
p between -1 and +1, partially similar
systems, and C.A. with non-parallel dose-
response curves. Also, 1n contrast to their
approach, we Include not only problt but also
loglt and Welbull transformations.
Basic probit lines for the action of the
Individual toxicants nickel (N1), copper (Cu).
potassium pentachlorophenate (POP), dleldrln
(HEOD), and potassium cyanide (CN) on male gup-
pies (Poec111a retlculata) are given 1n Table 5.
In this and the following tables, the weight of
each lot of fish Is the total weight of the ten
fish 1n a batch. The weight W modifies the
69
-------
fie.
concentration H of a toxicant such that the
•affective concentration* M/Vf1 (h - 0.67 -
0.81) remains the same either for a high actual
concentration ftnd. high average weight of Hsh
or a low actual concentration and a low average
weight of fish. In ether words, the Important
quantity Is concentration per weight raised to
the power h and not just concentration. Or:
larger fish can tolerate higher concentrations
for the same mortality rate.
TABLE 5. Problt of Mortality to Male Supples
(Poecilia reticulatal for Several
Toxicants. M(rag/l) 1s the Concentra-
tion of the Toxicant and M(g) 1s the
Weight of Each Lot of Hsh. The
relationships are from Anderson and
Weber (20)
6.5 - - 3.21 * 6.32 log
or
34.36
In the regression of the linear Melbull
transformation u • In k + *ln z, z - z-\ Is
then 34.36 and « • u-i Is given by ui *
ln(-ln(l-P)) - ln(-ln(0.067)) - 0.994. Similar
points are obtained for N.E.D. * 1.0, 0.5, 0,
-0.5, -1.0, -1.5. The Intercept A and slope
n are then given by:
Toxicant
Probit of Mortality
N1
Cu
PCP
HEOO
CN
Y
Y
Y
Y
Y
- -3
- n
- n
= 20
- 14
.21
.4
.77
.33
.71
+ 6
+ 7
+ n
+ 6
+ 11
.32
.46
.23
.84
.65
log(M/W°-67)
log(M/W°'72)
log(H/W°'72)
n en
log(M/W°-B')
1og(H/W°-?2)
n - (l/DHdw^dw^X^ - (I
where 0 » (Iw^Xlw.X2) - (Zw^
1-1 N; N - 7
Xj - In Z1
For N we obtain A = -9.4 and n •
2.99 (Table 6).
Table 6. Logit ana Weibull Parameters Corre-
sponding to the Probit Relationships
of Table 5
Logit and Weibull parameters corresponding
to the problt parameters in Table 5 should pre-
ferably be derived from the original test data.
However, since they were not available, we
determined approximate parameters by a fitting
process, using the weighting:
°1 2
w = " (1n Q} Weibull
logit
where
Qi » the survival fractions corresponding to
M.E.O. values of -1.5, -1, -0.5, 1, 1.5
YI - probit of QI
n< - number of test organisms in trial 1 (10)
1 - 1. 2 7
The logit and Weibull parameters (Table 6)
were then calculated using regressions based on
the linear transformations in Table 2 and the
weighting indicated above. As an example, the
value of M/W°-67 (Table 5) is calculated in
the following manner, considering Mi at N.E.O.
- 1.5:
Toxicant
Logit
Parameters
Weibull
Parameters
N1
Cu
PCP
HEOD
CN
-13.9
10.9
11.5
26.9
16.5
4.66
5.50
8.28
5.04
8.59
-9.4
6.5
6.9
16.8
10.1
2.99
3.53
5.31
3.24
5.51
The bivariate fitting was carried out as
indicated previously (12), except that we here
use minimum ch1-square as the criterion rather
than maximum likelihood. However, because of
the indirect determination of the logit and
Weibull parameters, it was estimated that a
larger stepsize. I.e., 0.1, was sufficient for
both X and p in search of the global minimum
for x* which is calculated according to the
formula:
(Orq.)
where qj • experimental survival fractions,
e.g., 70X in the first case and 20X
in the second (Table 7).
Q^ « calculated survival fractions.
70
-------
iu • number of ttst organism 1n trial
1 (10).
N - number of trials (6).
Ut systematically calculate x2 for several
combinations -of x and ». The pair producing the
global minimum of if Is retained.
TIM results for the binary mixtures (N1,
Cu). (rtP, HEOO), and (KP. CM) are listed In
Tables (7-9) and summarized In Table 10. There
1s little difference between the fits of the
problt and loglt models, both In terms of the
optimum values of x and p and the resulting x2-
However, the Welbull model shows some distinc-
tive differences. It produces the best fits for
the (HI. Cu) and (PCP, HEOO) pairs. For the
(PCP, CN) pair the problt or loglt models pro-
duce minimum x2 but this would appear to be
less Important because none of the fits are
particularly good in that case (P < 0.01) The
X values are the same and the p values
nearly so for a given binary mixture and
different models (Table 10). The reason that
the similarity parameter X and the correla-
tion p between the two tolerances are rela-
tively Insensitive to the form of the mathema-
tical model here 1s that there are only ten
fish 1n each experimental batch of the example
(20). Thus, the models are essentially fitted
to response probabilities between 10 and 90X.
•nd 1n this range there Is not a great deal of
difference between the fits of the problt.
loglt, and Uelbull models. However, as Illus-
trated by Christensen and Chen (12). the situa-
tion 1s different when high or low response
probabilities are Included. In that case, not
only will the estimates of x and p depend
upon the choke of model, but the problt model
may not fit at all. The advantage of using
non-normal blvariate tolerance models will,
therefore, be particularly evident when extreme
response probabilities are encountered as for
example in models for carcinogenesis.
TABLE 7. Evaluation of the Joint Action of Ni and Cu on Male Guppies Based on the Parameters
of Tables 5, 6 and the Computer Program HULTOX
Weight of
Each Lot
of Fish
(9)
1.53
1.07
1.27
1.30
1.23
' 1.23
Concentrations
(mq/1)
N1
12.23
15.56
14.17
10.77
15.15
H.79
Cu
0.049
0.082
0.084
0.063
0.071
0.058
Calculated Percent Mortality
for M1n. Chi-Sauare
Problt
(X-l; p-0.5)
16
83
66
28
64
53
Logit
(X-l; p-0.5)
16
83
67
28
65
53
Weibull
(X-l; p-0)
19
68
68
29
66
53
Observed
Percent
Mortality
(20)
30
— 80
70
30
80
80
TABLE 8. Evaluation of the Joint Action of PCP and HEOO on Hale Guppies Based on the Parameters
of Tables 5,6 and the Computer Program HULTOX
Weight of
Each Lot
of F1sh
(9)
Concentrations
(mq/1)
PCP HEOO
Calculated Percent Mortality
for M1n. Ch1-Sauare
Problt Loglt Welbull
(X-0.1; p~ 0.1) (X-0.1; p-0) (X-0.1; p— 0.2)
Observed
Percent
Mortality
(20)
1.51
2.15
1.76
1.79
1.51
1.94
0.26
0.40
0.31
0.40
0.29
0.41
0.005
0.00645
0.0063
0.0063
0.0048
0.0069
30
49
45
75
39
72
28
47
42
74
37
70
34
49
46
73
42
69
10
40
50
60
70
80
71
-------
TABU *. Evaluation of the Joint Action of PCP and CN on Male Supples Based on the
Parameters of Tables 5.6 and the Commiter Program NULTOX. The Height of
Each Lot of F1sh Has Been Set to l.SOg
Concentrations
PCP
0.233
0.231
0.257
0.257
0.246
0.177
0.135
0.146
0.175
0.169
0.153
0.139
Problt
(X-0.2; p— 0
8.5
13
54
48
22
4.6
Calculated Percent Mortality
for Mln. Chl-Souare
Loglt Weibull
1.8) (X-0.2; P— 0.8) (X-0.1; p— 0.8)
9.8
14
53
47
23
5.6
17
22
53
49
30
11
Observed
Percent
Mortality
(20)
10
10
40
100
10
10
TABLE 10.
Chi-Square for Binary Mixtures of Toxicants Considered 1n Tables 7-9 (four degrees of
freedom).
Toxicants
N1-CU
PCP-HEOD
PCP-CN
Model
Problt
5.79
(X-1,
7.83
(x-o.
13.2
(X=0.
P-0.5)
i; P— o.i)
2; p--0.8)
Loglt
5.72
(X-1;
8.12
(X-O.
13.2
(X-O.
P-0.5)
1; P-O
2; p-0.7)
Welbull
5.38
(X-1; p-0)
7.72
(X-0.1; p— 0
14.2
(X-0.2: p— 0
.2)
•8)
The estimation of parameters when three or
more toxicants are considered, using the above
method with x2 as criterion, is very cum-
bersome and we have not attempted it. Other
means of estimating parameters are currently
being explored.
Isobolograms for the three binary mixtures
of Table 10, based on the Weibull model, are
shown in Figure 3. The curves are drawn for
three values of the non-response probability Q:
0.1. 0.5, and 0.9. The symbols M and W of the
modified'concentration are defined in Table 5,
and h (0.67-00.81) is the exponent of the weight
of each lot of fish. CT and C2 are the
values of H/W**h for each toxicant that will
give the desired response when acting separate-
ly It is clear that the isoboles for Cu and
Ml (Figure 3a) are close to defining a straight-
line relationship characteristic of C.A. This
might be expected since X - 1; and although
p « 0 the variation of the response for p
between 0 and 1 is modest (12). The Isoboles
for HEOD and PCP (Figure 3b) are typical when
„ > i for R.M. which 1s Indicated by the
values of X and p that are both close to
zero Except for an Interchange of Indices,
these curves are 1n fact similar to the curve
labelled 1 1n Figure 3a of ref. (12), which is
strictly valid for R.M.
Algae. The use of the above multiple
toxicity model for algal growth rate based on
cell number was considered previously (21, 22).
The growth rate of the green alga Selenastrum
caprlcornuture and the blue-green Synechococcus
leopoliensis was modeled as a function of ionic
concentrations of Ni and Zn.
We consider here the growth rate of Selen-
astrum based on cell volume. The experiment
was designed such that for each point, equi-
toxlc concentrations of NI2* and Zn2* would be
combined. The culturing methods were as
described by the U.S. Environmental Protection
Agency (23), and Ionic concentrations were cal-
culated by the equilibrium speciation program
MINEQL (24). The results of such an experiment
are shown In Fig. 4. Just as for growth rate
based on cell number (21), the joint action ap-
pears to be close to C.A. (p =1; X = 0.9).
However, here the best model is logit rather
than Weibull.
CONCLUSIONS
The following conclusions may be drawn from
the present study:
72
-------
(c)
MOEX 0
0
U
M
C«l
c,
O.MZ
0.144
•.004
M
c,
ji.0
11.1
MOCX a
HfOO
c,
•OCX 0
01
c,
rv
c,
0 0.1 0.0073 0.320
(D O.S 1.00504 OJSS
(}) M
0
e^C,
1.0
MODIFIED CONCENTRATION M(mg/l)/W(g)«*n/C,
Fig. 3. Isobolograms for the effect of (a) (N1. Cu). (b) (PCP, HEOO), and (c) (PCP, CN) on male
• gupples based on the Weibull model with optimum values of x and p (Table 10).
Wood 'op
S,'2 .=26300 09506 m 2
In'' '=2533* •• i576inZ
1 0
in (Total ion Cancvnoon) f* *' & Zfl *
2T3
23
186
059 034
1 (Tom Concenmtfi) NI 4 in
Fig. 4.
Combined effect of N12+ and Zn2+
on the growth rate based on cell
volume (biomass) of the green alga
Selenastrum capricornutum. The test
results are best fitted by a bivariate
loglt model with X » 0.9 and p » 1.
(1) The Weibull model should be given serious
consideration as a replacement for the
probit model as a general dose-response
function for the quantal response of macro-
organisms with a tolerance distribution
(Group I organisms). The main reason is
that the Weibull model appears to give a
better fit to experimental data, and that
1t, therefore, 1s more likely to provide
valid mortality estimates by extrapolation,
particularly to low concentrations. The
better fit of this model supports a pre-
viously suggested mechanistic-probabilistic
basis in terms of chemical reactions be-
tween toxicant molecules and a key receptor
of the organism.
(2) Literature data for the growth rate and
yield of the diatom Navicula incerta Inhi-
bited by Cd, Cu, Pb, or Zn were fitted to
the univariate Weibull, probit, and loglt
models. The Weibull model provides
generally the best fit, thus supporting a
basis which was previously developed for
microorganisms (Group III and IV organisms)
when the growth rate based on cell number
was modeled as a function of toxicant con-
centration.
(3) A general noninteractive multiple toxicity
model was applied to literature data for
the toxlcity of binary mixtures of N1, Cu,
PCP, HEOO, and CN to male guppies (Poecilia
reticulata). We confirm that the action
' of (N1, Cu) and (PCP, HEOD) Indeed may be
approximately characterized by C.A. and
R.M., respectively. The estimates of the
similarity parameter x and the correla-
tion coefficient p are relatively insen-
sitive to the choice of model here because
the response probabilities mainly are in
the range between 10 and 90X, and in this
range there is not much difference between
the fits provided by the three models.
Nevertheless, in both of the above cases,
the Weibull model gives minimum chi-square.
(4) The combined effects of N12+ and Zn2* on
the growth rate based on cell volume (bio-
mass) of the green alga Selenastrum capri-
cornutum were approximately according to
C.A.. with X - 0.9 and p - 1. While
previous bioassays, In which the growth
rate was based on cell number, demonstrated
that the Weibull model was preferable, the
present results, based on cell volume.
indicate that the loglt model is best
suited to describe the combined response.
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Mixtures of drugs: non-Interactive action,
Biometrics ]£: 591-610.
(18) Christensen, E.R., Chen, C.-Y., and Fox,
D.F. (1986). Computer programs for fit-
ting dose-response curves 1n aquatic toxi-
city testing, AEEP's software library,
Dept. of Civil Engineering, Michigan Tech-
nological University. Houghton, Michigan.
(19) Chen. C.-Y. and Christensen, E.R. (1986).
MULTQX a computer program for the calcula-
tion of the response of organisms to mul-
tiple toxicants and multiple limiting
nutrients, AEEP's software library, Oept.
of Civil Engineering, Michigan Technologi-
cal University, Houghton, Michigan.
(20) Anderson. P.O. and Weber. L.J. (1975).
The toxicity to aquatic populations of
mixtures containing certain heavy metals.
In: Proc. Int. Conf. Heavy Metals in the
Environment, pp. 933-953, Institute of
Environmental Studies, University of
Toronto, Toronto, Canada.
(21) Christensen, E.R., Chen. C.-Y., and
Kannall, J. (1984). The response of aqua-
tic organisms to mixtures of toxicants.
lAWPRC's 12th Biennial Conference,
Amsterdam. Holland. Water Sci. Tech. 1_7.
1445-1446.
(22) Christensen. E.R., Chen. C.-Y.,end Fisher,
N.S. (1985). Algal growth under multiple
toxicant limiting, conditions. In: Proc.
Int. Conf. Heavy Metals 1n the Environment
held 1n Athens, Greece, Vol. 2, pp. 327-
329. CEP Consultants, Edinburgh, United
Kingdom.
(23) U.S. Environmental Protection Agency
(1978). The Selenastrum capricornutum
Printz Algal Assay Bottle Test. Report No.
EPA-600/9-78-018, Corvallis. Oregon.
(24) Westall. J.C.. Zachary. J.L.. and Morel,
F.H.M. (1976). MINEQL a computer program
for the calculation of chemical equili-
brium composition of aqueous systems.
Technical Note No. 18, Oept. of Civil
Engineering, Massachusetts Institute of
Technology, Cambridge, Massachusetts.
Acknowledgments. This work was sponsored by
the U.S. National Science Foundation Grant No.
CEE8103650. The assistance of C.-Y. Chen in
carrying out the numerical calculations is
gratefully acknowledged.
1A
-------
DISCUSSION
Richard C. Hertzberg, U.S. Environmental Protection Agency
Chrlstensen presents examples of the
application of a noninteraction multiple
toxicant Mdel to several data sets. Including
Mortality of fathead minnows and population
growth rate and yield of diatoms. He
concludes that the Mixture Helbull Is a
preferred model for similar acting chemical
pairs and Infers the type of noninteraction
between the mixture components by the values
of the model's parameter estimates. There are
three aspects of this work that should receive
critical attention: the usefulness of the
mixture models as descriptors"of mixture
tox1c1ty, the biological Interpretation of the
He1 bull and Us parameters, and the future of
modeling binary mixtures.
The feeling one gets 1n reading the paper Is
that the results of the mixture models are
tantalizing yet Incomplete. To his credit,
ChrUtensen's work does Include many desirable
characteristics: multiple dose levels,
different types of toxicants, two very
different species, and well-defined biological
end points. But several Hems are missing:
the models are not presented, the dose
adjustment model (divide dose by a power of
body weight) has no statistics on Us
parameters that might suggest the validity of
such an adjustment, and the descriptions of
the model fits do not Include significance
levels or even graphs. The latter 1s
Important since the Information that Is
provided (ch1-square values) shows only a
marginally better fH for the Welbull. which
1s an Inadequate criterion for model
preference.
Of more concern, perhaps, 1s the motivation
for the models. ChrUtensen states that the
models are to be considered empirical, yet he
then Infers, biological meaning to the value of
the Welbull parameters. The biological
properties should have been established first
(e.g., Cu and N1 are tox1colog1cally similar)
and then shown to be consistent with the
model's results (e.g., lambda=l). Two
similarly acting toxicants are often
characterized as being dilutions or
concentrations of one another so that, once
adjusted for potency differences, the two
chemicals should have the same dose-response
curves. Because of this, 1s seems that two
similar chemicals (lambda*!) should also have
the same tolerance distributions (rho-1). The
Inclusion of this constraint, and verification
by actual data, would Improve the support for
ChMstensen's approach. Without such support,
Inferences about toxic similarity from
parameter values are not believable.
The use of mortality as the toxldty
Indicator raises several Issues. First,
mortality 1s usually Interpreted as a
non-specific toxic end point, and thus 1t
provides little Information on toxic
mechanism. Consequently, the Inference about
toxic similarity Is confusing. The usual
definition of toxic similarity (EPA, 1986) 1s
that the same tissues and organs are affected,
and that the same type of damage or lesion
results. In contrast, mortality usually
results from failure of several organs and the
txact caust of death Is rartly Identified.
Second. Mortality Is useful primarily for
assessment of ecosystems. Presence/absence
and population size of Indicator organisms
have been used successfully for years to
evaluate water quality of lakes and streams.
But mortality 1s not particularly helpful for
human risk assessment. Particularly for
systemic toxicants (chemicals with a toxic
threshold), the preferred data would Include
doses showing several degrees of sublethal
effects along with doses showing no effects.
The problems with developing a general
mixture assessment methodology are only
touched on 1n Chrlstensen's discussion. These
Include having more than two components 1n the
mixture, multiple end points and varying
degrees of severity for each end point. The
extension of binary models, as has been done
for multistage cancer models (Thorslund and
Charnley, 1986), 1s one approach for
evaluating several components, particularly
for single end points. But the general
n-chem1cal model can become Intractable, as
Chrlstensen mentions, even for one end point.
The extension to multiple end points by
traditional methods seems out of the question.
One useful approach we are Investigating 1s
to combine expert Judgment w1tti generalized
linear models. We have adapted the work of
McCullagh (McCullagh and Nelder, 1983) to give
a multl-chemical model which uses Judgments of
the overall severity of the toxic reponse 1n
Ueu of response rates or numerical Intensity
measures of specific effects. In this way,
data describing several end points, even
purely qualitative descriptions, can be
modeled to give estimates of an "acceptable"
dose or of a dose corresponding to a low
risk. Consider the following data for
dieldrln-lnduced nephritis (FUzhugh et al.,
1964):
LESIONS
DOSE —
(ppm) None Slight Moderate Severe
0,0
0.5
2
10
SO
100
150
The multiple response curves plotted against
dose (given 1n Fig. 1) are not easily
Interpreted In terms of overall risk. The
cumulative response (F1g. 2) separates the
severity groups and allows an estimation of
the probability of seeing a given severity or
less for any given dose. The statistical
approach we are developing 1s similar. The
75
-------
steps are as follows:
1. The main covarlables (dose, duration.
species, route) are represented by
categories (Intervals for the continuous
variables).
2. Tbt response Is coded 1n term of a
lexicologist's Judgment of overall
severity to the animal. This code will
be from a predefined set of categories.
3. Apply HcCullagh's approach for ordered
categorical data:
a. Identify a link function to transform
the original response variable Into
one that 1s linear In the
covarlables. We are Investigating
the log cumulative odds:
where:
k-1
Pij
For a single covarlate, say dose.
then J Indexes severity, 1 Indexes
dose, and q^j 1s the log odds of
the severity being 1n category J or
less, given a dose In category 1.
Here p^ 1s the fraction of
responses of severity k at dose 1.
b. Regress q on the covaMates:
q * Ax t b
c. Calculate the risk of response from
the link function. For a dose d, and
severity s:
rds= Pr [response at level s or
less, given dose d]
= exp(Ad+b)/(l * exp(Ad+b))
The primary advantage of this method 1s
that the data constraints are minimal;
virtually any type of toxlclty data can be
•odeled to give doses that art 'acceptable* or
that correspond to low risk. In addition.this
approach yields maximum likelihood estimates.
The disadvantages are that Uttle Indication
1s given of the mechanisms of toxldty. and
that the dose-response relation Is limited by
the precision of the dose and response
categories. What remains to b* checked Is the
numerical performance of this method, and the
ease of determining a suitable link function.
Note that this approach also works with
complex (say. for n > 20 chemicals) mixtures.
If the mixture Is relatively stable over time,
then 1t can be treated as a slnglechemlcal
entity and the severity judgment reflects the
Impact on the test animal of all effects from
all components.
In summary, ChMstensen's work appears most
applicable to ecosystem assessment of simple
mixtures. The use of Welbull parameters to
Indicate the nature of the Interactions Is
Intriguing, and should be pursued. Including
validation by chemical pairs with know-.
mechanisms of toxic Interaction. Further, one
must agree with his caution against the
habitual preference for the problt model. For
human risk assessment, however, 1t seems that
other approaches such as I have outlined will
be required, particularly those which place
fewer demands on the quality and quantity of
the data.
REFERENCES
FHzhugh, .0., A. Nelson and M. Qualfe (1964).
Chronic oral toxldty of aldrln and dleldrln
1n rats and dogs. Fd. Cosmet. Toxlcol.
2:551-562.
McCullagh, P. and J. Nelder (1983).
Generalized linear models. Chapman and Hall,
New York. 261 pp.
Thorslund, T. and G. Charnley (1986). Use of
the multistage model to predict the
carcinogenic response associated with
time-dependent exposure to multiple agents.
These Proceedings.
U.S. EPA (1986). Guidelines for the health
risk assessment of chemical mixtures. Federal
Register (In press).
76
-------
RESPONSE
DIELDRIN KIDNEY TOX1CITY
so
100
DOSE (mg/kg)
FIGURE 1. EXWPLE OF DIFFICULT INTERPRETATION OF STANDARD OVERLAID
DOSE-RESPONSE PLOTS OF MILTIPLE EFFECTS. SOURCE: FlTZHJGH ET AL., 1S&4.
DIELDRIN KIDNEY TOXICITY
200
CUMULATIVE RESPONSE
100'
50
too
DOSE (mg/kg)
150
FIGURE 2. EXAMPLE OF PROVED INTERPRETATION DUE TO SEPARATION OF CURVES BY
USING OnJLATIVE RESPONSE. SOURCE: FlTZHUGH ET AL., 1964.
77
200
-------
MA
««. !» «SESS«o at JoiHT «no« or
1. PnaODOCTION
ladtvldaala are expo««u w .—„
toxic chemicals In the environment. The
aaaeaament of health risks fro* the exposure
becomea Increasingly important. The construction,
of mathematical models for predicting joint
toxicity by using only the Information about the
toxicity of individuals is difficult. Dose-
addition and response addition frequently have
been mentioned for evaluating the joint effects
of two toxicants, (Shelton and Weber, 1981; Reif,
1984). Two chemicals are said to be dose-
additive or are said to have "simple similar
joint action" (Flaaey, 1971) if one chemical acts
exactly as if it were a dilution of the other.
Response-addition or effect-addition has been
used in different contexts in the literature; the
most co=3on definition for response-addition is
that cocbined effect of the mixture is equal to
the sum of each effect alone, (Reif, 1984).
Synergism and antagonism represent a deviation
from additivity under the null model of
dose-additivity or response-additivity.
Hamilton and Hoel (1980) distinguished between
two purposes for studying the joint actions of
chemicals, "those studies conducted to provide
risk estimates from the joint exposure and those
studies conducted to elucidate the mechanisms of
Joint toxicity." In this paper, we propose a
mathematical model for presenting and analyzing
the data from mixture studies. The dose-response
function is modeled as a function of both the
proportions of chemicals in the mixture and the
total concentration of the chemicals. A
response-additivity is introduced for assessing
the Joint action of chemicals.
2. RESPONSE-ADDITIVE MODEL
Let x. be the proportion of chemical C
(1-1,2) in a mixture with total concentration T.
Then t.»Tx. represents the concentration of
chemical C. in the mixture. Suppose that F (t.)
represents the (dose) response function of
chemical C. at a dose level t.. It Is assumed
that the response of the mixture, R(t.,t-) •>
R(xltx2,T), can be expressed as
F2(T)
(1)
The terms x^CT) and x^T) «ay represent the
-expected' responses produced by administration
of the single chemicals, and EU^.T) then
represents the "excess" of the response over
r (i)
1
Produced ^ the mixture-
equation (1), the data were
total concentrations of the mixture
Figure 1. This model was first Introduced by
Scheffe (1958) for atudying mixture experiments
with only one concentration.
The joint action of the two chemicals la aald
to be 'response-additive' If EC^.x^.T) • 0, for
all x^ Xj, and T with ^^"l- That 1«, If the
joint action of two chemicals can be predicted by
response-additivity, then the response of the
mixture at the (total) concentration T can be
represented by the weighted average of the
responses produced by the individual chemicals at
the concentration T with the weights for
individual responses being equal to the
proportions of the cnemicals in the mixture. For
a fixed concentration T, the response-additive
model can be expressed as a linear function of
the proportion of a cnemical in the mixture. An
example of a plot of response-additivity is shown
in Figure 2. For a fixed concentration the
response can be represented by a straight line.
The response-additivity defined in this paper
is conceptually parallel to the dose-additivlty.
The joint action of a mixture is said to be
"dose-additive" or simple similar (Finney, 1971)
If
R(Xl,x2,T) - F^T+mx^) - F,(t^
(2)
where m represents the relative potency of the
second chemical to the first. (A more general
form of dose-additivity allows m to be a function
of T.) A common method to present the dose-
additivity is to use the isobolographic analysis
which shows the various combinations of dose
levels of the two chemicals which produce the
same level of response. The isobologram for
dose-additivity can be represented by a set of
straight lines. An example of a plot of the
isoboles for dose-additivity is shown in Figure
3. The isobole of a given response is a straight
line.
Without loss of generality, assume that F2(T)>
?.(T), i.e. m>l. If the joint action of C. and
C. is dose-additive then
F2(T)
(3)
That is, the response predicted by dose-
additivlty is bounded by the two responses
produced by the single chemicals of the same
total concentration. If the response function F.
is convex in the (dose) interval (T,mT), then the
response predicted by dose-additivity is less
than that predicted by response-additivity. On
the other hand, if the response function F. is
concave in the interval (T,mT), then response
predicted by dose-additivity is greater than that
predicted by response-additivity, Figure 4.
Therefore, a definition for "additive" joint
action of two chemicals can be
78
-------
F2(T) > Kx^Xj.T) > F^T) (4)
for any *i»*2' •"* * ****** *i * *2 * *" *wo non~
additive actions, synergism and antagonism, can
be defined by using equation (4). The
•ynmrslmtic (antagonistic) action occurs If the
response of the mixture la greater (leaa) than
the additive response, that la,
tj.T) < Ft(T)] (5)
This, definition agrees with that of Vendetti and
Goldin (196A) for studying the combination of two
drugs.
3. ASSESSMENT OF IKTERACTIVE ACTIOH
Suppose that the purpose of the experiment is
to understand the underlying Joint toxicity
(interaction) of chemical combinations. Termi-
nologies used for describing the joint actions of
mixtures are interaction, Independence, syner-
gism, antagonism, and additivity. Unfortunately,
these terms mean different things to different
authors (Kodell and Pounds, 1985). Equations (4)
and (5) define three possible models for
characterizing the joint action of two chemicals.
The assumption for the response-additive model
defined in this paper is that the sites of
primary action of the two chemicals 'are the same;
this type of action is called similar joint
action according to the classification of
Plackett and Hewlett (1967). The joint action of
two chemicals is simple similar or noninteractive
if the presence of one chemical does influence
the action of the other. Dose-additivity
commonly has been used for assessing the
interactive effects between two drugs in
pharmacology. In this section, we apply, the
response-additive model to assess dose-additive
Joint action.
Suppose chemical C_ is m times more potent
than C. at dose T. To assess dose-additive, the
dose measurement for chemical C. is scaled as T'
» mT so that both chemicals are equipotent, i.e.,
F.(T') • F-(T'). At the "concentration T1" In
i z
the mixture, the response predicted by response-
additivity, Equation (1) is
R(x1,x2,T')
') - F^mT)
for any "proportions" x^ and x_. The response
predicted by dose-additivity, Equation (2) is
M - F1(x1T'-hnx2T') - F^mT)
That is, at the concentration T' the response of
the mixture predicted by dose-additivity and
response-additivity is constant regardless of the
proportions of individual chemicals in the
mixture.
A procedure for testing dose-additivity can he
constructed. Suppose that doses mT of C. and
dosaga T of Cj produce tha same level, p, of
response, e.g., SOZ affect. (This can ba
obtained by plotting the dose-response curves of
each chemical.) Tha concentrations mT of C. and
T of C. will ba uaad aa tha standard preparations
for constituting various mixtures of the
experiment. Each mixture will contain x.mT of
compound C^ and XjT of chemical C2, where x.,x, >
0, and JL+X.-I. Let n. denote the number of
subjects in the experiment and r. denote the
observed number of effects in the J-th
preparation (mixture). The hypothesis of dose-
additivity can be test by using the chi-square
test for homogeneity
g
X " I
3-1
? U-P
where g is the number of preparatinos. If the
two chemicals are dose additive, then X has a
chi-square distribution with g degrees of
freedom.
4. RESPONSE SURFACE ANALYSIS
Suppose that the purpose of an experiment is
to study the relation between the different dose
combinations with the responses. The
experimenter may be interested in finding a
suitable approximating function for the purpose
of predicting future responses over a range of
dosage, or determining what dose combinations (if
any) can yield an optimum as far as the response
concerned. The common approach of this problem
is by a statistical curve fitting technique or a
so-called response surface method.
Assume that the observed values y from the
mixture contain variations e, the mixture
responses can be written as
y - R(XI,XZ,T) + e
(6)
The variations e are assumed to be independently
and normally distributed with zero mean and
common variance. The functions F.(T) and
E(x1,x2,T), in general, can be represented by
polynomial forms; that is, equation (1) can be
expressed as
1(VVI> - x,
b!2
Vt Jc,
l!2
(7)
For practical purposes, lower-degree polynomials
are normally fitted. For example, a quadratic
response model, a second degree polynomial
function for x and T, for the mixture can be
expressed as
79
-------
where B^T), B20
provided that B^T) + BU(T) > B2(T) and 32(T) +
B, (T) > BT(T) for all T; similarly, the minimum
respo-se occurs in Che experimental dose range if
B ,(T) < 0 provided that B^T) + B12(T) < B2(T)
and S2(T) + B12(T) < B^T).
Equation (7), alternately, can be expressed as
b2 "2 +
!2
T2
(9)
When the experimental dose levels are coded to
have zero mean (e.g., -1,0,1 for three
concentrations), the coefficients have
Interpretations. (Piepel and Cornell, 1985), e.g.,
the intercept term (b^ x^ + b2 X2 + b^2 ^i^
represent linear and nonlinear effects of the
proportions in the mixture at the average
concentration of the experiment .
If b!2° " b!2l " b!22 " °' then the J°lnt
action of the two chemicals is response-additive;
the response is linear with the proportion of a
given chemical at each concentration (Figure 2) .
Three special situations are of Interest:
1) If b^ • b21 - bx2 - b22 - 0, then R(x1,x2;T)
- (b1°x1 + b2°x2); the lines in Figure 2 are
coincident, the chemical concentration has no
effect on the response.
2) If b. -
and
(b1°x1 + b2°x2) +
DZ , then
+ b^T2; the lines in
Figure 2 are parallel, the response increases
by a constant amount as concentration
increases .
3) If b^ - b2° - b^ - b2l - 0, then R(x1,x2;T)
th* llne* to
Figure 2 are not parallel, the response
increases proportionally vith the
concentration.
Kquation (9) assumes that the experimental
variations are normally Independently distributed
with zero mean and common variance. However, many
data collected from the bioassay experiments do
not follow the model assumptions. For example,
Snee and Irr (1981) found that mutagenesis data
collected from a mammalian cell assay system did
not satisfy the assumptions of normality and
constant variance. Various transformations can
be used to achieve the model assumptions. For
analyzing dose-response relationships of 3uta-
genesis data, Snee and Irr (1981) suggested using
the Box-Cox (196-*) power transformation model
y - [R(x, ,xO] A + e for \ * 0;
log y • log [R(x1,x2)] + e for X - 0
(10)
where X is the power transformation parameter to
be estimated from the data. An application of
the model is given In the next section.
5. EXAMPLE
An experiment was conducted to study the
effects of mixtures of l-nitrobenzo(a)pyrene
(1-NBP) and 3-KBP on mutation induction in the
Salmonella reversion assay. Both chemicals are
suspected environmental contaminants and are
potent direct-acting mutagens in Salmonella
without exogenous activation (Pitts et al., 1984;
Chou et al., 1984). Assays were performed with
Salmonella typhimurium tester strain TA98 in the
absence of exogenous metabolic activation using
the methods described in Mar on and Ames (1983).
1-NBP and 3-NBP were synthesized,. free from
contaminating isomers, by the methods of Chou et
al., 1984). Mixtures of the two chemicals were
prepared using seven different proportions of the
two mutagens at the fixed total concentrations of
0.1, 0.2, and 0.4 ug of mutagen per plate. The
mixture proportions and the experimental results
are shown in Table 1.
TABLE 1. The number of mutants per plate produced
by mixtures of 1-NBP and 3-NBP
1-NBP :3-NI
Ratio
1:0
4:1
2:1
1:1
1:2
1:4
0:1
150
219
204
206
213
255
194
Revertants per Plate
0.1
,171
,165
,197
,202
,237
,284
,176
,151
,196
,208
,196
,205
,275
,210
212
258
462
480
379
527
286
0
,213
,333
,393
,495
,418
,503
,264
.2
,183
,349
,418
,475
,389
,489
,289
0.4
216
339
604
660
612
471
315
,198
,328
,520
,621
,737
,660
,333
,237
,305
,490
,572
,491
,605
,305
80
-------
The Box-Cox power transformation was used to
ensure that tht assumptions of normality and
homogeneous varlanct of experimental error were
satisfied. Using Che method given by Irr and
Snee (1982) to calculate the power.parameter X;
the estimated value of X was approximately 0.20.
Thus, the transformation y°*2 was used to fit the
dose-response functions for subsequent analyses.
The fitted equation with the estimated
coefficient standard errors for the data from
Table 1 is
y - (183 1-NBP + 283 3-NBP + 760 1-NBP*3-NBP)
(12.0) . (16.7) (73.1)
+ (147 1-NBP + 435 3-NBP + 4190 1-NBP*3-NBP)T
(99.0) (139.4) (610.9)
(ID
where T is coded as -.0133, -0.033, and 0.166.
Note that the coefficients for the quadratic
function of T are not significant. Equation (11)
shows mutagenic responses on 1-NBP and 3-NBP, and
the responses produced by each chemical are not
equal. The effect of the total concentration of
the mixture is linear with the response.
Increasing the total concentration affects both
the linear terms, b.l - 147 and b, • 435, and
^ 1 ^
the nonlinear term, b
12
4190, in the mixture
components. Moreover, it can be shown that a
aynergistic Joint action between the two
chemicals in the experimental dose range, total
concentration from 0.1 and 0.4 ug/ml, and the
mixture with proportions of 1-NBP to 3-NBP about
0.43 to 0.57 at total concentration. 0.4 ug/ml can
produce the strongest mutagenic effect.
REFERENCES
Ames, B., MaCann, J., and YamasakJ., E. (1975).
Methods for detecting carcinogens and mutagens
with the Salomella/maomalian microsome muta-
genicity test, Mutation Research, 31, 347-364.
Box, G.E.P. and Cox, D.R. (1964). An analysis of
transformations (with discussion), Journal of
Royal Statistical Society B, 26, 211-252.
Chou, M.W., Heflich, R.B., Casciano, D.A.,
Miller, D.W., Freedom, J.P., Evans, F.E., and
Fu, P.P. (1984). Synthesis, spectral
analysis, and mutagenicity of 1-, 3-, and
6-Nitrobenzo(a)pyrene, Journal of Medicinal
Chemistry, 27, 2256-2261.
Finney, D.J. (1971). Probit Analysis, Third
Edition, Chapter 11. Cambridge University
Press, Cambridge.
Hamilton, M.A. and Hoel, D.C. (1980). .Quantita-
tive methods for describing interactive
effects in toxicology. Technical Report No.
1-6-80, Montana State University, Bozeman,
Montana.
Irr, J.D. and Snee, R.D. (1982). A statistical
method for the analysis of mouse lymphoma
L5178Y call Tt locua forward mutation assay:
comparison of results among three labora-
tories, Mutation Research, 97, 371-392.
Kodell, R.L. and Pounds, J.G. (1985).
Characterization of joint action of two
chemicals in an in vitro test system,
American Statistical Association, Proceedings
of Biopharmaceutical Section, 48-53.
Maron, D.M. and Ames, B.N. (1983). Revised
methods for the Salmonella mutagenicity test,
Mutation Research, 113, 173-215.
Plackett, R.L. and Hewlett, P.S. (1967). A
comparison of two approaches to the
construction of models for quantal responses
to mixtures of drugs, Biometrics, 23, 27-44.
Piepel, G.F. and Cornell, J.A. (1985). Models
for mixture experiments when the response
depends on the total amount, Technometrics,
27, 219-227.
Pitts, J.N. Jr., Zielinska, B., and Harger, W.P.
(1984). Isometric mononitrobenzo(a)pyrenes:
synthesis, Identification and mutagenic
activities, Mutation Research, 140, 81-85.
Reif, A.E. (1984). Synergism in Carcinogenesis,
Journal of National Cancer Institute, 73,
25-39.
Scheffe, H.. (1958). Experiments with mixture,
Journal of the Royal Statistical Society, B,
20, 344-360.
Shelton, D.W. and Weber, L.J. (1981). Quantifi-
cation of the joint effects of mixtures of
hepatotoxic agents: evaluation of a theoreti-
cal model in mice, Environmental Research,
26, 33-41.
Snee, R.D. and Irr, J.D. (1981). Design of a
statistical method for the analysis of
mutagenesis at the hypoxanthlne-guanine phos-
phoribosyl transferase locus of cultured
Chinese hamster ovary cells, Mutation
Research, 85, 77-98.
Vendetti, J.M. and Goldin, A. (1964). Drug
synergism in antinioplastic chemotherapy,
Advance Chemotherapy, 1, 397-498.
81
-------
FIGURE 1. Mixture Design
FIGURE 2. Response-Addltivlty
Dose of
Proportion in Mixture
FIGURE 3. Dose-Addltlvlty
FIGURE 4. Response from Dose-Additivity
o
"o
w
o
Q
M
O
o.
(O
0)
DC
F,(T)
F, (MT)
= F2(T)
T Dose of C, MT
1:0 Proportion of C-, to C2 0:1
-------
DISCUSSION
Elizabeth H. Margosches, U. S. Environmental Protection Agency
X «• pleased to have Che opportunity to comment
on this paper. When Dr. Chen first sent M the
paper, several directions for rgamuts came to
sdod. At this conference we have already heard
•any speakers refer to the properties of response
additivity. Nevertheless > there are some special
points here.
Chen e_t al. define a response additive model
for which the outcome is the same as that under
the dose additive assumption, and then proposes to
test for dose additivity. This special case, how-
ever, where E(xi,x2,T) • 0, is, as Dr. Kodell
pointed out yesterday, the exponential case, which
has many well defined properties. One of the
problems here is that the method works from a
count of effects. Among the pluses: a test sta-
tistic is proposed; data are used on a noncancer
er.cpoint, mutagenicity.
Chen st_ al. quote Hamilton and Hoel (1980)
regarding two purposes for studying the joint ac-
tions of chemicals, as shown in Table 1. Studies
may be conducted to provide risk estimates from
joint exposure and they may be conducted to elu-
cidate mechanisms of Joint toxicity. The emphasis
in Chen e_t al. appears to be on the latter and, as
we've heard from several speakers, this is an
imortant facet of research. As an EPA statis-
tician, however, I must admit my concern is more
with the former, although our interest is in both
foci.
Can we expect one study to assist us in both
endeavors? Probably not. Can we find one method
of modeling to help in both?
What are the modeling questions asked in these
two perspectives? In the first, we assume the
components are unknown. We then try to predict
the curve at some other dose than that studied.
In the second, we can assume the components are •
known. Then we try to decide if, at some dose,
there is joint action (or compounded effect).
Any model that is chosen for use can only reflect
the extent of joint activity built into it. Sim-
ilarly, the shapes at low doses, the thresholds,
etc., depend on the underlying postulates, not
necessarily the true state of nature.
Thus, the two perspectives must have different
analyses. Providing risk estimates from joint
exposure calls for procedures that are robust
against misspecification in the range of interest.
Elucidating mechanisms calls for tests of full
versus reduced models like those of which Dr.
Machado spoke earlier. Chen et al. have provided
conditions for maximum response and minimum re-
sponse in the experimental range. What about in
the low dose range where I have to work so often?
Can the cancer model of which Dr. Thorslund spoke
earlier help with transformed cell assay data?
But it seems one of the greatest limits we
have placed on ourselves so far is that of deal-
ing with substances in pairs. As Dr. Litt de-
scribed yesterday, the Agency must deal on a daily
basis with toxicants combined in both unidentified
and unquantified mixtures, e.g., pesticides, waste
dumps. We need methodology to take us beyond
pairs.
What are our barriers to extension? I won't
pretend to have identified all of these, and I
offer just a few thoughts on ways statisticians
have already extended themselves in other set-
• tings. Three that cove to mind nave entered into
several papers at this symposium. (l)Looking at
all the cross-products: this becomes quite cum-
bersome with more than two compounds in anything
beyond near linear responses. Let's consider
adopting a matrix notation, so useful in the
analogous leap in regression. Or consider, as
Dr. Patil suggested yesterday, the multivariate
distributions that may be at work to produce the
phenomena we see as marginal distributions.
(2)Looking at pairvise isoboles: again, we're
bound by the paper plane. *r.at aoout colors,
faces, perspective, etc. It's almost ten years
since Gnanadesikan published his book on ways to
look at multivariate events. Let's consiaer
other grapnic devices, enlist the computer.
(3)Looking at complex biological systems: while
the organisms whose risk concerns us will almost
always be complex, whether as a human or as an
ecosystem, perhaps we can find other indicators
of the likely response. More work needs to be
put into examining and developing short term
assay surrogates for prediction.
In summary, in this paper, a narrowly defined
response addition
R(x1,x2,T) - XjFjCT) + x2F2(T) + E(x1,x2,T),
where E(x^,x2,T) » 0 for any x^, X2, T such that
Xj + X2 » 1, namely, the special case of linear
responses at fixed concentrations,, permits (l)the
construction of a test statistic and (2)the use
of short term data. Furthermore, it calls atten-
tion to the literature that uses both composition
and concentration to examine the behavior of
mixtures.
References
Gnanadesikan, R. 1977. Methods for Statistical
Data Analysis of Multivariate Observations. John
Wiley, New York.
Hamilton, M. A., and Hoel, D. G. 1980. Quantita-
tive methods for describing interactive effects
in toxicology. Technical Report No. 1-6-80,
Montana State University, Bozeman.
Table 1
FuzpoM provide risk e*tl*»te* elucidate Mchanlm*
rro» Joint exposure of Joint toxicity
Situation assume components ate aiauae components are
unknown; known;
predict curve at doae decide If joint action
not studied at dose studied
Method* procedure* robuit tests of full vs
need *taln*t aUapeclflca- reduced «odel«~
tlon
83
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STATISTICAL DIRECTIONS TO ASSESS EFFECTS OF COMBINED TOXICANTS
Ronald E. Wyzga, Electric Power Research Institute
ABSTRACT
tte papers presented at the ASA/EPA Conference
on Current Assessment of Combined Toxicant
Effects are discussed. The papers Illustrate the
existence of screening methodologies to Indicate
when "Interaction" between toxicants la likely.
This can help assess mixtures toxlclty for
mixtures of a small number of toxicants at dose
levels In the experimental range, but additional
methods need be developed when extrapolation from
one dose level to another Is required or when
more complex mixtures are assessed. The
conference provided some limited guidance on the
use of models for such cases, but greater
statistical efforts are needed.
KEYWORDS
Joint Action Models
Complex Mixtures
Combined Toxicant Effects
Interaction
1. INTRODUCTION
This paper attempts to summarize the jse of
statistics to address the toxicity of mixtures
and to suggest alternative statistical approaches
that might be taken to achieve further progress
in addressing the Issue. Emphasis is given to
the papers presented at this conference.
The toxicity of mixtures Is clearly an
Important subject. If there were only 100
potentially toxic agents, the possibility of
unusual or unexpected combined effects is hardly
trivial. Taking combinations of two agents at a
time, the matrix of combinations yield 4950
cells. If the probability of one agent
influencing the toxicity of another were even as
low as 0.01, there would still be 49 combinations
where the toxicity of the combined toxicants
would be different from the sum of the toxicity
of the Individual toxicants in assessing combined
toxicant effects. The real world of thousands of
agents and mixtures, far more complex than
binary, obviously has considerable potential for
a large number of "interactive" effects.
One of the problems in assessing combined
toxicant effects is that there is a whole range
of Issues to be resolved. Mixtures can be
defined at different levels of complexity. Much
of the research to date and of the research
reported here has been performed with binary
mixtures. This is probably due to two reasons.
First of all, as Kodell (1986) pointed out in his
introduction, the earliest work was performed
with drugs and pesticides, the objective being to
examine the effectiveness of one of these
substances in the presence of another. Hence
only simple combinations were studied. (The
simultaneous presence of environmental and other
agents was ignored or assumed to be unimportant.)
Secondly, binary substances are a conceptual
aid. The best approach for understanding a
mixture's toxicity profile is to consider simple
mixtures first. This can provide Insights on how
to analyM mot* complex mixtures, which realis-
tically reflect exposure. Environments are
complex; pur* mixtures do not exist. We do not
Inhale, Ingest or absorb pure substances or even
a handful of substances, but mixtures of numerous
substances. If, perchance, exposure were to be
pure, the purity would cease once the substances
entered the bloodstream. One potential approach
to assess mixture toxicity is to divide the
mixture into its components and to study these
singly and In combination to arrive somehow at an
estimate of the mixture's toxicity. Often,
however, the mixture is ill-defined; Its compo-
nents cannot be defined. In such circumstances,
one can only work with the total mixture and/or
its fractions. Binary experiments are still
possible, but assu-ne a different role here as the
experimental agents Tiay be mixtures themselves.
Time complicates the definition of a mixture.
Mixtures and exposures thereto can vary con-
siderably over time, and this variation can
Influence the mixture's toxicity. Thorsland and
Charnley (1986) show the temporal Importance of
cigarette smoking in a mixture with another
carcinogen. In reality, human exposure patterns
are even more complex, and it will be necessary
to estimate and characterize this time
variability and to determine its influence.
2. OBJECTIVES OF RESEARCH
Another problem associated with current
toxicity assessment approaches is that many
questions are asked of mixtures, and different
approaches are appropriate for different
questions. The questions will dictate the
research objectives and corresponding statistical
tools. .
The most commonly asked questions probably
relate to the three given below.
1. Under ambient conditions, is the mixture
hazardous?
a. Is interaction likely to occur? How is
it defined?
b. What is the dose-response surface for
the mixture?
2. How toxic is the mixture compared to other
mixtures? Other substances? Are similar
mixtures equally toxic?
3. What is (are) the toxic component(s) of
the mixture?
The papers at this conference address the
first question with most of them focusing on
question la, although the specific questions
addressed are variations of the question.
Several such as Weber et al. (1986) ask whether a
given joint action model fits a data set.
Machado (1986) and Chen et al. (1986) explicitly
ask question la as to whether interaction and
dose additivlty exist. Other papers examine the
presence of interaction over a broader range of
dose-exposure levels and hence try to describe a
dose-response surface. Thorsland and Charnley
84
-------
(1986) address tht toxicity of mixtures over dose
ranges where extrapolation Models er« required.
Chrlstensen (1986) considers the Issue but his
objective Is different. Very low doses (and
hence extrapolation) are of lesser concern for
fish than for humans, where risks to Individuals
of 10 or IMS ere of policy concern.
The collection of papers suggests that
question la can be answered Cor simple mixtures
of two to three substances. A response to this
question for more complex sdxtures Is hampered by
vnwleldy experimental designs and unrealistic
data requirements. This situation can be alle-
viated somewhat by frsctlonal factorial designs
although these were not explicitly discussed at
the conference. Question la Is Important for
screening purposes; answers to it can suggest
where "interaction" is likely to be present. A
caution, however, Is that the presence or absence
of "Interaction" at one set of dose levels need
not generally"imply the same result for other
dose levels. Thorsland and Charnley (1986), for
example, show that conclusions derived at "high"
dose levels may not be equally true at "low" dose
levels. Experimental results suggest this as
well. In a series of fire toxicology experi-
ments, tevin and coworkers (1986) demonstrate a
relatively complex "interactive" effect of CO and
CO, on the mortality of rats. Over a part of the
dose range, mortality response appears to
increase with increasing 2 concentrations for a
fixed CO level. The very opposite appears to
occur at other CO levels. Hence, a conclusion
based on experiments over a limited dose range
could not be generalized correctly.
Most of the historical terminology problems so
well described by Kodell (1986) relate to
question la because definitions of "Interaction"
were tied to specific models. As we progress
beyond this screening question towards
questions Ib, 2, and 3, much of this confusion
will be resolved.
3. GENERAL PROBLEMS IN ASSESSING
MIXTURE TOXICITY
3.1 Information Availability
The nature of available information will
obviously Influence the approach for addressing
the mixture's toxiclty. Most of the conference
papers assumed that it was possible to identify
the components of the mixture. If the components
are'unknown, the approaches discussed here must
be modified or replaced. This will be discussed
in the next section.
3.2 Pharmacokinetlcs
Another important information question is that
of pharmacokinetics. This issue was addressed by
Feder (1986) in his discussion of Thorsland and
Charnley (1986) and to a lesser extent by Weber
et al. (1986) and others who undertook some
studies of specific organ systems In an effort to
achieve "better" model fits. Obviously,
responses to a dose can be more accurately
estimated If the dose Is that at the site of
biologic activity. Unfortunately, the "effective
dose" often Is not known and the "administered
dose" la used In estimating the dose-response
relationship. This Is obviously less than
optimal In the case of a simple toxic, but the
situation becomes even more complex in the case
of a mixture. For example, misinterpretation
could arise If the relative composition of the
mixture ware to change aa a result of chemical
Interactions or of differential absorption,
distribution, metabolism, or elimination, which
varied with dose or some other factor independent
of the mixture. Current pharmacoklnetlc models
attempt to describe the fate of a single chemical
and do not treat complexities that mixtures can
introduce. Such complexities can distort the
estimated dose of a mixture at target sites,
where toxicity effects are Initiated. Pharma-
coklnetic assumptions about compositional changes
in the mixture would also have to hold across all
species involved in any extrapolation across
species, otherwise the validity of such extrapo-
lation would be in question. Given the
importance of this issue, more attention to
phannacokinetics is clearly warranted in
assessing the toxicity of mixtures. The develop-
ment of both pharaacolcinetic data and models for
mixtures is needed.
4. EMPHASIS ON COMPONENTS
The papers at the conference considered
synthetic approaches in which a mixture was
constructed from limited (two or three) compo-
nents. As indicated above, this emphasis
requires that the mixture be simple and well-
characterized. These requirements, particularly
the former, are not always realistic. At issue
is whether and how existing methods can be
adapted to more complex and realistic situations.
The complexity issue can be addressed by
extending the methods used to several variables
beyond the two or three considered. In this
regard, some of the methods are more amenable
than others. Those methods that depend upon
experimental designs are hampered by practical
considerations. Toxicology experiments can
rarely accept more than a limited number of
combinations of substances, otherwise, they
become too costly and uniform experimental
conditions for all combinations become difficult
to maintain.
Simple factorial designs clearly limit
consideration of mixtures more complex than three
or four substances, but fractional factorial
designs can extend the complexity of mixtures
studies considerably. For example, designs for a
mixture of 15 components could be constructed
which required only 52 treatment groups (for
combinations of doses), vet would still allow
estimation of the toxicity of all IS substances
singly and of pairs of six of the substances. A
simple factorial design for this mixture would
require 32,768 treatment groups.
Another approach to assessing the toxicity of
more complex mixtures is given by Thorsland and
Charnley (1986), namely, the use of a model to
estimate toxicity. Their results suggest that
for their model, toxicity at "low" doses is
additive across components in the mixture, I.e.,
"interaction" effects become negligibly smaller
as the dose level decreases. Under these
85
-------
results, mixtures of sevaral known components can
be eaaily addressed toy Adding the toxicity of the
components-. This requires, however, that the
toxicity of the components be known.
When toe components of * mixture are unknown,
two approaches are possible. A mixture with
SLoSn co-potent, can be fraction. ted Into
•utually exclusive «lxturaa; tha resulting
mixture, than can be analysed aa If thay ware
single aub.tances to estimate any "Intaractlon"
of tha raaulting mixtures. Such an approach has
bean considered to address the toxicity of
unleaded gasoline, a very complex mixture whose
constituents are not completely specified.
(?ader at al. 1984).
Whan the components of the mixture are not
known, a second approach Is to study the mixture
directly as has been done with cigarette snoke.
If the mixture toxicity is of interest, it may
not matter whether or not there la Interaction
among the mixture's components. The toxicity
cou^d be assessed for several mixtures in the
same class (e.g., different brands of cigarettes,
vapors from different gasolines or exhaust fumes
from different diesel engines) to determine If
the toxicity is relatively robust across the
class of mixtures. Feder et al. (1984) discuss
this approach as well.
Extrapolation of toxicity from high to low
doses could Introduce a problem with the latter
approach. Extrapolation models have been dev-
eloped for single substances, and their appli-
cation to a mixture could cause problems.
Consider the example given by Thorsland and
Charnley (1986). They give In Table 1 a bioassay
design which gives an Interaction tens large
enough to double the risk over that predicted by
additlvlty at low doses. Under that design, for
x at a level of 1.05415 x 10° the risk is about
iSc 10"5. For x, at 2.10828 x 10'3, the risk Is
also about 1 x 10'5. Under an additive model,
the risk of a mixture of xx and x2 would be
2 x 10 , whereas the true model gives the risk
"
,
of 4 x 10" • Now if only a mixture of
an
-------
where 0^ Is the true carclnogenlclty of the
mixture, e« Is some error associated with the
•aaaur* of 7i such as the error due to
extrapolating from rat* to humans or the error
aaaociatad with • abort-term test. The f could
b* a vector of the toxlcltle* of the major
components of gasoline and X^ Is the vector of
concentrations of the components. For example,
f(XifH) - X.B, the model could be Interpreted as
an additive model under which the toxicity of the
mixture Is the sum of the toxicitles of Its
constituents. In this case, 6^ is a measure of
Interactions among the mixture constituents.
Given prior distributions on 6j, e^, and B, one
can estimate the posterior distribution of the
mixture toxicity given the data y. One can
extend the context here by defining £, such that
y. « 0^ + ej, where 8£ represents another mixture
for which no observed data are available. Other
extensions are possible. See Harris (1983) and
DuMouchel and Harris (1983).
6. CONCLUSIONS
The papers at this conference suggest that
statistics to date has concentrated upon the
problem of whether "Interaction" exists and how
it can be characterized. In this area, we have
made considerable progress. We now have valuable
screening tools that indicate when interactions
may be important. Now, we need to ask more
specific questions such as how Important the
interactions are at doses that nay be different
from those in the experiments where "interaction"
is measured. Interpolation and extrapolation are
required. These are roles for models that
attempt to describe quantitatively the complex
biology or toxicology of mixtures.
Models provide a means to describe and
summarize experimental results and to relate them
to underlying biology, but models for mixtures
are In their Infancy. A research priority Is the
development of improved models to address mixture
toxicity. Thorsland and Charnley (1986) provide
an important example of the direction that such
models can take.
Models are imperfect tools. As such, they
have limits. At best, they reflect the limits of
biological knowledge. Models also delve into the
unknown and unknowable when addressing such
issues as high-to-low dose extrapolation. In
these areas, models may be the only available
tool, but their results are subject to consider-
able uncertainty, a greater uncertainty than they
may Imply. The limits and uncertainties of
models need to be stated aa part of their use.
In reality, modeling efforts often lag behind
biological developments. Hence, one way to
improve models is to achieve greater under-
standing of biological mechanisms. Biological
Intuition also can help direct modeling and
statistical approaches. Ueber et al. (1985), for
example, help identify greater needs by following
their Intuition to illustrate the poor behavior
of xinc-nickel interactions in the context of
simple models.
Models and statistics support the major
strategies to assess mixture toxicity, but models
and statistics are only ana criterion for
development of strategies. Pragmatism and
biology are foremost considerations. Pragmati-
cally, it Is not possible to test every combi-
nation of substances In every mixture. The
challenge before us is to uae statistics to move
•way from this approach towards on* that Is
consistent with biology.
INFERENCES •
BRODERIUS, STEVEN 3. (1986), "Joint Aquatic
Toxicity of Chemical Mixtures and Structure-
Toxicity Relationships," presented at the
ASA/EPA Conference on Current Assessment of
Combined Toxicant Effects, May 5-6, 1986,
Washington, D.C.
CHEN, JA.1ES J. , HEFLICH, ROBERT N. , and HAS3,
BRUCE S., (1986), "A Response-Additive Model
for Assessing the Joint Action of fixtures,"
presented at the ASA/EPA Conference on Current
Assessment of Combined Toxicant Effects,
May 5-6, 1986, Washington, D.C.
CHRISTENSEN, ERIK R. (1986), "Development of
Models for Combined Toxicant Effects,"
presented at the ASA/EPA Conference on Current
Assessment of Combined Toxicant Effects,
May 5-6, 1986, Washington, D.C.
DUMOUCHEL, WILLIAM H., and HARRIS, JEFFREY £.
(1983), "Bayes Methods for Combining the
Results of .Cancer Studies in Humans and Other
Species," Journal of the American Statistical
Association, 78, 293-315.
?EDER, PAUL J. (1986), Discussant's comments on
paper by Thorsland and Charnley, presented to
ASA/EPA Conference on Current Assessment of
Combined Toxicant Effects, May 5-6, 1986,
Washington, D.C.
FEDER, PAUL J., MARGOSCHES, Elizabeth, and
BAILAR, John. (f984), "A Strategy for
Evaluating the Toxicity of Chemical Mixtures,"
Draft Report to U.S. Environmental Protection
Agency, EPA Contract No. 68-01-6721,
Washington, D.C.
HARRIS, JEFFREY E. (1983), "Diesel Emissions and
Lung Cancer," Risk Analysis, 3, 83-100 and
139-U6.
KODELL, RALPH L. (1986), "Modeling the Joint
Action of Toxicants: Basic Concepts and
Approaches," presented at the ASA/EPA
Conference on Current Assessment of Combined
Toxicant Effects, May 5-6, 1986,
Washington, D.C.
LEVIN, BARBARA C., PAABO, M., GUERMAN, T. L.,
HARRIS, S. E., and BRAUN, E. (1986), "Evidence
of Toxlcologlcal Synerglsm Between Carbon
Monoxide and Carbon Dioxide," submitted for
publication.
MACRADO, STELLA G. (1986), "Assessment of
Interaction in Long-Term Experiments,"
presented at the ASA/EPA Conference on Current
87
-------
Assessaent of Combined Toxicant Effects,
Nay 5-6, Washington, D.C.
SIEMIATtCKI, J. and THOMAS, D.C. (1981),
"Biological Models and Statistical
Interactions: An Example frosj Multistage
Carcinogens,* latematlonal Journal of
Epidemiology, 10, 383-387.
TBORSLAHD, TODD V. and CHARNLET, GAIL. (1986),
"Use of the Multistage Model to Predict the
Carcinogenic Response Associated with Tl»e-
Dependent Exposures to Multiple Agents,"
presented at the ASA/EPA Conference on
CurrentAsacsaaent of Combined Toxicant Effects,
May 5-6, Washington, D.C.
WEBER, LEVERM J., MDSKA, CARL, YINGER, ELIZABETH
rOIKMEISTER, aad SHELTON, DENNIS. (1986),
"Concentration aad Response Addition of
Mixtures of Toxicants Dslng Lethality, Growth,
and Organ Syste* Stadias," presented at the
ASA/EPA Conference on Current Assessaent of
Combined Toxicant Effects, May 5-6, 1986,
Washington, D.C.
88
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A: ASA/EPA Conference on Current Assessment of Combined Toxicant Effects Program
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APPENDIX B: Conference Participants
ASA/EPA Conference on
The Current Assessment of Combined Toxicant Effects
May 5-6, 1986
Washington, D. C.
John C. Bailar
468 N Street, S. W.
Washington, D. C. 20A60
R. Clifton Bailey
WH 586, EPA
401 M Street, S. W.
Washington, D. C. 20460
Steven P. Bayard
CAG RD-689'
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C. 20460
Jeff Beaubier
TS-798, EED, OTS
USEPA
401 M Street, S. W.
Washington, D. C. 20460
Judith S. Bellin
ORB RD 681
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C. 20460
Hiranmay Biswas
WH-553
7702 Middle Valley Drive
Springfield, Virginia 22153
Steven J. Broderius
Energy Research Laboratory
Environmental Protection Agency
Duluth, Minnesota 55804
Mary J. Camp
USDA
5800 Eastpine Drive
Riverdale, Maryland 20737
Richard A. Carchman
Medical College of Virginia
Box 613
Richmond, Virginia 23298
Joseph S. Carra
Environmental Protection Agency
401 M Street, S.W. TS298
Washington, D. C. 20460
Hans Carter
Medical College of Virginia
Box 32, MCV Station
Richmond, Virginia 23298
Eric Y. Chai
Shell Development Co.
PO Box 1380
Houston, Texas 772251
Chao W. Chen
Carcinogen Assessment Group
Environmental Protection Agency
2313'Falling Creek Road
Silver Spring, Maryland 20904
James J. Chen
Biometry Division
National Center for
Toxicological Research
Jefferson, Arkansas 72079
Jean Chesson
Battelle Washington Operations
2030 M Street, N. W., Suite 800
Washington, D. C. 20036
Eric Christensen
Department of Civil Engineering
University of Wisconsin
Milwaukee, Wisconsin 53201
Vincent James Cogliano
ORD, OHEA, CAG
Environmental Protection Agency
401 M Street, S. W.
•Washington, D. C. 20460
James M. Daley
PM223
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C. 20460
Kurt Enslein
President
Health Designs, Inc.
183 Main Street
East Rochester, New York 14604
91
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'i.V.C./H'i.'djil:
»
.:.
Linda S. Erdrelch
OHEA-ECAO (ORD)
26 West St. Glair Street
Cincinnati, Ohio 45268
Thomas R. Fears
National Cancer Institute
7910 Woodmont Avenue
Landov Building, Km. 3B04
Bethesda, Maryland 20892
Paul I. Feder
Battelle Columbus Laboratories
Applied Statistics and
Computer Application Section
505 King Avenue, Room 11-9082
Columbus, Ohio ^3201
Bernice T. Fisher
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C. 20460
Mary J. Frankenberry
TS-798
Environmental Protection Agency
401 M Street, S.W.
Washington, D. C. 20460
Paul H. Friedman
OSW - WH-562B
Environmental Protection Agency
401 H Street, S. W.
Washington, D. C. 20460
David Gosslee
Statistical Group Leader
Math. & Statistical Research
Martin Marietta Energy Systems
Building 9207A - PO Box Y
Oak Ridge, Tennessee 37830
G. Jay Graepel
E. I. du Pont de Nemours & Co.
Haskell Laboratory
PO Box 50 - Elkton Road
Newark, Delaware 19714
Gary Forrest Grindstaff
E329 (JS-798), 401 M Street, S. W.
Environmental Protection Agency
Washington, D. C. 20460
James Leonard Hansen
TJnion Carbide Corporation
PO Box 8361, 770-203A
South Charleston, West Virginia 25526
92
Richard C* Hertzberg
Environmental Criteria and
Assessment Office
Environmental Protection Agency
Cincinnati, Ohio 45268
Joseph F. Heyse
Merck Sharp & Dohme Res. Labs
WP16-100
West Point, Pennsylvania 19486
Stephanie Irene
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C. 20460
W. Barnes Johnson
Stat. ?ol. Branch, PM 222, USEPA
401 M Street, S. W.
Washington, D. C. 20460
Henry D. Kahn, Chief
Statistics-Section - WH 586
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C. 20460
Ralph L. Kodell
Division of Biometry
National Center for
Toxicological Research
Jefferson, Arkansas /2079
Aparna M. Koppikar
CAG/OHEA/ORD RD689
401 M Street, S. W.
Washington, D. C. 20460
Daniel R. Krewski
Chief, Biostatistics &
Computer Applications
Environmental Health Directorate
Health & Welfare Canada
Ottawa, Ontario K1A OL2
CANADA
Herbert Lacayo, Jr.
PO Box 15521
Arlington, Virginia 22215
Emanuel Landau
Staff Epidemiologist
American Public Health Association
1015 15th Street, N. W.
Washington, D. C. 20005
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Barbara A. Leczynski
Battelle Washington Operations
2030 M Street, N. W.
Washington, D. C. 20036
Walter S. Liggett, Jr.
National Bureau of Standards
Gaithersburg, Maryland 20899
Bertram D. Litt
Office of Pesticides
Environmental Protection Agency
TS-769C2
1921 Jefferson Davis Highway
Arlington, Virginia 22201
Stella G. Machado
Radiation Epidemiology Branch
National Cancer Institute, NIH
LAN 3A22
Bethesda, Maryland 20205
Sam Marcus
National Center for Health Statistics
13417 Keating Street
Rockville, Maryland 20853
Elizabeth H. Margosches
Office of Toxic Substances
Environmental Protection Agency
TS-798
401 M Street, S. W.
Washington, D. C. 20460
Margaret McCarthy
Div. of Public Health
University of Massachusetts
Atnherst, Massachusetts 01003
Bruce Means
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C. 20460
Suresh Moolgavkar
Fred Hutchinson Cancer Research Ctr.
1124 Columbia St.
Seattle, Washington 98104
Paul D. Mowery
SCI Data Systems
530 College Parkway, Suite N
Annapolis, Maryland 21401
Cornelius J. Nelson
OTS/EED/DDB
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C. 20460
Jerry'L. Oglesby
SCI Data Systems
530 College Parkway, Suite N
Annapolis, Maryland 21401
G. P. Patil
Center for Statistical Ecology
and Environmental Statistics
Pennsylvania State University
University Park, Pennsylvania 168C2
Reva Rubenstein
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C. 20460
Frederick H. Rueter
Consad Research Corporation
121 North Highland Avenue
Pittsburgh, PA 15206
Michael Samuhel
Battelle Washington Operations
2030 M Street, N. W. , Suite 800
Washington, D. C. 20036
Jitendra Saxena
Environmental Protection Agency
(WH 550)
401 M Street, S. W.
Washington, D. C. 20460
Cheryl Siegel Scott
TS-798
Environmental Protection Agency
401 M Street, S.W.
Washington, D. C. 20460
Robert L. Sielken
Sielken, Inc.
3833 Texas Avenue
Bryan, Texas 77802
Janet Springer
FDA
11204 Schuylkill Road
Rockville, Maryland 20852
93
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^-^^'^^^^^
Ms. Judy A. Stober
Health Effects Research Lab.
26 West St. Clair Street
Cincinnati, Ohio 45268
David J. Svendsgaard
Biometry Div./HERL MD55
Environmental Protection Agency
Research Triangle Park, NC 27711
Todd W. Thorslund
ICF Clement Associates
1515 Wilson Boulevard
Arlington, Virginia 22209
Lavern J. Weber
Oregon State University
Mark 0. Hatfield
Marine Science Center
2030 South Marine Science Drive
Newport, Oregon 97365-5296
Dorothy Wellington
6402 Middleburg Lane
Bethesda, Maryland 20817
Ronald E. Wyzga
Electric Potter Research Institute
P.O. Box 10412
3412 Hillview Avenue
Palo Alto, California 94303
Grace Yang
Department of Mathematics
University of Maryland
College Park, Maryland 20742
Mr. Robert P. Zisa
Office of Compliance Monitoring EN-342
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C. 20460
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