United States
          Environmental Protection
           Office of Policy, Planning
           and Evaluation
           Washington, DC 20460
          Statistical Policy
ASA/EPA Conferences on
Interpretation of
Environmental Data
          I. Current Assessment of
          Combined Toxicant Effects
          May 5-6, 1986


This document has not undergone final review within EPA and should not
be used to infer EPA approval of the views expressed.

        Statistical Policy
ASA/EPA Conferences on
Interpretation of
Environmental Data
        I. Current Assessment of
        Combined Toxicant Effects
        May 5-6, 1986


    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

    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

                          INDEX OF AUTHORS

ANDERSON, Perry  	  30    LITT,  Bertram D	  44
BRODERIUS, Steven J	  45    MACHADO,  S.6	  22
CHARNLEY, Gail  	......   9    MARGOSCHES,  Elizabeth H	  83
CHEN, Chao  	  28    MUSKA, Carl   	  30
CHEN, J.J	  78    PATIL, G.P	  63
CHRISTENSEN, Erik R	  66    S HELTON,  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

                  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 I. 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
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.  CHRISTENSEN,
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

                       Ralph L. Kodell, National Center for lexicological  Research
   The  problem  of  modeling the  joint  action of
drugs  and  environmental  toxicants  has  seen  a
resurgence  of  interest  recently,  due to  a
heightened awareness of  the need to  protect
health and   environment,  and  the  attendant
regulatory  considerations.    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 et  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).   Host  current efforts  to study
this  type  of  joint  action  are  based   on  the
seminal work  of   practitioners  such as Bliss
(1939), Gaddum  (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   "synergistic"   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
bioatatistics, pharmacology,  toxicology  and

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
describe the  same phenomenon and  the  same  term
means different things to different authors."
   While  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
"nonlnteractive"  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 and nomenclature associated
         with the broad classifications of non-
         interactive and interactive joint action.

Concentration     Response      Response
                    Addition      Multiplication
Similar Action
              Interactive Action


   Enhancemen t




and  toxlcologist,   the  concept  of  addition  or
"additivity" can imply something  about either the
doses (concentrations) or  the responses (effects)
of   toxicants   acting   together.     To   the
biostatlstician, 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

 TABLE 2.  Concepts of noninteractive joint action,
          categorized by scientific disciplines  in
          which they are used.  Cell entries
          represent terms or notions within each
          discipline that are commonly used to
          describe the concepts of noninteraction.
          An empty cell implies that the discipline
          does not embrace the concept.

Additivity  Summation
            Additivity   Multipli-

 Simple     Uncondi-    Conditional
 Similar     tlonal     Independence
 Action   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

 Null Models for Noninteractive Joint Action
    The  primary focus  of  this paper  will be  on
 null  models  of  concentration  and  response
 additivity as applied  in a pharmacological /
 toxlcological  context.  These models and  concepts
 will 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  the1 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),   Finney  (1952, 1971),  Hewlett  and
 Plackett  (1950,  1959),  Placlcett  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  Placlcett
 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 joint action are based either
on  concentration  addition  or  on response
addition, or at least  they include these types of
joint action as special cases.  Among  the authors
who have adopted  the  concept  of  concentration
addition in modeling noninteractive joint action
are  Smyth et  al.  (1969),  Casarett  and  Doull
(1975),  Piserchla  and Shah (1976), Berenbaum
(1977),  Eby  (1981),  and  Unkelbaeh 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 Hachado and  Bailey  (1985).
Authors  who  have modeled  on the basis  of both
concentration addition  and  response addition
Include  Broderius and  Smith (1979),  Shelton and
Weber (1981), Chou and Talalay (1983), Kodell and
Pounds (1985), Christensen  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-addltion"   and  "hetero-addition"  to
describe  a   broad  concept  of  concentration
addition  and a  narrow  concept of response
addition, respectively.  Steel and Peckman  (1979)
introduced  the  notion  of  an  "envelope  of
additivity" that  is bounded by Loewe's  iso- and

   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),  Finney (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
(Finney,  1971; Hewlett and Plackett,  1959).
   Let  P(d;f) denote the  probability  of  a toxic
response   to  concentration  d.  of   toxicant   i
(1-1,2)  such that

  for some monotonic functions F, (i-1,2).  If one
  toxicant is  a  dilution of  the  other,  then d.  
  pd, , where p is the relative potency of toxicant
  2   to toxicant 1.   The probability of a toxic
  response  to  the  combination of  d.  and  d_,
  assuming concentration addition, is

           p^+dj)   -  r1(dl-pd2)

                     -  F2(d1/p+d2)  .

     The  pharmacological approach to  assessing
  concentration additivity has been  through the use
  of isobolograms (Hewlett,  1969), which are plots
  of  pairs  of  doses  of the two  toxicants  that
  jointly give fixed levels of toxic response.  The
  curve that  represents  a given constant response
  is called an isobole (Figure 2).   Under  the broad
  definition  of  additivity, these isoboles  are
  straight  lines,  but  they  are not  necessarily
  parallel.    Under the narrow  definition  of
  concentration additivity, with perfect positive
  correlation   of  tolerances,  these isoboles  are
  parallel straight lines with  slope equal  to the
  negative of  the relative potency.
     The biostatistical approach to assessing con-
  centration additivity  has involved the fitting of
  dose-response models.   As a simple illustration,
  consider  the   parallel line  assay  technique
  whereby  a  suitable  linearizing  transformation

  (e.g., probit), F ~ (d.) - a4+8  18 d., ls "**
  (Finney, 1971).   Setting   ^  - B2  yi*W P   "
  exp[(a,-a.)/B ].   Another  simple method  is  the
  slope ratio  assay technique  whereby   F.  (d.) 
-  a i + B^, Oj, - o2 and 'p   82/B1.-JThe Joint
  response to  d.  and  d.  is  predicted  using either
  F, or F, with estimated parameter  values, and the
  goodness-of-fit of the model is assessed (Kodell
  and  Pounds,  198S).    Often  models  of greater
/ complexity have been used (Hewlett and Plackett,
  1959; Christensen and  Chen,  1985).
  Response Additivity
     As above, some of the principles and concepts
  that  underlie  response  addition  will  be given
  prior   to   presenting  a  formal  mathematical
  definition.    Under  the  broad  category  of
  independent 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)  expressed
  the principle that  the  toxicants  have  different
  sites  of  action.   Hewlett and  Plackett  (1959)
  modeled biological independence without assuming
  statistical  independence.    That   is,   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,"  assuming
  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, 1939;
  Finney, 1971;  Ashford and Cobby, 1974).
   With  P(d ) as defined above,  the probability
of  a  joint  toxic  response,  assuming  response
additivity, is

         P(d1+d2)  -  P(dj)  + [!-P(d1)]P(d2)

                   -  P(d2)  + [!-P(d2)JP(d1)  .

That is, the response to the second toxicant  over
and above  that of  the  first is simply an added
effect based on the proportion not  responding  to
the first toxicant ,  and vice versa.   Note  that
                            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(dj)*P(d2), will not greatly
influence  the  joint  response.    However,  some
authors have just added responses,  without  regard
to their magnitude (Holtzman t al. , 1979;  Ozanne
and  Mathleu,  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
   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.+d2)  as

       +         "         ''  for  suitably
chosen F.  (e.g.,  Kodell  and  Pounds,  1985).

P(dj+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
   The  setting  of water quality  standards  for
multiple   contaminants  is  an  example of  an
activity that requires  either knowledge  of  or
assumptions  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 toxlcity
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 carcinogens, the  individual  risks

might be added.  The  Committee  stated  that this
approach  assumes   that interactions  are  not
present and that the  risks are small  enough so
that adjustments for joint probabilities are not
   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+d,, of  toxicants  1 and  2  under

concentration  additlvity,  then  d1  and  d,  must
satisfy (Finney, 1971)

                   dl     d2
                     +  <   1  .
where ir. and IT. are the respective proportions of
toxicants 1 and 2 in the mixture.  Under response
additivity, if R is an acceptable level of risk
for a combination,  d.+dj, of  toxicants  1  and 2,

then d.  cannot pose an individual risk exceeding
RI  and  d,  cannot pose  an individual  risk

exceeding R,, where Rj+Rj^R.
    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 - exp[-X2d2]  .

With a double logarithmic linearizing  transforma-
tion,  parallel  lines with slope- 1 are  obtained,
enabling  estimation  of  X , A.  and the  relative

potency,  p  -  Xj/X., where dj-djp     Thus, under

an  assumed concentration-additive Joint  response,
                   - exp[-X1(d1+Pd2)]
                           ^ - X2d2]  ,

 However,  assuming  a  response-additive joint

 P (d+d) - FW) + F(d) -  F(d)*F(d)
- 1 -
                           + 1  - exp[-X2d2] - 1
              - exp[-X1d1 -
   Thus the assumption of either  concentration or
response additlvity  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 as the dose approaches zero.

   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  from an earlier
paper  (Plackett  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 similar
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  additlvity has
suffered  from inconsistent  nomenclature,  as
pointed out by Hewlett  (1969).    Interestingly,
Hewlett (1969) reserved  the  term  synerglsm 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  iaobolographic   representations  of
interactive  Joint action.
    With  respect  to   attempting   to   refine
characterizations  of joint  interactive  effects,
Loewe  (1957)  seemed  critical  of  the  role  that
biostatlstics  has played in this effort.   He was
probably correct,  to the  extent  that  he was
saying  that  tolerance  distribution  models  that
depend   on  quantal  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 (Rothman,  1976;  Hogan et  al..  1976).
However,  it corresponds also  to  a  model  of
mutually exclusive (and  therefore  nonindependent)
events  (Kodell and  Gaylor,  1986).   Under  the
additive  model of  relative  risk,  the  relative
risk due  to  two agents  in combination  is simply
the sum of their individual relative risks.  More
specifically,  RR^ -  V&1  +  RR2  -   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 baaed on
a  model  of   "conditional"  independence  in  a
statistical    sense,   for   an   event   space
appropriately defined (Kodell and Gaylor, 1986),
having arisen  originally from the multiplication
of attributable risks (Walter,  1976; Walter  and
Holford,  1978).   As its name 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..  " &R.  *  RR,.   Departures
from -this model are termed either synergistic or
   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), Hamilton  (1982)
and Reif (1984),  the latter three  being concerned
specifically  with  joint  carcinogenic  risk.
Notably, Hamilton  and Hoel (1978) have considered
concentration  additlvity,  response  additivity,
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 nonidentifiability 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 nonidentifiability aspects
of  his  postulated  multistage model  for  joint
carcinogenic!ty.   It should  be noted  that  apart
from      theoretical     considerations     of
nonidentifiability,  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

   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 is
also   a  great   deal   of   inconsistency  and
disagreement in nomenclature and  concepts.   It is
recommended that attempts  to assess  combined
toxicant effects  be  kept as simple as  possible,
in  light  of the  crude  data generally  available
for  such  assessments.   Investigators  should be
careful to  define their own terms precisely and
to  fully  understand  the  terminology  of others.
Terms   such  as   additivity,   independence,
synergism,  and antagonism  should  not   be used
loosely.  As has  been shown, departure  from one
type of additivity, say concentration additlvity,
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
         noninteractlve joint action.  The  shape
         of  the underlying dose-response curves
         governs the type of error that  might be
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                                       Joint Action Studies
                                           Type of Agent
Type of Effect
Type of Effect
                 I                        I
              Intended                 Adverse
                      Nature of Effect
  Adverse                 Intended
     I     Nature of Effect
            Therapeutic                 Toxic

mal S
ture Mix

fe Ss
ture Mix
ife Opt
ture Mix


Scientific Disciplines

Environment Toxicology
Bio statistics

     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., 50%).  For
          a simple dilution, isoboles for various response levels are parallel straight lines.
                                   Isobole  for
                                                Isobole  for
                           Isobole  for
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.

                                 RESPONSE ASSOCIATED WITH TIME-DEPENDENT
                                       EXPOSURES TO MULTIPLE AGENTS

                      Todd W. Thorslund and  Gail  Charnley,  ICF  Clement Associates
   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 significant increases in cancer risk are
observed in either epidemlological studies or
cancer bioassays.  For 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
(Yang  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-
xylase that metabolize  polycycllc  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 form 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 forma tion.of  the carcinogenic
   The nonlinearity of  the typical  chemical-
biological interaction  strongly suggests that
mechanisms of carcinogenicity that  depend 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

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 to the degree of exposure at the
molecular level.
   For constant exposure to a single agent, the
transformation rate from stage i to stage 1+1 may
be expressed as
     a.  background transformation rate,

     6. - 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 from the appearance of a cell in the
kth stage to death by a tumor, the age-specific,
agent-induced  cancer death rate [h(x,t)J is ex-
pressible as
h(x,t) -  n  (a
                           (t-w)fc  /(k-1)!,   (2)
     t  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 -/h(x,v)dv
     1-exp -  n  
     causing tumor is approximately constant and
     equal to the value w;

   o The probability that a given cell will cause
     a tumor death is very small;

   o An organ contains N cells of a specified
     type, each one of which is capable of caus-
     ing a tumor death;

   o N 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[dPk(t-w)/dt] -
and the probability of death from that tumor by
age t in the absence of competing risk is
              - exp -
                         h(v)dv .-
     I - exp - /* N[dPk(v-w)/dv]dv.
   To illustrate how equations 5 through S 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
   For continuous, constant exposures, the trans-
ition rates are constants (over time) that are
obtained from equation 5 by substituting Xj for
Xj(t).  Using this notation, the transition rates
have the form

     X(t) - X - * + J51 y S^Jtj,         (9)

and the possibility of a death from a tumor by
time t is

     P(x.. ,x,,...,x- ,t) - 1 - exp -
        12      m  k-1
                      n  Xi(t-w)K/k!         (10)

At low environmental levels of exposure,

     P(x1,x2,...,xm,t)  :
                              Xj] (t-wHk!,  (11)

k-1      k-l

i-0      i-0
               k-l  rk-l        -j  .

                2  Uiraij/tti f  2 sij pijxijl
               i'O  I 1*0        J 3*1
 since all  higher-order  exposure terms are 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  more cell types.   If two  agents affect dif-
 ferent cell types, their  effect on the produc-
 tion of tumors  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 that  joint exposure will produce
 a tumor is equal to the sum  of  the probabilities
 for each exposure.  When  the agents act on dif-
 ferent stages of the  same cell  type,  there is a
 multiplicative  exposure effect  term as well as
 the additive terms.
    At high doses,  the multiplicative  exposure
 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 to 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-
 gistic 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  i*-*1 and the second,  the jch
 stage and  no other transition rates are affected,
 it  follows that

               s2 - 0
s # J
Substituted into equation 5, this gives the
     Xj " aj + 8j2 X2

   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
   Consider a model of the form of equation 13
that has the following properties:

   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 92 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

P(x1,x2)-l-exp(-0.000005) (1+189,728x1)(l+94,864x2)

or                                           (14)

P (x^ x,) -1-exp- (0.000005+0.948640x1+0.474320x2


   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 99% 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.
                                                        Example of Interaction Effects when Multiple-
                                                        Agent Exposures are not Continuous and
                                                        Concurrent over Time

                                                           Variable and noncontiguous exposure patterns
                                                        may be accounted for by treating the time-
                                                        dependent exposures, xj (t) , as 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 :
                                x(t) -
                                x2(t) -

                                                                             82 < C < f2
     P(x1,x2)-l-exp-[A0(l+B1x1)(l+B2x2)],    (13)       where
                                s. - starting time of exposure to first

                                f. - stopping time of exposure to first

                                s~ " starting time of exposure to second
                                     agent, and

                                f - stopping time of exposure to second

                           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
                                                                                         t < s,
                                                             xo(t)   Voixi
                                                             X (t) - a   s - 1,2	k-2  0
For w  0,
equation 7

     h(t) -
           the age-specific rate defined in
   Since Pfc-i(t) is functionally dependent upon
si and fi and Xk-l(t) is functionally dependent
upon S2 and 2, it follows that h(t), as defined
in equation 16, is dependent upon the ordering
over time of si, f]_, 32, and f2-  For example,
if 31 < 32 < fP<    ,

           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.
           No  synergism (i.e.,  effect greater than one) ex-
           ists  if the  exposure that  affects the last stage
           ends  before  the exposure that affects the first
           stage begins.  Also, the greatest synergism ex-
           ists  when exposure that affects the first stage
(18)        ends  before  that which affects the last stage
           starts.  In  this situation, the relative risk
           rises slightly from 1 + 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
           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
           form  may be  very complex.
              In the final section, the  most important prac-
           tical problem concerning joint exposure will be
           investigated  namely, how to cope with the
           potential interaction of cigarette smoke and
           other carcinogenic agents.

           Joint Effect of Cigarette  Smoke and Other
           Agents on Respiratory Cancer
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 ca.n 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

                                                           As a first step in attempting to estimate how
                                                        smoking cigarettes modifies 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 Feto (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:
                       " A.
              o British cigarettes and/or smoking patterns
(20)             are different from those in the United
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) - /' {h[x.(v),x
                C (h[x1
addition, we assume that each individual in the
cohort began smoking at age si and continued un-
til the end of the observation period.  Also, we
assume a. constant lag or weighting time of length
w, which will be estimated from the data.  Under
these assumptions, the equations for the transi-
tion rates may be expressed as
                                   ,...,k-2  (22)
where the number of cigarettes smoked per day has
the functional form

           . *1             sl - C
             0              elsewhere.

   To incorporate a constant lag time of length
w, we simply replace t with t-w.  In addition, we
can only estimate the ratio of the transition
rates, which we denote with capital letters and
equivalent subscripts.  Using these two conven-
tions, the age-specific death rate from respira-
tory cancer may be written as
                 < t < s.+w

                          < t
   The parameters A,
                                  and w can be
estimated from the data in Table 3 using the max-
imum likelihood method.  To do so, it is assumed
that the observed number of respiratory cancer
deaths in each cell has a Foisson distribution
with mean h(x,t)PY, where PY is the total number
of person-years observed for each cell.  The
parameter estimates that maximize the likelihood
are shown in Table 4.  The goodness of fit of the
model is illustrated  in Table 5.  It is assumed
that for each cell, s^ equals 19.2, the average
age at which people started smoking for the en-
tire cohort.
   The parameters 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.
     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, if k < 3 or k > 7, the fit is 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
     X0(t) " aO
                                                        For the case where X2(t)  X2 for all t, the age-
                                                        specific rate under this added assumption has the
                                                                             [l+B02x2]  w < t < Sj + w
h(x.,x,,t) -
                                                                          .  ,

                                         B02 ' 602/(V
                                       To obtain information about the parameter B'o2>
                                    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

                                                          r    A      r   \ki
                                    Of course, only the whole term, (A/k)B-2(t-w) ,
                                    can be estimated 'from the quantal animal data
                                    alone; however, in conjunction with the human
                                    data, BQ2 may be estimated separately.
                                       The augmented risk associated with continuous
                                    exposure to X2 while smoking xj. cigarettes per
                                    day from age 3} to t under the assumption of no
                                    competing risk may be expressed as


                                       [l-exp-/Jh(xlj0,v)dv].                     (27)

                                    For a low background rate, the augmented risk is,
                                    to a close approximation,

   To illustrate the general approach, we shall
assume that the bioassay gave a linear term esti-
mate of


Substituting this value and w - 13.642, t - 70,
s " 19.2, and B^.i j_ - 0.31044 into equation 28
gives the numerical result
P(x2/x1,t-70)-0.2x2 }l+0.31044x
   Let us assume that without cigarette use the
predicted risk is 1'10~5 based only on the animal
bioassay.  This implies that x. equals 5-10~5.
Using equation 29, we calculate the augmented
risk associated with the second agent alone in
the presence of cigarette smoke for individuals
who started smoking at age 19.2 and continued
until death or age 70.  These results are de-
picted in Table 6.
   Thus, a person who smokes two 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 1-1Q-* if the individ-
ual smokes two. packs a day, when the voluntary
risk he or she assumes for smoking is about
I'lCT1 or three orders of magnitude higher.
   In summary, the approach suggested here to
adjust for cigarette use employs

   o Human data to- estimate the effects of ciga-

   o Animal 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

ARMITAGE, P.  1985.  Multistage models of car-
   cinogenesis.  Environ. Health Perspect.
ARMITAGE, P., and DOLL, R.  1954.  The age-
   distribution of cancer and a multistage theory
   of carcinogenesis.  Br. J. Cancer 8:1-12
   1974.  The occurrence of organohalides in
   chlorinated drinking water.  J. Am. Water
   Works Assoc. 66:703-706
CHEN, J.J., and KODELL, R.L.  1986.  Analyses of
   two-way chronic studies (Submitted for publi-
   MAN, R., ALVARES, A.P., and KAPPAS, A.  1977.
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CRUMP, K.S., and HOWE, R.B.  1984.  The multi-
   stage model with a time-dependent dose pat-
   tern:  Applications to carcinogenic risk as-
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DAY, N.E., and BROWN, C.C.  1980.  Multistage
   models and primary prevention of cancer.
   JNCI 64:977-989

DOLL, R., and PETO, R.  1978.  Cigarette smoking
   and bronchial carcinoma:  Dose and time rela-
   tionships among regular smokers and lifelong
   non-smokers.  J. Epidemiol.  Community Health

   TOLOKONTSEV, N.A., eds.  1979.  Quantitative
   Toxicology.  John Wiley & Sons, New York

HAMILTON, M.A.  1982.  Detection of interactive
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HAMILTON, M.A., and HOEL, D.G.  1979.  Detection
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   Unpublished manuscript

   1983.  Analysis of interactive effects between
   carcinogenic treatments in long-term animal
   experiments.  Unpublished manuscript
           REIF,  A.E.   1984.
              JNCI 73:25-39
                   Synergism in carcinogenesis.
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              ment Exam.  23:234-243

           SIEMIATYCKI, J., and THOMAS, D.C.   1981.   Bio-
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           THILLY, W.G.  1983.  Analysis of chemically in-
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              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.
           WONG,  L.C.K.,  WINSTON,  J.M., HONG,  C.B.  and
              PLOTNICK, H.  1982.   Carcinogetiicity  and tox-
              icity of 1,2-dibrdmoethane in the' rat.
              Toxicol. Appl.  Pharmacol. 63:155-165
           YANG,  n., TANNENBAUM, S.R., BUCHI,  G., and LEE,
              G.C.M.  1984.  4-Chloro-6-methoxyindole is  the
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              fava bean (Vicia fava).  Carcinogenesis

                            FIGURE  1

                                                               p,- ,(t)
      III	-\	1I
                         2            f2            fl
       NOTE:  X(o) is defined in equation 16 and P(  ,  in equation 17.
                              TABLE  1

                          BIOASSAY DESIGN
x-                   0     1.05414-10~5   4.8743-10~3      1-lfl"1
                             1-10"5           ~         9.0503-10"2
2.10828-10"5        110"5   4-10"5


2'IQ"1         9.0S03-10"2
"3                           9.852'IQ"1
NOTE:   This  is the design required to estimate  an  interaction
        term  large enough to  double the risk over  that predicted
        by  additivity at environmental levels of exposure.
        Underlining indicates a test group in the  hypothetical

                                                   TABLE  2
\  {hJ
                          -  h(0,0)Jdv4-|  {hlx^
                                                                  ,!)]  +h|0,x2(v)l  - 2h(0,0)jdv
                      Time  Interval
0  to t/2
                                      t/2 to  t
                                           '  X2(t)
                                               Form of  R*
0 xx
2 xx
0 0
x, 0
1 + A/2k
1 * A(i^r)
1 + A/2k
1 * $
1 * 3
1 * t
V& l
1 i
I""': ^ 1 _ U
^^^^ V
^*A i
                                                     TABU 3

                                  RUMRATOIIY CANCER DATA FROM TOLL AND PBTO  (1*71)
 Median Ae
                                                  Average exposure (Cigarettes  per Oy)--i1
                                                             XI. 3
42. J y*r old
  Ho. of cncti obMcrad           0.0      0.0      0.0      1.0      0.0      1.0      0.0      1.0      0.0
  Mo. of ptnon-ytari ob>*CTd   17,M<5  1.21C.O  2,041. S  3,795.5  4,124.0   7.04C.O  2,523.0  1,715.5    S92.5
47. S y**r* old
  No. of cancer* obitcvtd           0.0      0.0      0.0      1.0      1.0      1.0      2.0      2.0      0.0
  No. of ptron-ytr obcv*d   IS. 032. S  1.000.5  1,745.0  3,205.0  3,995.0   6.4S0.5  2,545.5  2,123.0   1,150.0
52.5 yr old
  No. of canetc* obut**d           1.0      0.0      0.0      2.0      4.0      (.0      3.0      3.0      3.0
  Ho. of p.ron-y..t obi.cv.d   12,22.0    053.5  1,5(2.5  2,727.0  3,271.5   5,513.0  2.C20.0  2,224.5   1,211.0
57.5 years old
  No. of cannr* ottrv*d           2.0      1.0      0.0     1.0      0.0      1.0      5.0      6.0      4.0
  No. of ptraon-ycara obatrvtd   1,905.5    2S.O  1,355.0  2,211.0  2,444.5   4,357.5  2,101.5  1,923.0   1,0(3.0
(2.5 yr old
  No. of canctr* obacrvtd           0.0      1.0      1.0      1.0      2.0     13.0      4.0     11.0      7.0
  No. of p*rion*yari obatrvvd   (,240.0    50).$  1,0(1.0  1,714.0  1,129.5   2,1(3.5  1,501.5  1,3(2.0    824.0
(7.5 yara old
  No. of canctra oburvcd           0.0      0.0      1.0      2.0      2.0     12.0      5.0      9.0      9.0
  No. of praon-y
                                       TABLE  4

Coefficient                                   Maximum  Likelihood  Estimate

A                                                        0.283404971489-10"10

B01                                                     0.575320316865

Bk-l,l                                                 0.310436883121

Lag  time  (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.
    43.5 .. old
     M. < womti okMiwd  0.0     0.0     0.0     l.i     0.0    1.0     o.o     l.l     t.o
     to. ot cnnn Of**!'***  0.190J7  0.044700  0.11017  0.1(171  O.illlO  1.1U1   1. 12111   0.41000  0.20M9

    41.1 yc> !
     to. ( wc.i. otoCM4            I.I     1.1     1.1    1.1     J.I     1.1     (.0
     to. 1 MMf> tlttlntt  .HM<  I.I71111  1.11411  I.4HH  1.174  1.1 til   1.1141   l.M  I.MHf
      to. l cwc.0 okMcn4  1.1     I.I     1. 1     1.1     4.1    .     1.1
      to. ( o4wc.ii nxiouo  o.iotM  *.iu  t.771

    il.l Iftfl old

      to. of cc.e. okMiv.<  0.0     0.0     1.0     1.1     1.0    11.0     S.I     t.o     0.0
      to. Of cuc.tl (KMlet^  1.0179   0.11707   1.0111   1.7110   4.1104  11.147   7. IMS   7.9UI  7.402*

    71.1 r*"> >U

      to.  e okMintl  1.0     1.0     1.0     4.0     4.0    10.0     7.0     1.0     S.O
      u>. .1 owmt. n^lM  O.lll  0.1M74   1.2071   l.OMO   4.01H  O.tMl   <.1I01   1.11K  9.9017
    77.$ y*c old

      Ho. of euer obMrv4  2.     t.9     .     .     5.0    1.0
      Ho. of e**c*< pcdict*d  t.i3  0.14771   1.41M   a.Ml   3.13M  4.7UJ
    MOTtt   C.ll. M.C. coll^Md . tbc th. ocdlet.d vlu. ! fc..k
          Ir..doo . 40 - 4  II.
                                       TABLE  6

                          FOR  VARIOUS  SMOKING  LEVELS
Cigarettes Smoked Augmented Risk
per Day on Associated with
Average Second Agent


 Paul  I.  Feder.  Battelle  Columbus  Division

    I  enjoyed  reading  the Thorslund  and  Charnley
 paper.   It  1s well written  and presents good
 methodology and useful applications.
    The main theme of  the paper 1s the description
 and estimation  of health risks associated with
 low dose environmental exposures  to multiple
 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  1s that  the presence or absence of
 empirically determined,  high dose Interactions
 observed In 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, It 1s necessary to
 understand  the  biological and chemical  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 components,
 thereby  altering the  effects of others.  Certain
 mixture  components may modify the pharmacoklnetlc
 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 pharmacoklnetlc considerations
 when they state "...For  the mathematical model  of
 the carcinogenic response...It 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
   Thorslund and Charnley generalize the
 multistage model to account for multiple 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 In 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
    Thorslund and Charnley state "... At high
 doses the multiplicative exposure effect term can
 dominate...and the Joint effect can be much
 greater than the sum of the Individual  effects.
 However, If 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 addltlvlty 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 addltlvlty,  the
 viewpoint above 1s somewhat of an overstatement.
 It discounts pharmacoklnetlc Interactions such as
 saturation of elimination or repair processes and
 1t Ignores the question of what constitutes a
 "low" dose.  Several examples will  be presented
 below In which the Thorslund and Charnley model
 1s predictive of Joint toxldty of a two
 component mixture at environmental  levels of
 exposure, but yet where component addltlvlty does
 not hold.  Thus,  the Thorslund and Charnley model
 1s not synonymous with component addltlvlty of
 r1sH~at low, environmental  exposure levels.

 Implications of the  Thorslund and Charnley Model
    The simplest example of the Thorslund and
 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)]
 At low environmental  exposure levels,  P(U,V)  can
 be approximated  as

 P(U,V)  *  A  + ABU + ACV + A8UCV
        5  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
 addltlvlty 1s  a reasonable assumption It Is
 necessary to determine  conditions under which Pll
 Is  small  relative to  P10,  P01.  The expressions
 for POO,P10,P01,P11,  Imply that

  Pll  P10P01/POO *  (P10/POO)P01
      * (P01/POO)P10.

 Thus Pll  Is 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,

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 term 1s small 1f Rll = R10R01 1.
   Therefore, what constitutes a "low" dose 1n
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
ep1dem1olog1cal examples that show the
relationship between joint effects and Individual
component effects at environmental levels of
exposure.  We Illustrate the predlctlveness or
lack thereof of the Thorslund and Charnley model
for these examples.

   1. Lung cancer associated with smoking
      (component 1) and uranium mining (component
POO - .57 x 10"4
POO + P10  5.87 X 10
POO + P01  2.27 x 10
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)7.57
       .57 + 5.3 + 1.7 + 15.81 - 23.38.
The observed value Is 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 1s predictive at the
environmental level of exposure but componentwise
addltlvlty does not hold there.

   2. Lung cancer associated with smoking
      (component 1) and asbestos work (component

   POO * 1.13 x 10"4     ,
   POO + P10 = 12.3 x 10"?      P10/POO  9.88
   POO + P01 - 5.84 X 10~*      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)71.13
           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 1s
predictive at the environmental level of exposure
but componentwise addltlvlty does not hold there.
                                                    3. Lung cancer associated with smoking
                                                       fcomponent 1) and asbestos mining
                                                       (component 2)
                                                 ROO = 1
                                                 ROO + RIO
                                                 ROO + Rol
                                                 The additional relative risk for smoking Is large
                                                 whereas that for asbestos mining 1s not.

                                                    R(U,V) - 1 + 11 + 0.6 + 6.6 - 19.2.

                                                 The observed value Is 19.0.  In this example the
                                                 component 1 additional relative risk 1s 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
                                                 addltlvlty does not hold there.

                                                    4. Abnormal sputum cytology associated with
                                                       smoking (component 1) and uranium mining
                                                       (component 2)
   POO -
   POO +
   POO +
P(U,V) -
                                                                 P10  -
                                                                 P01  -
                                                                 .04  +
.11           P10/P11 - 1.75
.08           P01/P11 - 1.0.
.07  + .04 + (.07)(.04)7.04
              The  observed  value Is .22.   In this example 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
              addltlvlty does  not  hold there.

                5.  Oral  cancer associated with smoking
                    (component 1)  and alcohol use (component 2)
                                                           ROO  -  1
                                                           ROO  +  RIO
                                                           ROO  +  R01
                                                        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 addltlvlty;  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
                                                           ROO =  R01
                                                        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

componentwise add1t1v1ty; 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

   1. The model predicts some observed component
      Interactions at environmental levels.

   2. The model does not predict all observed
      component Interactions at environmental

   3. Environmental exposure levels 1n a number
      of the examples were sufficiently high for
      the product term In the model's expression
      for risk to dominate.  Thus,  the Thorslund
      and Charnley model Is not synonymous with
      componentwise addltlvlty of risks at
      environmental exposure levels.

   4. What constitutes "low" levels of exposure
      and "high" levels of exposure for the
      purposes of the model Is 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 addltlvlty In the
      Thorslund and Charnley model.

   5. Irrespective of whether or not the model
      predicts component addltlvlty, 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.


   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 In the absence of
specialized mechanistic Information.  The model
does not always predict componentwise addltlvlty
at low, environmental levels of exposure.  It
predicts some, but not all, observed
environmental Interactions among mixture
   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 1s nol  The USEPA Mixtures Guidelines
(1985), page 11 state "...Even 1f a risk
assessment can be made using data on the mixture
of concern or a reasonably similar mixture, 1t
may be desirable to conduct a risk assessment
based on toxldty data on the components 1n 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 component 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 1n 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 In the .composite risk estimates at
differing levels of decomposition would Indicate
the presence of synerglstlc 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 1t


(1)   Re1f,  A.E., Synerglsm In Carc1nogenes1s,
      Journal  of the National Cancer Institute,
      Vol. 73,  No.  1,  1984, pp 25-39.

(2)   Thorslund,  T.W.  and Charnley,  6.,  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.

                      S. 6. Machado, Science Applications International Corporation
  This paper will address the problem of asses-
sing interaction between carcinogens or toxic
substances in long-term factorially 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 mammary 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
  In the statistical and epldemlological 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
  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
noninteractive 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.


  The hypothesis to be tested is that of inde-
pendence of action, I.e., of tumor inducing
potential, between carcinogens given in combina-
tion.  Suppose, in a 2 x 2 experiment with
treatments A and B, that noo animals receive no
treatment and njQ, ngi, nj^ animals receive,
respectively, doses d^ of A, d]j of B and
(d^ + d]j).  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 (l,j) remains tumor-free up to time t.
Let Qij - qij(T) where T is any time after the
last event.  Let mjj be the number of animals
with tumors in group (l,j) at time T.  Finney's
hypothesis of simple independent action of A and
B is:

              HO  QnQoo - 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:
                      *ij   ij-ij
          HijCl - Qij)   Qij

  The log-likelihood Is first maximized with
{Qij} as four Independent parameters, i.e.,
Qij " tnij-m^jj/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 (tqn(t)qoo(t)]/[qio(t)qoi(t)]) - 0

for all t.

  Let Xij(t) - -(d/dt)  (log(qij(t))} denote
the hazard function  for the ocurrence of a tumor
for an animal in the group (i,j); then HQ
becomes :
/ Uu(t)
- X10(t) -
                                       dt  - 0
 for all  t, or equivalently,

 Xu(t) + Xoo(t) -  Xxo(t) -  Xoi(t) - 0     (1)
 for all  t.

Synergism corresponds to the expression on the
left of (1) being greater than zero and, con-
versely, antagonism corresponds to the expression
being less than zero.
  If the proportional hazards assumption is
made, namely that Aij(t) may be expressed as
A(X)(t)fij where f jj does not depend on t,
then the null hypothesis becomes, without loss
of generality:
HQ:  1
the arbitrary scale factor having been absorbed
into the arbitrary function AQQ(t).  The
alternative hypothesis allows for all three
parameters to be free.  Let f - (f<30f10>f01
f 11 ) ' .  For testing HQ it is convenient to
express f in terms of parameters {8} .  Let
             Bl     UH
TM(B)  - (l.e  ...,e  )' for arbitrary M>-1
and let W be any 4x3 matrix of constants with
columns 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(3), 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 Lg. LC
are, respectively, the maximized log-likelihood
functions under the saturated and constrained
models; X has approximately %i  distribution
under the null hypothesis.  Technical details for
the likelihood maximization are described In
Machado and Bailey (1985).


  The data for this example is from Table 2 of
Korn 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:

                             C - -294.588

                            3  -  /0.25\

      - -5.31
  The likelihood ratio test, X - 6.21 (o "
0.013), indicating significant departure from the
null hypothesis; the interaction is antagonistic,
from the sign of VAB*?.  This result corresponds
to those of Korn and Liu.
  For comparison, the time-Independent likeli-
hood ratio test was 2(Lg - LC),- 4.32; this
statistic has approximately XL  distribution,
thus A  0.039, again indicating significant


  A problem which may occur is that one or
more groups may have no animals with tumors.
This leads to an infinite solution for the  {0}
in the original parametrization.  The model can
often be expressed in terms of alternative
parameters and maximum likelihood estimates
found without the groups which have no animals
with tumors.  For example, in the 2x2 case,
if no animal in the control group has a tumor,
so that Aoo(t) "  thls group may be excluded
from the analysis and f_
be modelled by WJi(A> with
                        /I   0\
                         0   1
                        \1   I/
                                                      This  represents  the additive model  subject  to
                                                      fOO " 0*   1^ c^e 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

                                                      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 diethylstilbestrol (DES)
                                                      and dimethylbenzanthracene (DMBA) In  the
                                                      induction  of mammary adenocarcinomas  in female
                                                      ACI rats (Shellabarger  et al., 1980).  The
                                                      results of the test for interaction are:

LS - -152.46

9  -  /-0.52\
      I 1.47/

       f0.60 I
                                                                    - 2.74

                                                                                    LC  - -156.848

                                                                                    *  -   -0.68

                             A   A   /\
  The test statistic X  8.77 (a- 0.004),
indicating very significant departure from
the null^hypothesis.  Since the contrast,
fll-?10~f01 Is greater than 0, the inter-
action is synerffistic.

  The likelihood ratio test from the time-
independent test is 6.61 (* 0.01), again
indicating significant Interaction.


  The proportional hazards assumption should
be checked since gross departures from propor-
tionality may well affect the behavior of
the interaction tests in an adverse way.
Kalbfleisch and Prentice (1980, 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 qij(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 time 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,Tl.
Let LS(1), 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(Lg(l) +
Lg(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(Lc(l) +
Lc(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 tq 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 nonproportlonality, 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*


  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-mirius-log" plot for
the data of Example 2.  The plot indicates some
departure from proportionality since the curve
for the group receiving both DBS and DMBA seems
steeper than those of the groups receiving a
single 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:  LS(!) - -80.63, LC(!) " -83.36,
(fl, 62) - (-1.27,1.29) and ifor the later
time period:  1^(2) - -71.00, Lc(2) - -72.78,
0.10) Indicating no strong
evidence for lack of uniformity; the estimated
f) coefficients are not very similar but are far
from significantly different.  The xi  tests
for interaction for the early and late time
periods are 5.45 (a - 0.020) and 3.56
(o - 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 OES and DMBA in this experiment.


  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 2 x 2 case,
suppose events occur at time, ti, t2,  ., and
suppose that there are no tied events.  Let
where nij(tk) is the number of animals'in
group (i,J) exposed at time t^-0, n^Ct^) 
ijnij (ck)i atld the failure occurred in group
(i,j).  The statistic for testing Finney's
hypothesis of independent action is:
                 r zk
          z -
              (Z Zj/)1/z

which has approximately N(0,l) distribution.
The terms in the numerator,  {Zfe}, 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 (a - 0.013).  Note 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 (o 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
feels uneasy about assuming proportionality of


  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 i,j,k-0,l.  Let
fijk. where fijk is Inde-
pendent of t.  Let q(t) be the vector of the
{qijk(t)}  -with the subscripts in the order
(000,100,010,110,001,101,011,111) and let f be
the vector of  {fijkJ  with the subscripts
in the same order.  Let the columns of the
design matrix
I! -a
                                  c -3
be labelled in order, VQ, VA, VB> v^, vg, 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.:
    :  (1)  VAB'logCq) - 0 , (ii) vAC'log(q) - 0,
     (iii)  vBC'log(q) - 0,  (iv) VAjjc'logCq) - 0
  Under the proportional hazards assumption, as
in the previous section, HO becomes:
      (i)  VAB'f - 0
    (iii)  vBC'f - 0
                        vAC'f - 0
                              - 0
  A joint test of the four parts of HO is made
by comparing the constrained model f - WT3(B),
where W is an 8 x 4 matrix of constants with
Columns orthogonal to VAJJ, VAJJ, vBc an
                                             with the saturated model,  f  WTyCB);  the
                                             resulting likelihood ratio statistic has
                                             approximately XA  distribution.   One choice
                                             for W is to take as its columns  VQ,  VA,  vjj, vo
                                             Sequential tests for single interactions are
                                             made by modelling the specific constraints by
                                             suitable choice of W.  For example,  to test for
                                             the three-way Interaction, model f by WjT^B),
                                             where Wj is 8 x 7, orthogonal to v^gcj and make
                                             a one degree of freedom comparison with the
                                             saturated model.  Further, to then test  for the
                                             AB interaction, model f by W2Ts(B),  where
                                             W2 is 8 x 6, orthogonal to VAB and vj^jc, and
                                             compare with the model WiT$((J).   Leaving out
                                             one constraint at a time leads to a  series of
                                             one-degree of freedom comparisons in the usual

                                             10. EXAMPLE 3

                                               The data for this 2x2x2 example are from
                                             a one-year experiment to assess  possible inter-
                                             action between DMBA, procarbazine (PCZ)  and
                                             x-irradiation (X-ray) in the induction of mam-
                                             mary adenocarcinomas or- fibroadenomas  in female
                                             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 numbers of  rats with  one  or more
                                             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
                             Treatment group     Number

                             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

  The maximized log-likelihoods were:
Lg - 510.981, LC " -511.422 resulting in
test statistic for overall interaction, -^ -
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 chl-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 {fijfc} from the saturated
and constrained models are very similar:

f - (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-minus-log" plots showed close to constant
separation between all of the curves and thus
is there no reason to doubt the proportionality

of the hazard functions. Thus the three treat-
ments act Independently In the Induction of one
or more 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 less understood measure of carcinogenesls,
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
  Treatment group       Number

    Control                35
    DMBA                   37
    PCZ                    37
    DMBA & FCZ             37
    X-ray                  37
    DMBA 4 X-ray           37
    PCZ and X-ray          36
    DMBA, FCZ & X-ray      37
Number with 2
or more tumors

  The likelihood ratio test for no two-way or
three-way interactions was  ty  " 10.48 (a -
0.035), indicating the presence of some inter-
action.  The test for no DMBA and X-ray, or FCZ
and X-ray, or DMBA, PCZ and X-ray interactions
was xi  " 2.77 (a > 0.1), which is far from
  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 synergism 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.

 Finney, D. J. (1971).  Frobit analysis, 3rd ed.
Cambridge:  Cambridge University Press.
 Hogan, M.D., Kupper, L.L., Most, B.M., Haseman,
J.K. (1978).  Alternatives to Rothman's approach
to assessing synergism (or antagonism) in cohort
studies.  American Journal of Epidemiology 108,
 Kalbfleisch, J. D. and Prentice, R. L. (1980).
The statistical analysis of failure time data.
New York:  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, F.N., Parish, S., Peto, J., Richards, S.,
Wahrendorf, J. (1980).  Guidelines for simple,
sensitive significance tests for carcinogenic
effects in long-term 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, Y. 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, B., Stone,
J. P.   and Holtzmann, 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.

                                               FIGURE 1

                                     PLOT OP   log(-log(q(t))) v. log(c)

                                     SOW-LIU DATA

 1.0 *
               1:   Control*

               2:   HTA                                                                    3

               3:   HHNG

               4:   NTA t MNNG                                                            3

                                                                                    3 3     4
-0.5                                                                                     4

                                                                               3    4

                                                                             I     44   2 2  2

...5;                                            '                                   2

                                                                           34      2    ,!
-2.0 i                                                               2    4            I
-2.5 f
                      2                                  4              1

-3.5 i                                                                1

-4.0 +

-4.5                                                 I

     "i*5	1*6    5*7s!5	s!5     6?0      6*,\	6*2	6*3*     6*4* " 6*5   " 6.6


                                                FIGURE 2

                                        PLOT  OP  log(-log(q(t  vs. log(t)

                                        DBS,  DHBA EXPEUMEHT
LKH2 |

                  2:  DBS                                                4         *

                  3:  DNBA                                              4

 'S              4:  DES t OKBA                                  4

 0.0                                                 4                             3



-1.0                                          4
                                                            2      2 2  22 22 2

                                          4     2                           "   "3
-1.5                                                                       3

                                                              3   3
                                                            3 3

                                     3     33


-3.5                              3-
      4.0       4.2       4.4       4.6       4.8       5.0       5.2       5.4       5.6      5.8


                          Chao W. Chen, U.S. Environmental Protection Agency
   From Machado's presentation we have seen that

                qijk i.J.fc " t 1

play a key role in the hypothesis testing of no
interaction when time-to-event data are avail-
able.  The null hypothesis of no interaction, for
the case of a 2x2 design, is
for every t.  For the case of a 2x2x2 design, the
null hypothesis of independent action of the
three treatments has four parts corresponding to
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 but 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,
       for every t.  This alternative hypothesis
       uses the same information in an additive
       sense rather than in a multiplicative

   3.  The implication of the null hypothesis
       used by Machado to test Independent action
       for a 2x2x2 design of an experiment.

1.  Testing the Synergistic (Multiplicative) Ef-
    fect of Two Carcinogens under the Simple Mul-
    tistage Carcinogenesis

   Under the Armitage-Doll multistage model, the
probability of cancer by age t at constant dose 
rate d has a. form
                                                is  equivalent  to the null hypothesis

                                                                   H0:  bll " <>

                                                The log-likelihood ratio statistic of chi-square
                                                with one  degree  of freedom can be used to test

                                                   Although F(t,d) satisfies the proportion haz-
                                                ard assumption,  and therefore Machado's proce-
                                                dure is applicable to test the hypothesis of no
                                                interaction, the proposed procedure is more
                                                specific  and can be easily used  in routine risk
                                                assessments where the goodness-of-fit of a dose-
                                                response  relationship must first be determined,
                                                usually on the basis of data from multiple-dose

                                                2.   Alternative  Null Hypothesis  of No Interaction
                                                    on the Basis of Latent Period

                                                   Let TOO. T10 T01 an<* Tll be random variables
                                                representing,  respectively, time to cancer death
                                                of  an animal exposed to dose rate 0, d^, djj and
                                                (d^+ds) under  the condition of no competing risk.
                                                Let MIJ  min(Tjj, L) where L is the time when
                                                the study terminated.  It follows that the expec-
                                                ted time  to cancer death (latent period) is given
                                                and the life-shortening due to the exposure is
                                                             -  x E(MOCT
          1     L
          L     0
                                                                              ~ qii
    t}, . .., tn are the time to cancer death,
    CQ - 0, and
   foj - Kaplan-Meier estimate of qjj.

The estimate of standard deviation is given by
is asymptotically distributed as a standard nor-
mal under HQ.

3.  Implication of the Null Hypothesis used by
    Machado in a 2x2x2 Design

   The null hypothesis used by Machado is

                   HQ: V'f - 0
where V  V^
tors given below:
                                 are column vec-
                                         PU1 " PIOO - POIO - POOl * 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  E^gg.   If
                                 there is no pairwise interaction  [i.e., E(AB)C,Q
                                  0, etc.], the null hypothesis HQ of  Machado is
                                 equivalent to the null hypothesis of E^c - 0.
                                 However, in general, E^gg - 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
                                 pairwise interactions are zero.   It seems intui-
                                 ively true that if all pairwise Interactions  are
                                 positive, there oust be a synergistic  effect.  On
                                 the other hand, if all the pairwise interactions
                                 are negative, there must be a synergistic effect.

                         as used by Machado.
   The null hypothesis HQ corresponds to four
HABC " Pill ~ P110 ~ P011 ~ P101
       PQIO + POOl ~ POOO
     " (Pill ~ P101 ~ P011 * POOl) ~
       (PI 10 " PIOO ~ POIO * POOO)
where (Efji^C'l and (Ej})(;,g are 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.
            ~ POll * P101 + P001>
      (P110 ~ PlOO ~ POIO ~ POOO)
    " C-1

                                 USING LETHALITY,  GROWTH  AND ORGAN SYSTEM STUDIES

                  Lavem Weber,  Perry Anderson,  Carl Muska,  Elizabeth  Yinger  and Dennis  Shelton
                                              Oregon State University
   Dose response relationships are the most
single unifying concept to the many 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
independent 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 of the
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 Bliss1 model in an
effort to provide a less restrictive form.  The
following diagram is their scheme with four
distinct types of action.
Simple similar
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"
   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 nonnally 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 models for studying toxicant
Interactions.  The results to be discussed
Involved tests of the model using lethality
(Anderson and Weber 1977), growth (Koikemeister
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 the measured concentration of
the permissible level of each toxicant should 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 LC5Q.  The concentration of each toxicant
1n a mixture is then expressed as a fraction of
Its corresponding LC5fl 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 would
be "similar joint action" or in Hewlett and
Plackett's 1t would be "simple similar".
   A multitude of terms have been suggested to
describe the various types o-combined toxicant
effects.  AHens (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 in 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

toxicant mixtures; however, Plackett and Hewlett
(1952) presented examples of chemically related
Insecticides which gave nonparallel lines.  They
and other toxlcologists (Arlens and Simonis,
1961) have stated, and we believe rightfully so,
that parallelism and hence complete correlation
of individual susceptibilities is 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 s a + b log x (where y 1s the %
response to each toxicant and x 1s its concen-
tration), the regression equation for a binary
mixture can be represented by (Finney, 1971):

   ym = aj + b log (^ + p^) * b log Z       (1)

     y  * % response to the mixture
     a, * y intercept o_the first toxicant
     b   common slope
     IT, a proportion of the first toxicant in the
     Tp * 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, LCgg, etc.),
equation (1) incorporates the entire dose
response curve.
   Response addition 1s 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 is 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
quantal 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 is
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 is 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  (Pm) can  be represented
        PB 1f
                       * 'b
where P. and PB 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:
Pm ' PA * PB
                     - P>
' (2b)
   In the limiting case of complete and positive
correlation (r * 1), individuals very susceptible
to toxicant A in comparison with the population
will be correspondingly very susceptible to
toxicant B.  In this situation the proportion of
animals responding the the mixture is equal to
the response to the most toxic constituent in the
mixture.  Mathematically this is represented by:

   Ps p   if P  > P
 U   *Q  IT TQ b r*
 rlD      on
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 addition
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

   This expresses a linear function between
survival time and dose of different sizes of silk
worm larvae.  W represents weight, Y the
dependent variable (death of fish in our case)
and M the mean daily 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  is 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
                   n Factor
     Copper chloride                 '0.72
     Nickel chloride                 0.67
     Zinc chloride                   0.3
     Dieldrin                        0.81
     Potassium pentachlorophenate    0.72
MIXTURES:  Anderson & 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
    . 6
    x 5
                             nickel.  We  assumed  that  as  constituents  of a
                             binary mixture,  copper  and nickel  would
                             contribute to  the mixture's  toxicity  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 Ni.
                               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 relationship between
                             the  lethal effects of pentacholorphenate  and
                             dieldrin supported (Bliss 1939) the "independent
                             joint action"  or response addition hypothesis.
                             All  mortality  of fish 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
        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 Hi  (0.994)
        and a relative potency (p)  of 6.58 x 10"  .

       Table 2.  Toxlcltv study of gupples exposed to mixtures of KCP and HEOD
of PCP
log M/W81
for HEOD
S Mortality
log M/r"
for PCP
S Mortality
for PCP
S Mortality
for mixture
) Mortality
       From Anderson 4 Weber, 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.  D1eldr1n 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
   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,  copper  and zinc,  we
were able to clearly describe an interaction
which 1s super-additive.

Muska and Weber (1977)

   Completion of these quantal 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, hypothetical  dose response
curves for two toxicants (A and  B) are plotted 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 dally assayed concentrations, of the  predicted  mortality of fish
exposed to mixtures of HEOD, KPCP, Cu and N1.
Predicted Mortality Proportion
1 " (1'PKPCP)(1~PHEOD^1"PCu-Nl) * Pm
1 -
1 -
1 -
1 -
1 -
1 -


- .316)(1 - .22)(1 - .057) = 0.50
- .4)(1 - .36)(1 - .136) = 0.66
- ,212)(1 - .045)(1 - .023) = 0.27
- .268)(1 - .184)(1 - 0.045) = 0.43
- ,758)(1 - .198)(1 - .084) = 0.82
-.655)(1 - .277)(1 - 0.081) = 0.89


X2 = 5.57
d.f. = 4.0


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
is varied and the ratio of the concentrations
for the individual toxicants is 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 in 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
(r), 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  in  the  two types  of
                                                   addition.   At  threshold or below threshold
                                                   concentrations of  toxicants A  and B,  a mixture
                                                   acting  in 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 is
                                                   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 is
                                                   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 high  levels  of response  (in  this example, for
                                                   responses greater  than  84% probit of 6.0)
                                                   mixtures  acting in a response  additive 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
                              (Y = 9 + 4X1
                        -I 0
                                        -05         0.0         05

                                         LOG TOTAL CONCENTRATION  (X)
 Figure  2.   Hypothetical dose response curves  for toxicant A (1:0),  toxicant B  (0:1 ) 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 in Figure 2 can be readily
conceptualized with isobole diagrams, a technique
introduced by Loewe (1928, 1953).  Isoboles are
lines 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 10%, 50% or 90% 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 50% 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 is 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 express
                                 the  incidence of an all-or-none effect (usually
                                 death)  when varying concentrations  are applied to
                                 a group of  organisms.   The curve is derived by
                                 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.
                                                                          I: 100
2.0       4.0
                                         6.0      8.0
                                         TOXICANT B
                                                                             I : 1000
                 Figure 3.   Isobole diagram for quaatal response data.  Isoboles  for
                            concentration and  response addition were determined from
                            hypothetical dose response curves in Figure 1.

   As Clark (1937) and others have pointed out,
it is possible to represent any graded response
as a quantal 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 fail 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 is a
difference in the way the two types of data are
measured.  For quantal 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
average  response  of a  group  of  organisms.
Therefore,  the  response  of each individual
organisms to the  toxicants is 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 toxicity 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 addition
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 suppose 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

                             Figured.  Uobole diagram for graded response data.

 in  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
 (i.e. 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 and  for delineating  the
 various  factors which can  influence  the relative
 toxicity of multiple toxicants.  However,  in
 practice,  isoboles are  difficult to  derive
 requiring  a series of dose 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:   Muska  and Weber (1977);
 Koikemeister 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
   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 lexicologically by
 different mechanisms of action.    As we know the
 parallelism of curves is  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
 (Koikemeister and Weber,  1978).  Our assumption
 based upon available data  and. parallel  growth
 dose response curves was  that they would be
 concentration additive.   Mixtures  proved to  be
 infra-concentration 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 the toxicants  on  the food consumption
 of  the fish was supra-additive relative to the
 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  the
 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  sublethal
 concentrations  of  a  copper and  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

                                                       0 a
                                                       . 3 P
                                                              I m




                                                       2 -5- o 
                                                         i o "
                                                       5  * X

                                                        3 -  Q
                                                        5 O-
                                                        ( rr
                                                        a 3-
o 5



_  100





o   50
UJ   40
                  a   a
                                  Cu-Ni MIXTURE
     -6.0    -5.5    -5.0    -4.5
                            LN TOTAL CONCENTRATION  (mg/l)
            Figure 7.  Dose response curve! how ing effect* of copper, nickel and their mixtures
                      (obierved and predicted) on food consumption 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:  She!ton and Weber (1981)

   Mortality (quantal  response) and growth
 (quantitative) response 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 examined.   All  experiments were performed
                                       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 water ad
                                       libitum.  The  animal  room  was maintained at a
                                       12-hour light/dark cycle with an ambient
                                       temperature of 70-72F.
                                          The toxicants were carbon tetrachloride
                                       (CC1.), monochlorobenzene  (MCB) and acetaminophen
                                       (ACEr).  The CC1. and MCB  were dissolved in corn
                                       oil  and ACET was dissolved in 0.9% NaCl at 40C.
                                       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, 48, 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, TO) are shown in Table
                                       4.  The TDgo's were  used to calculate the potency
                                       ratios  for  the toxicants.  MCB and ACET were
                                       found  to  be approximately equipotent in producing
                                       liver  damage whereas  CC14 appeared about 35 times

Table 4. Dose response characteristics of selected hepatotoxlcants on plasma alanlne aminotransferase  activity 1n male
albino mice.
TD50 Potency,
Carbon tetrachloHde
Honochl orobenzene
(14.2 - 19.9)
(395 - 466)
(485 - 643)
unole/kg ratio "
109.5 1.0
(92.5 - 129.6)
3807 34.8
(3505 - 4136)
3694 33.7
(3209 - 4252)
Slope j
USD) t value0
8.40 -0.45
8.31 -0.7?
P value8
*A positive response Is defined as a plasma alanlne amlnotransferase elevation i3 SO above the control meal (10  2 IU)

 Determined from the dose response regression equation.  Parentheses Indicate 95X CI.

CT050(MCB or ACET)/TD50(CC14), umole/kg comparison

 T value determined when slope of dose response curve for MCB or ACET 1s compared to that of carbon tetrachloHde.

'in each case slopes were not significantly different from parallel at the P value Indicated.
            From Shelton and Weber (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 CC1_4 (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 + MCB Mixture.   A theoretical dose
  response curve for the  binary mixture of CC1. and
  MCB at a molar dose 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 (CCl.-.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 CC1. 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
     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 CC1. + MCB mixture were clearly
                                               predicted  by  the equation for concentration
                                               addition.   It is evident that the response of a
                                               given dose of a CC1.  + MCB mixture is  not  merely
                                               the sum of the  toxic"  effects of the CC1, and  MCB
                                               given singly.   Instead, the addition of the
                                               effects follows a log-linear relationship  with
                                               respect to the  total  concentration of  both CC1.
                                               and MCB in the  mixture.
                                                  The  interpretation of the joint effects of the
                                               CC1. +  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  not
                                               present any striking  differences between the  two,
                                               any observed  differences in joint action,  when
                                               combined with CC1,, is largely unexplained.   It
                                               has been inferred that acetaminophen may damage
                                               the hepatic endoplasmic reticulum (Thoreirsson et
                                               al., 1973).   If this  is the case, then this  could
                                               affect  the activation of CC'L, with resulting


                                                  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

             a. 5
                      CARBON TETRACHLORIDE   /  .
                     O MONOCHLORO8ENZENE
                     x CCI4:MCB (observed)
                   	CCI:MCB (predicted)
                                         DOSE (/imole/Kg)
Figure 8.  Oose response curves illustrating the effects of carbon tetrachloride (CC1J,  mono-
           chlorobenzene (MCB)  and the 1:38 mixture (CC1.:MCB) 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.
                     CARBON  TETRACHLORIDE
                    o ACETAMINOPHEN
                     x CCI4:ACET (observed)
                   	CCI4:ACET (predicted)
             cc. 5
Figure 9.  Dose response curves illustrating the effects of carbon tetrachloride  (CCl ), acetaminophen
           (ACET) and the 1:36.6 mixture (CCl.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,

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 than 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 approach appears to offer a method for
evaluating the effects of combined 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 it is 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 addition
does not necessarily mean that the toxicants act
upon similar biological systems, but only that
they appear to do so.
Partial support provided by NIH Grant ES-00210
Anderson, P. D. and Weber, L. J. (1975)  Toxic
    response as a quantitative function of body
    weight.  TQX. Appl. Pharm. 13:471-483.

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 (Editor),
    North-Holland Publishing Company, Amsterdam,
    p.  286-311.

Ariens, E. M.  (1972)  "Adverse drug
    interactionsinteractions of drugs on the
    pharmacodynamic 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.   (1985)   A
    general  noninteractive multiple toxicity model
    including  probit,  logil  md  weibull
    transformations.   Biometrics 41:711-725.

 Clark,  A.  J.   (1937)   "General  Pharmacology",
    Heffler's  Handbuch der Experimentellen
    Pharmakologie,  W.  Heubner  and J.  Schuller
    (Editors), Verlag  von Julius Springer,  Berlin,
    Volume  4.

 Fedeli, L., Meneghini, L.,  Sangiovanni,  M.,
    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. Appl.
    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  quantal response.   Spec.  Rep,
    Ser., Med. Res.  Coun., Lond., no.  183.   His
    Majesty's  Stationary Office.

 Gaddum, J.  H.  (1953)  "Bioassays  and
    mathematics",  Pharmacological  Reviews,

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.

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.

Koikemeister, E. A. and Weber,  L. J.   (1978)  An
   effect of zinc and nickel on growth of the
   juvenile guppy Poecilia reticulata.  Proc.
   West. Pharmacol. Soc. 21:483-485.

Koikemeister, E. and Weber, L.  0.  (1979)  Some
   effects of multiple toxicants on growth of the
   guppy, Poecilia reticulata.   Proc. West.
   Pharmacol. Soc. 21:483-485.

Lloyd, R.  (1961)  The toxicity of mixtures of
   zinc and copper sulphates to rainbow trout
   (Salmo gairdneirii Richardson).  Ann.  Appl.
   Biol. 45(3}-.535-538.

Loewe, S.  (1928)  Die Quantitativen  Probleme der
   Pharmakologie, Ergeb. Physiol. Biol. Chem.,
   Exp. Pharmakol., 27:47-187.

Loewe, S.  (1953)  The problem  of synergism and
   antagonism of combined drugs.  Arzneimittel
   Porsch.  3:285-290.

Marking, L. L.  (1985)  Toxicity of chemical
   mixtures in Fundamentals of  Aquatic
   Toxicology, ed. by Rand, G.  M. and
   Petroche11i, S. R.  Hemisphere Publishing
                       p. 164-176.
             S.  R.
Corp.,  Washington.
Muska, C. F.  (1977)  Evaluation of an approach
   for studying the quantitative responses of
   whole organisms to mixtures  of environmental
   toxicants.  Ph.D. Thesis, Oregon State
Muska, C. F., and Weber,.L. J.  (1977)  An
   approach for studying the effects of mixtures
   of environmental toxicants on whole organism
   performances IN "Recent Advances in Fish
   Toxicology:  A Symposium" (R. A. Tubb, ed.)
   p. 71-87.

Plackett, R. L. and Hewlett, P. S. (1948)
   Statistical aspects of the independent joint
   action of poisons, particularly insecticides.
   I.  The toxicity of a mixture of poisons.
   Ann. Appl. Biol.  35:347-358.
Plackett, R. L., and Hewlett, P. S.  (1952)
   Quanta! responses to mixtures of drugs.  J.
   Roy. Statis. Soc. B.  14:141-163.

Reitman, S., and Frankel, S.  (1957)  A
   colorometric method for determination of serum
   glutamic oxalectic and glutamic pyruvic
   transaminases.  Amer. J. Clin. Pathol.

Shelton, D. W. and Weber, L. J.  (1981)
   Quantification of the joint effects of
   mixtures of hepatotoxic agents: Evaluation of
   a theoretical model in mice.  Environmental
   Research 26:1246-1255.

Sprague, J. B.  (1970)  .Measurement of pollutant
   toxicity to fish.  II.  Utilizing and applying
   bioassay results.  Water Research 4(l):3-32.

Thorgeirsson, S. S., Sasame, H., Potter, W. Z.,
   Nelson, W. L., Jollow, D. J., and Mitchell, J.
   R.  (1973)  Biochemical changes after
   acetaminophen- and furosamide-induced liver
   injury.  Fed. Proc.  32:305.

Trevan, J. W.  (1927)  The error of determination
   of  toxicity.  Proc. Roy. Soc. London Ser. B.
   101, 483-514.

Turner, N. and Bliss, C. I.  (1953)  Tests on
   synergism between nicotine and pyrethrins.
   Ann. Appl. Biol. 40:79-90.

Warren, C. E.  (1971)  Biology and Water
   Pollution Control.  W. B. Saunders Company,

Weber, L. J. and Muska, C. F.   (1977)  Multiple
   toxicants in the environment.   In Proceedings
   of  the 8th Annual Conference on Environmental
   Toxicology, 4-6 October 1977.  281-298.

                            Bertram D. Litt, EPA/OPP/HED
    The paper by Dr. Weber 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
mathematical models.  More important,
they have demonstrated that neither
structure-activity-relationships (SAR)
nor parallelism of the allometric
responses of individual 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 sophisticated combinations of chemi-
cal residues in the air he breathes,
the food he eats, and frequently even
the water he drinks.  Weber's paper has
shown that combination of toxicants can
result in either superadditivity or
reduction in toxicity below that pre-
dicted by simple additiyity 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
The work just summarized by Dr. 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 tg.  A second study
would repeat the initial tg effects as
part of a series of observations to
evaluate a) dimunition 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 which
are reinforcing and -those which show
antagonistic toxicity end-points.
Secondly these studies should be used
to identify LCsg 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 should be
keyed to levels indicated by physiolo-
gical and environmental factors rather
than the considerations listed in the
guidelines for technical grade


                                Steven J.  Broderius,  U.S.  EPA,  ERL-Duluth

  Most studies evaluating the toxicity of
environmental pollutants to various aquatic
organisms and systems have involved exposures
to separate toxicants.   Relatively few
investigations have defined the adverse
effects of mixtures 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 might
also overlap.  As waste treatment  technology
is advanced and implemented,  nonpoint
pollution from sources  such as  agriculture and
atmospheric deposition  will contribute to a
greater 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
  Water quality criteria should insure that
the discharge levels of separate toxic
chemicals 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 firmly 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., Sprague,
1970; Anderson and Weber, 1975; Marking, 1977;
Muska and Weber,  1977;  EIFAC, 1980; Alabaster
and Lloyd, 1980;  Calamari and Alabaster, 1980;
Konemann, 1981b;  Hermens et al., 1985;
Broderius and Kahl,  1985; Spehar and Fiandt,
1986) that summarize and review much of the
information on combined effects of mixtures of
toxicants on aquatic organisms and approaches
used to evaluate  these  effects.   It is
apparent from these articles that additional
work must be conducted  to characterize the
joint action of multiple toxicants, especially
at sublethal levels.  This paper summarizes an
approach to explore basic principles which
govern the toxicological issues pertaining to
the joint action  of multiple toxicants.


  Various terms and schemes for classifying
and naming effects of chemicals to describe
the response of test organisms to two or more
toxicants, as predicted from the separate
toxicity of the individual substances, have
been recommended.   The  different forms of
joint action have  been  graphically illustrated
and discussed by  Sprague (1970), Muska and
Weber (1977),  and  Calamari and Alabaster
  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

by Plackett and Hewlett (1948,  1953,  1967)  and
Hewlett and Plackett (1959).   Considering
these general  biological  phenomena,  the
different types of combined effects  can 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 same  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  quanta!
responses to mixtures of  interactive  toxicants
are very complex and are  not  described by
simple formulas (Hewlett  and  Plackett, 1959,
1964).  Certain parameters required  for the
models are also normally  unattainable when
evaluating the effect of  a number of  toxicants
on whole 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 sublethal
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 same
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 mode]  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 to a mixture of toxicants
acting  independently may or may not be
correlated.  Therefore, the response curves
for each toxicant of a mixture may or may not
be parallel or similar in shape.  If the
response curves for compounds in a mixture are
dissimilar or if the modes 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 summing in various ways each
response produced  by the separate toxicants.
The proportion of  individuals of a group that
are expected to respond or the degree of
response  for each  individual organism exposed
to specific components and combinations
exerting  response  addition depend upon the
responses  to the  individual compounds and the
correlation between the 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 -1, 0,
and +1.  For mixtures of many chemicals the
correlation coefficient (r)  is expected to
vary from  0 to +1  (Konemann, 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  prerequi site.
   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


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Combinations falling exactly on the upper and
right boundary of the square correspond to
areas 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 manner to that
presented above, isobole surfaces can be
defined for three toxicants.  This terminology
and classification scheme for the toxicity of
two chemicals can,  with certain modifications,
be extended to chemical mixtures containing
several toxicants.


  A mechanistic approach incorporating
toxicant-receptor theory to assess joint
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 exert
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 similar 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
j 01 nt 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
concentration-response curves for the separate
component toxicants and all mixtures are
non-parallel or are dissimilar in shape.   This
type of joint action  is also predicted  if
there is a known difference  in toxic action
between the constituents.  Initially,
experiments were conducted with mixture's of
only two toxicants with multi-chemical
mixtures tested when  confidence in
interpreting the simpler systems was obtained
or when a need for such information became
  To' allow for a more comprehensive
interpretation and 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
(1981b)  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
(i.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.


Testing Conditions, Apparatus, and Procedure

  The 96-h acute toxicity tests with 30-day
old  laboratory cultured juvenile fathead
minnows  (Pimeohales promelas) were conducted
according to test conditions and with an
apparatus described by Broderius 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 up to 21 toxicants.  Seven ratios
of two test chemicals were used to define  the
binary  isobolograms with four concentrations

following an 80% dilution factor at each
mixture ratio.
  The values for the n-octanol/water partition
coefficients (log P) were taken from Hansch
and Leo (1979),  Veith et al.  (1979), and Veith
et al.  (1985) or as calculated from the ClogP
version 3.2 computer program developed by the
Pomona College  Medicinal Chemistry project
(Leo and ffeininger, 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
(LC50) and their 95% confidence limits were
determined from relationships fitted
mathematically by the trimmed Spearman-Karber
method (Hamilton et al., 1977).  Concentra-
tion-response slopes were determined by a
least squares linear regression program.
  The manner in which the combined effects
of mixtures of  two or more toxicants are
calculated by the quantitative toxic unit,
additive index,  and mixture toxicity index
approach have been outlined by Sprague (1970),
Marking (1977),  and Konemann (1981b),
respectively.  The procedures used to analyze
results by concentration and/or response
addition models are according to those
proposed by Anderson and Weber (1975).   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).


Concentration-Response Curves

  Acute lethality tests were conducted with
juvenile fathead minnows in order to define
the toxicity 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
log 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 l-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 II
and uncoupler chemicals, respectively (Table
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.

Isobole Diagrams

  Acute toxicity 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
l-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
                     mi nnows
                                                        Normalized  concentration-response
                                                        relationship  (Y=a+bX)
Mode of
toxic action Reference chemical
Narcosis I 1-Octanol
Narcosis 11 Phenol
Uncoupler 2.4-Dinitro-
oxidative phenol
Slope r2
+ 1 .
+ 1
5 0.724
.8 0.562
1 0.730
           phosphory1 at i on

Y-59.1  + 13 5X
   3.18   0.792
            J	1	I	L
                                           J	L  I
                                                       I   I   I  I
         -5            -4            -3            -2
                  Toxicant Concentration (Log M)
Figure 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 7, mortality,
          respectively.  (B) Normalized plot of data  in Part (A)  as  adjusted
          according to the potency  of  1-octanol.   (From Broderius and  Kahl,

strictly additive joint toxicity was also
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
additive type of joint action would be
predicted for binary mixtures of these
chemicals.  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 b'inary mixture 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 mixtures of 1-octanol
and 2-chloroethanol provided interesting but
explainable  results.  The 96-h LC50 for
1-octanol  was  unchanged up to the LC50 level
for 2-chloroethanol.  The toxicity of
2-chloroethanol, however, was markedly reduced
by the presence of  octanol.   It  is proposed
that the presence of  octanol inhibits the
metabolism of  2-chlorocthanol to a more toxic
metabolite and thus results  in a complex
isobole diagram.  From the approximately 75
isobole diagram relationships that we have
generated, the majority display  a response
exemplified  by the  first  two diagrams (rijure
3 and 4).   The complex type  of joint action,
as exemplified by  1-octanol  and
2-chloroethanol, was  observed in only a few of
0.02    0.04
                                             0.06     0.08
                                          t-Octanol   (mM)
0.12    0.14
            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 latter tests
frequently  included primary aromatic amines
(aniline  derivatives) as one of the test
chemicals.   In only one instance has a
markedly  more than strictly additive type
joint action been observed in binary mixtures
of industrial organics.

OSAR and  Joint Toxicitv - Narcosis 1 Chemicals

  If the  results from joint tuxicity tests  arc
co make an  important contribution to aquatic
toxicology,  a certain basic understanding  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
                    goals,  our mixture testing effort is related
                    to an acute toxicity data base that is being
                    systematically  generated for a program 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
         1  .81-
0.04     0.06     0.08     O.t
        1-Octanol   CmM)
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  organic chemicals is presented in
Figure 6.   The  solid  square data points define
an approximate  water  solubility line above
which there are  very  few observed data
points.   This line, therefore,  defines a zone
beyond which an  acute response is not expected
in a four day test.   It is apparent that the
data do not fall  into many obvious patterns
when the acute  response is plotted only with
log P.  Virtually  all of the test data fall
within a log P  range  of about -1 to 6 and the
acute toxicity  is  in  general directly related
to log P.   Veith et al. (1985) observed that
almost 50% of the  20,000 discrete organic
                      industrial  chemicals currently in production
                      have  log  P  values  less than 2.0.   Therefore,
                      since  our data base is representative of the
                      TSCA  chemicals, the 96-h LC50 to juvenile
                      fathead minnows of most industrial chemicals
                      is  expected to be  approximately 10  M or
                      greater.  There also appears to be a base line
                      toxicity  (Figure 6) 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
          I  .4i-
0.04    0.06     OJD8
       !-Octanol   (mM)
                                                                          0. 12     ol 4
            Figure 5.   Isobole diagram depicting  the  96-h  LC50 values and confidence limits
                       for juvenile fathead minnows exposed to different mixtures of
                       1-nptanol and 2-chloroethanol  (-.-.- predicted relationship for
                               addition with r=-l).   Vertical arrows indicate greater than

ketones (Figure  7).   From this  plot  it  is
apparent that the  majority of the  tested
ketones conform  to a response model  line that
Veith et al.  (1983)  have  characterized  by  a
mode of toxic action called Narcosis  I.  This
procedure was repeated for 22 other  chemical
groupings and it was observed that greater
than 50" 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 cytoplasmic activity  as  a
result of the absorption  of foreign  molecules
into biological  membranes.  The environmental
concentration necessary to produce this
response is independent of molecular 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  might 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 I  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 isoboles are in  general
                                                   characterized by a diagonal line that
                                                   describes a strictly  additive type of joint
                                                   action.   This suggests that the fathead minnow
                                                   perceives these  chemicals as  having the same
o  '
            o o
                                                                                             -4  Z

                                                Log  P
            Figure  6.   Acute  toxicity  to  the  fathead  minnow  of  approximately 600  industrial
                       organic  chemicals  as  related to  the octanol/water partition
                       coefficient  (Log P)    Water solubility of  alkyl alcohols  indicated  by
                       square  data  points.

or a very similar mode  of  toxic  action.
  A second type  of experiment  has  been
conducted to document  the  joint  toxicity  of
mixtures containing two or more  Narcosis  I
toxicants.   An attempt  was made  to prepare
test concentrations of  these mixtures on  an
equal  proportion basis,  based  on LC50
concentrations of the  individual chemicals.
Using  the mixture toxicity index (MTI)  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., MTI
~ 1).   Therefore, a concentration addition
type of joint action has not only been
demonstrated for chemicals from  the same  class
but also for chemicals  from seven different
classes and in equitoxic mixtures  containing
up to  21 chemicals (Broderius  and Kahl,  1985).
  We have conducted acute  toxicity tests  with
several alkyl alcohols,  which  produce a
classical narcosis type of toxic action.  The
                              acute toxicity of these alcohols has been
                              observed to increase with increasing log P and
                              decreasing water solubility.   The relationship
                              is apparently linear for the  homologs tested,
                              with the acute response covarying with water
                              solubility at log P values less than 4.0.
                                The alkyl 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 mode of action,  characterized by
                              membrane expansion,  may be modeled jointly,
                              even though ethers,  ketones  and benzenes are
                              in general slightly more toxic than alcohols.
                              The joint action of test chemicals associated
                              with the Narcosis I SAR were  expected to be
                              characterized by the concentration addition
O  -4
              NARCOSIS  I
                                                                      -   a
                                                                     -2   0
                                                Log  P
            Figure 7.   Acute toxicity to the  fathead  minnow  of  industrial  ketones as  related
                       to the octanol/water  partition coefficient  (Log  P).  QSAR model  line
                       for physical  narcosis  (Veith et  al.,  1983).

model.  Our results  indicate that this was true
for numerous  binary  and  equitoxic mixtures of
up to 21  chemicals.
  Konemann (1981a)  conducted 7 or 14 day
equitoxic acute  toxicity tests using guppies
fPoecilia reticulata)  and mixtures containing
up to 50  industrial  chemicals.  Hermens et al.
(1984)  conducted 48-h  acute toxicity tests
with Danhnia  magna  and mixtures containing the
same 50 chemicals as tested with guppies.
ffhen these data  are  plotted against the
Narcosis  1 bilinear  SAR  model line of Veith et
al. (1983) (Figure  9), a good log P and
biological activity  dependent correlation is
noted among ail  three  model lines.  This
suggests  that the sensitivity of different
fish species  and daphnids to non-specific
anaesthetic-like chemicals  is similar since
the Narcosis  I model relationships in Figure 9
are all quite similar.   Schultz and Moulton
(1984)  have recently reported a similar
relationship  with a  different activity scale
between log P and biological activity in
Tetrahvmena pvriformis for  49 aromatic
industrial chemicals.
                                  The type of joint action that Konemann
                                 (1981b) and 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 LC50 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,
                                 1972; Konemann, 1981 a; and Hermens and
                                 Leeuwangh, 1982) have suggested that physical
                                 unspecific toxicity can be minimally expected
                                 of  most hydrophobic organic chemicals at some
                                 concentration.  This  is expected unless a
                                 chemical is metabolized or its effect is
                                 masked by overwhelming irreversible and more
                               _toxic effects from specific structural
                                l-Octanol  (mM)
                                                                       TOXICANT H
                                                                      l-Hexanol (fry)
                                                                     O l-Hexanol  (juveniles)
                                                                     A 2-Octanone
                                                                     a Oiisopropyl Ether
                                                                     * Tetrachloroethylene
                                                                     O 1,3-Dichlorobenzene
                                                                     -* n-Octyl Cyanide
                                                                     V n,n-Oimethyl-P-Toluidine
           Figure 8.   A composite  isobole  diagram of 96-h LC50 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 minimally based  on
concentration addition of their  minimal
unspecific toxicity.   This contribution  of  a
compound in a nonionizable form  can be
calculated from the  Narcosis I QSAR (Konemann,
1981b;  Veith, 1983;  and Hermens  et  al.,
1984).   In mixtures  with only a  few compounds
with different specific and more toxic action
this unspecific toxicity might not  markedly
contribute to the observed response.   In a
mixture of numerous  differently  acting
compounds at equitoxic concentrations, the
specific toxic effects might 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 additive 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.
QSAR and Joint Toxicitr - Narcosis II  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
    -J -2

    C -4
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
activities 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 many of the
monoesters 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 chemicals that we have
tested  include the substituted and
halogenated phenols.  These compounds can
generally be thought of as not chemically or
biologically reactive.  However, depending
upon the substituents present on the molecule
the hydroxyl derivative might 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, 1979). Therefore, it was
anticipated that non-log P related effects
might be important in determining their toxic
response and thus not modeled by the Narcosis
  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 halogenated' 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
toxic action characterized by Veith et al.
(1985)  as  Narcosis II.   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 I 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 uncouplers (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 and should
not interact in a concentration additive
manner.  Those within a mode, however, should
be strictly additive in their joint action.
   It has been proposed that the QSARs for
Narcosis II and uncoupling of oxidative
phosphorylation 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 been used extensively.
  Hermens and  Leeuwangh (1982) 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)  with 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 resulted
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.

Future Research

  The direction of  future  research  in
evaluating the  environmental  hazards posed by
multiple toxicants  should  include not only the
acute response  but  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  with daphnids,  various
freshwater fishes,  and a few  other  organisms.
The incorporation of  new test  organisms and
endpoints such  as the African  Clawed Frog
(Xenopus laevis) to study  teratogenic effects
(Schultz and Dumont,  1984), and the rainbow
trout embryo for carcinogenic  effects (Black
                          et al., 1985) might 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 proven useful as a dis-
                          criminating tool in identifying pairs of
                          chemicals that have a suspected similar or
                          different mode of toxic action.   As testing
                          has expanded into multiple chemical mixtures,
         -2 -
     O  -6
     s  -8
                                                                      UNCOUPLER MODEL
                                                       Antfmycln A
               2.0             4.0
                      Log  P
            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  phosphorylat ion (I) or that inhibit electron transport
                       and thus the  metabolism of  oxygen (0).

it has been the traditional approach to test
equitoxic mixtures.   In future testing it
might be desirable to plan experiments
according to a multifactorial design.  With
this approach all  combinations of several
different sets 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
  Our selection of test chemicals has been
guided 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
have attempted to  test chemicals within and
between different  QSAR's, assuming that we are
establishing how chemicals jointly act with
similar and different modes of action.
Reference chemicals have been used to
represent various  modes of toxic action.
Future experiments will include those
chemicals that have a "more specific" mode of
toxic 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 mixtures 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 (1981b).   More sophisticated
techniques as  reported by  Durkin (1981)  or
Christensen and Chen (1985) might be more
instructive  in defining the degree  of joint
action and similarity among chemicals  in
  Various  relationships have been derived
between  toxicity  and the  octanol/water
partition  coefficient as  the dominant
parameter.   This  has proven  adequate  to
describe the  relationships for  non-specific
organic  toxicants but might  be  inadequate  for
chemicals  with more  specific  primary
modes-of-action.  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 might  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 need to be empirically
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                      G. P. Patil and C.  Taillie,  The Pennsylvania State University

    The author deserves commendation for his
 paper prepared for presentation at the ASA/EPA
 Conference on Current Assessment of Combined
 Toxicant Effects to a joint audience of
 participants from various related disciplines.
 As he puts it,  "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 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 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
' proven most useful as a discriminating tool in
 identifying pairs of chemicals that  have a
 suspected similar or different mode of toxic
 action.  As testing has expanded into multiple
 chemical mixtures, it has 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
 chemicals jointly act and to broaden the
 application of test results.  We have attempted
 to test chemicals within and between different
 QSAR'a assuming that we are establishing how
 chemicals jointly act with similar and different
 modes of action.  Reference chemicals 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
 chemicals in mixtures ...   An untested but
 potentially powerful approach to predicting
 joint toxicity of mixtures deals with N-apace
 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 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 chemicals in different clusters
 is too complicated to be presented by simple
 models and will need to be empirically
    The author should be complimented for his
 effort in developing these complex problem areas
 and in communicating them to the substantive
 scientists, statistical methodologists, and
 managers.  The paper covers a broad  spectrum of
 issues and approaches pertaining to aquatic
 ecotoxicology,  risk assessment, monitoring and
 mangement with particular emphasis on matters
 relating to the perceptive isobole diagrams and
 the widely recognized QSAR techniques.

   We  initially propose to briefly discuss and
 formulate some of the basic  statistical aspects
 of the approach leading to the  isobole diagrams,
 and  subsequently  offer a few remarks pertaining
 to their role  and use for field situations.
   Let the  toxicants  be denoted by A,  B,  C,
Let  X
                       denote  the  tolerances  of
an  individual  to  the  toxicants  A, B,  C,  ...
respectively.   Let  B^,  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
same 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
(XA,Xg)  are expected to be positively
correlated.  A correlation of zero is expected
if  the sites are dissimilar.  Negative
correlation,  while possible, appears  to be

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

combination with one another.  Let  (BA,BB) be

the joint concentration (exposure level) of the
two chemicals.  The mode of action of  A  and  B
should determine, in terms of the organisms'
tolerances (XA,Xg), which organisms will show a

response to (BA,BB).  Formally then, the mode of
Joint action can be defined as a rule that
assigns to each joint exposure level (BA,EB)  a
region in the two-dimensional plane  (XA,Xfi)  of
possible tolerance values.  A given organism
shows a response to  (BA,BB) if and only if its
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 (EA,EB), is the integral

of the bivariate tolerance distribution over the
region associated with (BA,BB).  Both the joint
tolerance distribution and the mode 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 mode of action from observations
made upon the response function.
                   Mode of
   The mode of joint action needs to
satisfy at least the following requirements
(where R is the response region associated with

     (i)  The point  (EA,EB)  lies on the
          boundary of  R.  This reguirement
          appears to rule out physical
          interactions between the
                R and if XA
If  (XA,XB)  is in

and  XB  XB, then  (XA,XB)  is also

in  R.   In words,  if an organism
shows a response then so will all less
tolerant individuals.
If  E'.  < E.  and  ED ^ En  then the
R'  < R
          response region associated with

          (EA,EJ>) is a subset of the response

          region associated with (EA,Kg).

   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 its boundary a straight line with
negative slope; the magnitude of the slope is
the relative potency of the two toxicants.
Notice  that all points along this straight line
                                           Figure 1.  Response regions (shaded) for three
                                           different modes 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
                                              determine the same response region and,
                                              therefore, the same value of the response
                                              function.  It follows that, in the case of
                                              concentration addition, the isoboles (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
                                                 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 response 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? * xS = constant.
                                            Figure 2.  Example of nonlinear  law of
                                            substitution.  Response regions  have circular
                                            arcs for their boundaries.  All  chemical
                                            combinations along one of these  arcs produce
                                            identical responses.

In common with concentration addition, all
self-similar modes of action have the two
properties that (i) 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 senae of concentrating its
probability mass on a one-dimensional subset of
the (XA,XB) plane).

   A second mode of joint action is known as
response addition.  This occurs when an organism

shows .a response to  (EA,KB)  if and only if it
would respond to  B^  acting alone or to  Eg

acting 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 sum of the responses to  A  and the
responses to  B  (after adjusting for double
   Response addition is not a self- similar
mode of action; for example, the points  (B^.Eg)

and  (EA,EB)  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.,En)  is  1 - F(B.,Bn)  where F
               A  O              AD
is the survivor function of the tolerance


   This section hopes to identify a few
statistical issues that seem to be implicit in
the approach that Broderius has presented.  This
is not an exhaustive list, but only indicative
and preliminary.

3.1  Isobolea 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  Isoboles 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 slopes
in his probit  diagrams  and  nearly degenerate
tolerance distributions.  Even 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 as  well  as 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  Broderius study,  which
assume synchronous  exposure,  carry over to the
asynchronous exposure that  is common  under field
             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 EPRI 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_ortality due to pollution  (multiple
 chemicals  included),  environment, habitat,  and
 fishing that has involved multivariate multiple
 time series and categorical  regression related
   Broderius1 paper develops  a promising
 approach to the contemporary  issue of multiple
 toxicants and raises  several  challenging and
 fascinating technical problems such as:
 statistical graphics  of combined effects,
 multivariate tolerance distributions, binary
mixtures and multivariate results, svnergism
 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.


                         Erik R. ChHstensen. University of WisconsinMilwaukee

   Adequate  unlvarlate  dose-response functions
are necessary 1n order to develop a satisfactory
multiple toxldty model. We Investigate here the
use of  unlvarlate Welbull and  problt distribu-
tions with  literature  data for the  quantal  re-
sponse of  fathead  minnows  (Pimephales oromelas)
to  27  different  organic  chemicals.  We  also
examine fits  of  the Weibull, proWt,  and loglt
models  to  literature data  for  the  growth  rate
and yield  of  the diatom Navicula  incerta inhi-
bited by  Cd,  Cu.  Pb.  or Zn. The  Welbull  model
appears to provide  a  superior fit  for both fish
and   algae,   thus   supporting   a   previously
developed  mechanistic-probabilistic   basis   In
terms  of   chemical  reactions  between  toxicant
molecules and receptors of the organisms.
   The  application  of   a   general   multiple
toxicity model  1s demonstrated  using published
experimental  results   regarding  the  action  of
binary combinations of  N1,  Cu,  potassium penta-
chlorophenate, dieldrin,  and potassium  cyanide
on male  gupples  (Poecilia reticulata).  We  also
analyze results  of our own  experiments  regard-
ing  the  combined  effects  of   N12+  and  Zn2*
on the  growth rate based on cell  volume of  the
green  alga Selenastrum  capricornutum.   Most  of
the multiple  toxicity  data  are fitted  well  by
the model.

   Aquatic Ecotoxicology 1s 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
   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  is
Important.  It is well known that the ionic form
of metals such as Cd, Pb, Mi, or Cu is generally
more  toxic  than  the  complexed  forms (3).   For
organics,   e.g.,    polychlorinated   biphenyls
(PCB's)  or   polycyclic  aromatic   hydrocarbons
(PAH's), the octanol-water partition coefficient
is  of  interest.   This  is  because there  1s often
a  correlation  between  this  coefficient,  the
lipophility,  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
many  different  compounds   and   a  variety  of
organisms  such  as fish  and algae  (2,5).   How-
ever, in most cases,  only one  toxicant has been
considered  1n  any  given  experiment.    This  is
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.

   The  response  of  aquatic  organisms  to toxi-
cants can  be  evaluated  from bioassays conducted
1n the  laboratory or 1n the field,  or in some
cases,  from the  observation of  actual  ecosys-
tems.   Possible  forms for  laboratory bioassays
are shown  1n  Table  1  (6).  For most macroorgan-
isnis,   or   mixed  cultures   of  microorganisms
(Groups I  and  II),  there 1s  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   1s  no
tolerance  distribution   for  Individuals  which
will  respond 1n the same way to the toxicant.
   The  response  can  be  quantal  or continuous.
An example of a  quantal response  1s 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  is extended
to apply also to Group IV organisms.

   Dose-response  models  for a  single toxicant,
assuming  a fixed  time  of exposure,  e.g., 96h,
are  shown  In  Table 2.  Of  these, the   probit
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 Weibull transformation (9).
   The  probit,  loglt,  and  Weibull  models must
be  considered  mainly  empirical  although some

                       TABLE 1.  Populations of Organisms Considered 1n Bloassays
                                                TYPE OF RESPONSE
                             Quanta! Response
                                               Continuous Response
 Tolerance Distribution
 for  Individual Organisms
 All Organisms from a Single
 (No tolerance distribution
 for Individual organisms)
                      Group I

                      Response: death of an organism
                      Classic problt analysis
                      Binomial statistics

                      Group III

                      Pure culture of microorganisms
                      Special case:  Synchronous
                      Response: growth rate based on
                      cell number
                                         Group II

                                         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  Welbull  Transforma-
          tion with  the  Problt  and Loglt Trans-
  Probability of
   Response or
Relative Inhibition
Weibull   u - In k + T, In z    P - 1 - exp(- eu)

Problt    Y - a + B log z      P - |(Uerf(^))

Logit     l = e + 4, In z       P* 1/(1 + e~l)
     *z 1s a toxicant concentration
      k, n.. a, B, 9, 4> are constants; A - In k
theoretical basis has  been  claimed.   The problt
model  1s  based  on  the  often found  log-normal
distribution  1n  biological  systems.   The  logit
model  is valid  for  certain  types  of  autocataly-
sls  and  enzyme kinetics  (Group  III  and  IV  or-
ganisms)  (10,  11).    The  parameter  <>  is  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  is  related   to  the   multistage
model  in carcinogenesis and  is identical  to  the
single-hit model for n = 1 (14).

   Fish.   To  illustrate differences between  the
probit  and  Weibull   models,  we  shall  consider
the  experimental  results  of Broderius and Kahl
(15)   on   the  mortality  of  fathead   minnows
(Pimephales promelas)  in the  presence  of each
of  27  different  organic  chemicals.  A  plot of
the  results  obtained by these  authors  1s shown
1n  F1g.  1,  where the  toxldtles  have been nor-
malized   (M   96h   LC50)   to   the   potency  of
1-octanol.   The  normalized experimental  results
and  the  problt  line (  = 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.
                                              Sb   6

                                                      --  WEIBULL
                                            F1g. 1.
                                       TOXICANT CONCENTRATION (Log M)
                                   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   Broderius   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  LC50-values only,  and  not  the
                                            slopes,  it  1s  not entirely appropriate to use a
                                            statistical  criterion  such  as  chi-square  to
                                            compare  the goodness  of fit of  the  two models.

However,  since  the  slopes  of  the  27  dose-
response  curves  were  fairly  similar,  and  the
mortalities  were   fairly  evenly   distributed
between 0  and  100X, a  comparison may  still  be
valid.  From  F1g.   1  1t  1s  seen  that  the  test
data tend  to follow the curved Welbull  function
rather  than  the  straight problt  line.   Similar
observations on  other  bioassay  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  90%)  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  Is
rather  trivial  for  values of  log  M between -4.1
and -3.9.  However, at  log  M   -3.8,  the problt
model  predicts that  255 out  of  105  organisms
will survive, while the corresponding number for
the Welbull function  1s only  5.   Similarly,  at
log M = -4.3,  the  problt model  Implies  that  al-
most no organisms are affected (only  4), whereas
a  total of  1230  are  killed  according to  the
Welbull model.

TABLE 3. Number of  Fish Killed (fathead minnows.
         Plmephales promelas) out of an Initial
         Population  of10s as  Predicted  from
         the Problt and Welbull  Models.    The
         parameters  of   the  problt  model  (a  =
         59.1;  0 -  13.5)  are  from Broderlus  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.
(log M)

Corresponding to broken vertical lines 1n F1g.  1
   Algae.   The  models  for  one toxic  substance
listed  1n  Table  2  have  been applied  to  the
growth  of  the  diatom Navicula  Incerta exposed
to  Cd,  Cu.  Pb, and  Zn.   The raw  data  are from
Rachlin, Jensen, and Warkentlne (16).
   The  results for  Navicula incerta  are  given
1n Tables 4 and Fig. 2.  From Table 4 it is seen
that the  Welbull  model  provides the better fit
compared to the problt and loglt models when the
number  of  degrees of  freedom are  two  or more.
The  slope n  appears  to assume  the  value  0.5
for Cu,  Pb,  and Zn when growth  rate  is used as
a  parameter.    The  interpretation  of   n may be
the number  of  .toxicant  molecules  per receptor
of  the organisms,  and  the  implication  in  the
present  case   1s,  therefore, that each of  the
metals  Cu,  Pb. and  Zn combines  with  two recep-

   We have  expanded  Hewlett and Plackett's (17)
blvarlate normal model to Include any mono-
tone   tolerance  distribution   for  Individual
.toxicants,  such as  a loglt or Welbull distribu-
tion, and  n toxicants (12).   Let  us consider a
general blvarlate 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  (\ = 1),
different  (x * 0),  or  partially  similar bio-
logical  systems (0  <  X  <  II).   The other para-
meter  p  1s  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  1s  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  1s  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,  1t 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)   is  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  univariate  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).
    Fish.   We  shall  here  analyze  the   results
obtained  by  Anderson  and  Weber   (20).   They

TABLE 4.  Fit of  the  Weibull, Problt,  and  Loglt Distribution  to Growth  Data for  the  Diatom  Navicula
          Incerta.  The Raw  Data  are from RachUn,  Jensen,  and Warkentlne (16).  Concentrations  are  1n


Toxicant df*
Cd 1 -2.13 0.895
Cu 2 -2.59 0.561
Pb 3 -2.26 0.561
Zn 6 -1.75 0.431
Cd 1 -1*31 0.797
Cu 2 -1.72 0.554
Pb 2 -2.07 0.650
Zn 6 -2.59 0.958
a 0
3.71 1.53
3.49 0.831
3.74 0.807
4.01 0.665
4.21 1.66
3.94 1.03
3.83 1.01
3.32 1.69
6 4>
-2.18 1.12
-2.61 0.641
-2.19 0.625
-1.66 0.495
-1.31 1.18
-1.77 0.745
-1.99 0.755
-2.91 1.27

*Degrees of Freedom
           e 0.8
           S 0.6
           uj 0.2
                                     Navicula incerta

                       LOG CONCENTRATION (ZINC, mg/l)
                         Navicula incerta

          LOG CONCENTRATION (ZINC, mg/l)
Fig. 2.   Fit of the Welbull, problt and loglt models to growth parameters for Navicula Incerta:
          (a) relative  growth  rate, and  (b)  relative yield,  both  based on  cell  number.   The raw data
          are from RachUn, Jensen, and Warkentine (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,  in  contrast  to  their
approach,  we  include not  only problt  but  also
loglt and Weibull  transformations.
   Basic  problt  lines  for  the  action  of  the
individual toxicants  nickel  (N1),  copper (Cu),
potassium  pentachlorophenate   (PCP),  dleldrln
(HEOD), and potassium  cyanide  (CN) on male gup-
pies (Poecllia reticulata) 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  in a  batch.   The  weight  W  modifies  the

concentration  H of  a  toxicant such  that  the
"effective  concentration'  M/Wn  (h  =  0.67  -
0.81) remains  the  same  either  for  a high actual
concentration  and  high average  weight  of  fish
or a  low  actual  concentration  and  a low average
weight of  fish.   In other words,  the  Important
quantity  1s  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.   Probit of  Mortality  to   Male  Guppies
          (PoeclHa   retlculata)    for   Several
          Toxicants.  M(mg/l)  1s  the Concentra-
          tion of  the  Toxicant and  W(g)  1s  the
          Weight   of Each  Lot  of  F1sh.    The
          relationships  are  from   Anderson  and
          Weber (20)
      6.5 = - 3.21 -H 6.32 log
   In  the  regression  of  the  linear  Welbull
transformation  u  =  In k  +  nln  z,  z  =  z-\  1s
then  34.36  and  u  =  u-i  Is  given  by  ui  =
ln(-ln(l-P)) -  ln(-ln(0.067))  = 0.994.   Similar
points are  obtained for  N.E.O.  -  1.0,  0.5, 0,
-0.5,  -1.0,  -1.5.   The  Intercept  A and  slope
n are then given by:
Probit of Mortality
= -3
- 11
- 11
= 20
= 14
.21 <
.4 ^
.77 H
.83 <
.71 H
> 6
K 7
K 11
> 6
K 11
81 )
                                                        where   0

                                                                1-1 ..... N;  N = 7

                                                               X, - In z,

                                                        For N we obtain A - -9.4 and n = 2.99 (Table 6).
                                                        Table 6.  LogH  and  Welbull  Parameters  Corre-
                                                                  sponding to  the  Probit  Relationships
                                                                  of Table 5
   Loglt  and  Welbull  parameters  corresponding
to the probit parameters  1n  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:

                Q1         2
       w, = n, Hr- (In QJ     Welbull
Qi = the survival fractions corresponding to
     N.E.D. values of -1.5, -1, -0.5, 1, 1.5

Y} = probit of Q^

n^ = number of test organisms 1n trial i (10)
     1=1,2	7

   The  loglt  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  N/W-67 (Table  5)  is  calculated in
the  following  manner, considering  Ni  at N.E.O.
=  1.5:
              e          4
   The  blvarlate  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
Welbull  parameters,  1t  was   estimated  that  a
larger  stepsize.  I.e., 0.1,  was sufficient for
both X and  p  in  search of the  global  minimum
for  x2 which  1s  calculated  according   to the
         = experimental survival fractions,
           e.g.,  70% in the  first  case and
           in the second (Table 7).
         = calculated survival fractions.

      n^ - number of test organisms 1n trial
           1 (10).
       N - number of trials (6).

   We systematically  calculate x2  for  several
combinations of X and p.  The pair producing the
global minimum of x2 1s retained.
   The  results  for  the   binary  mixtures  (N1,
Cu),  (PCP,  HEOO), and  (PCP,  CN) are  listed  1n
Tables (7-9) and  summarized  1n 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  Uelbull  model shows  some distinc-
tive differences.  It produces the best fits for
the  (N1,  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  1n  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 /> 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,
                                    and in  this range  there 1s  not a  great  deal  of
                                    difference  between  the  fits   of   the   problt,
                                    loglt,  and  Welbull  models.   However, as Illus-
                                    trated  by Chrlstensen  and Chen  (12),  the situa-
                                    tion is  different  when high   or  low  response
                                    probabilities  are  Included.   In that case,  not
                                    only will   the  estimates  of   x  and  p  depend
                                    upon the choice  of model,  but  the  problt model
                                    may  not  fit  at all.   The advantage of  using
                                    non-normal   bivariate   tolerance   models  will.
                                    therefore,  be particularly evident  when  extreme
                                    response  probabilities  are encountered  as  for
                                    example in models for cardnogenesis.
TABLE 7.  Evaluation of the Joint Action of Ni  and Cu on Hale Guppies Based on the Parameters
          of Tables 5, 6 and the Computer Program HULTOX
Weight of
Each Lot
of F1sh
1 1.23
Calculated Percent Mortality
for Mln. Chl-Sauare
(X-l; p-0.5)
(X-l; p-0.5)
(X-l; p=0)
__ 80
TABLE 8.   Evaluation of the Joint Action  of  PCP  and  HEOD  on  Male  Guppies  Based  on  the  Parameters
          of Tables 5,6 and the Computer  Program MULTOX
Weight of
Each Lot
of Fish
Calculated Percent Mortality
for Min. Chi-Sauare
Probit Loglt Weibull
(X=0.1; p=-0.1) (X=0.1; p=0) (x=0.1; p=-0.2)




































TABLE 9.  Evaluation of the Joint  Action  of PCP and CN  on Male Guppies Based  on  the
          Parameters of  Tables  5,6 and  the Computer  Program  MULTOX.   The Weight  of
          Each Lot of F1sh Has Been Set to l.SOg



Calculated Percent Mortality

(X-0.2; p 0.8)
for M1n. Ch1-Square
Log it
(X-0.2; p 0.8)

(X-0.1; p 0.8)
TABLE 10.    Ch1-Square for  Binary Mixtures of  Toxicants Considered  in  Tables  7-9  (four  degrees  of


(X-l, p-0.5)

(X-0.1; p0.1)

(X-0.2; p0.8)
(X-l; p-0.5)

(X-0.1;  p-0

(X-0.2;  p0.7)
(X-l; p-0)

(X-0.1; p0.2)

(X-0.2; p0.8)
   The  estimation  of  parameters  when  three  or
more  toxicants  are considered, using  the  above
method  with  x2  as  criterion,  1s  very  cum-
bersome  and we  have  not  attempted  1t.   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  1n  Table 5,
and h (0.67-00.81) is the exponent of the weight
of  each  lot  of  fish.   C]  and  C?  are  the
values  of  M/W**h  for  each  toxicant  that  will
give  the  desired response  when acting separate-
ly.   It is clear  that the isoboles  for Cu  and
Ni (Figure  3a) are close to defining a straight-
line  relationship  characteristic  of  C.A.   This
might  be  expected  since  X-l;   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
n  >  1  for  R.M.   which  is   indicated  by  the
values  of  X  and  p  that  are both   close  to
zero.   Except  for an  interchange  of   indices,
these  curves  are  in  fact  similar  to the curve
                            labelled  1  in 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
                            capricornutum and  the blue-green  Svnechococcus
                            leopoliensis  was modeled as a  function of  ionic
                            concentrations  of N1 and  Zn.
                               We consider  here  the growth  rate of  Selen-
                            astruro based  on  cell volume.   The  experiment
                            was designed  such that  for  each  point,  equi-
                            toxic 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
                            MINEOL (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.


                                 The  following conclusions may  be  drawn  from
                            the present study:

                        INDEX  0


 Cu    Nl

0.202   31.0

0.144   20.7

0.084   11.1
0 0.1
(D 0.5
(3) 0.9

0  0.1

(2)  0.5









                                      C,/C, 1-0           05    C|/C, 1.0   0

                                        MODIFIED CONCENTRATION M(mg/l)/W(g)**h/C,
                                                                                    c,/c, 10
                                     \ 655 day ' (8volume)
                                   SMnasifum capficmnuluni

                                     Nl*2 ?=2.6300 09506InZ
                                     Zn*2 f=2 5834 15576 In Z
                               In (Total km Concentration), Nt * & Zn *
                            11    059 0.34
                               In (Total Concentration). Nl 4 Zn
Fig. 3.  Isobolograms  for the  effect  of  (a)  (N1,  Cu),  (b)  (PCP,  HEOO).  and  (c)  (PCP,  CN)  on  male
         gupples based on  the Welbull  model with optimum  values  of  X and p (Table 10).

                                                              models.     The   Welbull   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-
                                                         (3)  A general  nonlnteractlve multiple toxlcity
                                                              model  was  applied  to  literature  data  for
                                                              the toxldty of binary  mixtures of N1,  Cu,
                                                              PCP, HEOO,  and CN to male gupples  (Poecllia
                                                              retlculata).   We  confirm  that  the  action
                                                            * of  (N1,  Cu)  and  (PCP,  HEOO)  indeed may  be
                                                              approximately  characterized  by   C.A.   and
                                                              R.H.,  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  1n
                                                              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 Welbull 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  bloassays,   in  which  the  growth
                                                              rate was based on  cell number,  demonstrated
                                                              that the Wei bull model  was  preferable,  the
                                                              present  results,   based  on  cell  volume,
                                                              indicate  that  the   logit   model  is   best
                                                              suited to describe the combined response.
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  bivarlate
         logit model with x = 0.9 and p = 1.

(1)  The Welbull  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  Welbull  model  appears  to give  a
     better  fit  to experimental  data, and  that
     it, therefore,  is  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  Welbull,  probit, and  logit

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                                                          (2) Calamari,   0,   Chiaudanl,  and   Vighi,  M.
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     chemical   Injury  to   ecosystems.    SGOMSEC
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 (3) Bowen.  H.J.H.  (1966).  Trace  Elements  1n
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 (4) Wong, P.T.S.,  Chau,  Y.K.,  Kramar,  0.,  and
     Bengert,   G.A.  (1982).  Structure-toxidty
     relationship   of   tin  compounds  on  algae.
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 (5) RachUn,   J.W.,  Jensen, I.E.,  and  Warken-
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     the  green alga  (Chlorella  saccharophlla)
     to selected   concentrations  of  the  heavy
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 (6) Chrlstensen,  E.R.  (1984).   Aquatic ecotoxi-
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 (7) Flnney,   D.J.   (1971).   Problt   analysis.
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 (8) Hewlett,   P.S.  and Plackett,  R.L.  (1979).
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 (9) Chrlstensen,   E.R. (1984).   Dose-response
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(10) Segel,   I.H.   (1975).    Enzyme   Kinetics:
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(11) Sunda,  W.G.   and   Huntsman,  S.A.   (1983).
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     manganese  and copper on cellular  manganese
     and growth 1n  estuaHne and oceanic species
     of the  diatom Thalass1os1ra.  Limnol.  Ocean-
     pgr.  28 (5):  924-934.

(12) Chrlstensen,  E.R., and Chen.  C.-Y.  (1985).
     A general nonlnteractlve multiple  toxlcity
     model Including problt, loglt. and  Welbull
     transformations,  Biometrics 4^:  711-725.

(13) Chrlstensen,   E.R.  and  Nyholm,  N.  (1984).
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(14) Carlborg,  F.W.  (1981).  Multi-stage  dose-
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(15) Broderius. S.  and Kahl.  M.  (1985).   Acute
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(16) Rachlin,   J.W.,  Jensen, T.E.,  and  Warken-
     tine, B.  (1983).   The  growth  response  of
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(18) Chrlstensen,  E.R.,  Chen,  C.-Y.,  and  Fox,
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     nological  University,  Houghton,  Michigan.

(19) Chen, C.-Y. and  Chrlstensen,  E.R.  (1986).
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(20) Anderson,   P.O.  and Weber,   L.J.  (1975).
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(21) Chrlstensen,   E.R.,   Chen,    C.-Y.,   and
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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.

                    Richard C. Hertzberg, U.S. Environmental Protection Agency
  Chrlstensen presents examples of the
application of a noninteraction multiple
toxicant model to several data sets, Including
mortality of fathead minnows and population
growth rate and yield of diatoms.  He
concludes that the mixture Welbull 1s 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
toxlclty, the biological Interpretation of the
Welbull and Us parameters, and the future of
modeling binary mixtures.
  The feeling one gets 1n reading the paper 1s
that the results of the mixture models are
tantalizing yet Incomplete.  To his credit,
Chrlstensen'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 fit for the Welbull, which
1s an Inadequate criterion for model
  Of more concern, perhaps, 1s the motivation
for the models.  Chrlstensen 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 lexicologically similar)
and then shown to be consistent with the
model's results (e.g., lambda*!).  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=1) should also have
the same tolerance distributions (rho=l).  The
Inclusion of this constraint, and verification
by actual data, would Improve the support for
Chrlstensen's approach.  Without such support.
Inferences about toxic similarity from
parameter values are not believable.
  The use of mortality as the toxlclty
Indicator raises several Issues.  First,
mortality Is usually Interpreted as a
non-specific toxic end point, and thus 1t
provides little Information on toxic
mechanism.  Consequently, the Inference about
toxic similarity 1s confusing.  The usual
definition of toxic similarity (EPA,  1986) Is
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
exact cause of death 1s rarely Identified.
Second, mortality 1s 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 In  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-chemlcal 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 Is
to combine expert Judgment with generalized
linear models.  We have adapted the work of
McCullagh (McCullagh and Nelder, 1983) to give
a multi-chemical model which uses Judgments of
the overall severity of the toxic reponse 1n
lieu 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
d1eldr1n-1nduced nephritis (Fltzhugh et al.,
  DOSE   		-		
 (ppm)   None     Slight   Moderate  Severe
  The multiple response curves plotted against
dose (given In  F1g. 1) are not easily
Interpreted 1n 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

steps are as follows:

   1. The main covaMables  (dose,  duration,
      species, route)  are represented  by
      categories  (Intervals  for  the  continuous

   2. The response Is  coded  1n  terms 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
         covaMables.   We are  Investigating
         the log cumulative  odds:
         For a single covarlate,  say dose,
         then J Indexes severity,  1  Indexes
         dose, and q^j Is the log  odds of
         the severity being 1n category 3  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 * 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(Adtb))

   The primary advantage of this  method Is
that the data constraints are minimal;
virtually any type of toxldty data  can be
modeled to give doses that are "acceptable" or
that correspond to low risk.  In addition,this
approach yields maximum likelihood estimates.
The disadvantages are that little Indication
1s given of the mechanisms of toxldty, and
that the dose-response relation 1s limited by
the precision of the dose and response
categories.  What remains to be checked 1s 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 It 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, ChHstensen's work appears most
applicable to ecosystem assessment of simple
mixtures.  The use of Wei bull parameters to
Indicate the nature of the Interactions Is
Intriguing, and should be pursued, Including
validation by chemical pairs with known  '
mechanisms of toxic Interaction.  Further, one
must agree with his caution against the
habitual preference for the probH 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.


FUzhugh, 0., A. Nelson and M. Qualfe (1964).
Chronic oral toxlclty of a'ldrln and dleldrln
1n rats and dogs.  Fd. Cosmet. Toxlcol.

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).

                                 DIELDRIN KIDNEY TOXICITY

                                           DOSE (mg/kg)
                                DIELDRIN KIDNEY TOXICITY

                                           DOSE (mg/kg)


          J.  J.  Chen,  B.  S. Hass, and R. H. Heflich, National Center for Toxicological Research
   Individuals are exposed  to  various mixtures of
toxic  chemicals  in  the  environment.    The
assessment  of health  risks  from  the  exposure
becomes 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" (Finney,  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  common definition  for response-addition is
that combined  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.

   Let  x.  be the  proportion of  chemical C.
(i-1,2) in  a  mixture with  total  concentration T.
Then t "Tx.  represents  the concentration of

chemical  C.  In the mixture.   Suppose  that  *^(tj)
represents  the  (dose)  response  function of
chemical  C. at a dose level  t..   It is  assumed
that  the  response  of  the mixture,  R(t^,t2)   "

R(x.,x.,T), can be expressed as
   R(XI,XZ,T) -

          xx FX(T) + x2 F2(T) + E(x1,x2,T).   (1)

 The  terms x.F,(T) and x.F-(T) may  represent the
 "expected"  responses produced by administration

 of  the   single  chemicals,  and   E(x1>x2>T)  then
 represents  the  "excess"  of the response  over

 x F  (T) + x F  (T) produced by the mixture.
    In equation (1),  the  data were  collected  at
 different total  concentrations   of   the  mixture
 with  each  concentration  consisting of  several
 different  proportions  of  the  two chemicals,
Figure  1.   This  model was  first introduced  by
Scheffe (1958)  for studying mixture  experiments
with only one concentration.
   The joint action of the two  chemicals  is  said
to be "response-additive" if E(x.,,x2,T)  0,  for
all x. , x2, and T  with X..+X -1.   That is,  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 chemicals  in the mixture.   For
a  fixed concentration T,  the  response-additive
model can  be expressed as  a linear  function of
the proportion of  a chemical 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)
   R(x1,x2,T) -
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
   Without loss of generality, assume that F2(T)>
F.(T),  i.e. m>l.   If the joint action  of  C.  and
C  is  dose-additive then
                                                                     F1[(x1-hnx2)T] > F1(T)
That   is,  the  response  predicted  by  dose-
additivity  is  bounded  by  the  two  responses
produced  by  the single  chemicals  of  the  same
total concentration.  If the response function FI
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

for any
and T with
                             + x,
                                     1.   Two  non-
 additive  actions,  synergism and antagonism,  can
 be   defined  by   using  equation  (4).     The
 synergistic  (antagonistic)  action  occurs if  the
 response  of  the mixture  is greater (less)  than
 the additive response, that is,
   R(xlfx2,T) >
                                 < F^T)]      (5)
This, definition agrees with that of Vendetti  and
Goldin (1964) for studying the combination of  two

   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,  1983).  Equations  (4)
and  (S)   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 equlpotent, i.e.,

F^T') -  F2(T').   At  the  "concentration  T1" in

the mixture, the response predicted by response-
additivity, Equation (1)  is
for any  "proportions"  x^^  and x-.   The response

predicted by dose-additivity, Equation  (2) is
That is, at the concentration T1 the response of
the mixture predicted by dose-additivity  and
response-additivity  is  constant  regardless of the
proportions of  individual  chemicals  In  the
   A procedure  for testing dose-additivity can be

constructed.   Suppose  that doses  mT of  C.  and
dosage  T of  C,  produce  the  same  level,  p,  of
response,  e.g.,  50%  effect.    (This  can  be

obtained by plotting  the  dose-response  curves  of
each chemical.)  The  concentrations mT  of  C,  and
T of C2 will be used as the standard preparations
for   constituting   various  mixtures  of  the
experiment.   Each  mixture will  contain XjmT  of

compound C. and x2T of chemical  Cj,  where x..,x2 >
0,  and  X.+X -1.   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

   X -  Z     JJ	
       j-1     n.j p (1-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

    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(xlfjc2,T) + e
                                                      The  variations e are  assumed  to  be independently
                                                      and  normally  distributed with zero  mean and
                                                      common variance.    The  functions   F.(T)  and
                                                         ,^,x2,T),  in general,  can  be represented  by
                                                       E(x^,x2,T),  in

                                                       polynomial  forms;  that  is,  equation (1)  can  be
                                                       expressed as
                                                                                             bU2  T >
                                                      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

where B.(T), B2(T), and B12(T)  are  defined by the
last equality of  the equation.   This model was
proposed by Fiepel and  Cornell  (1985),  and was
referred to as  the mixture-amount  model.   Non-
polynomial  functions of dose T, e.g., log T, may
be appropriate for certain bioassay responses.
   It  can  be  shown  that the  maximum  response
occurs in the experimental dose range if  B.-(T)>0

provided that B^T) + B12(T) > B2(T)  and B2(T) +
B12(T) > B.(T) for all T;  similarly,  the minimum

response occurs in the experimental dose  range  if

B12(T) < 0  provided  that B^T) + B12(T)  <  B2(T)

and B2(T) + B12(T) < B^T).
   Equation (7), alternately, can be expressed  as
                       + b2x2 +
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  +  b12 Xj^)
represent  linear  and  nonlinear effects  of   the
proportions  in the  mixture  at  the  average
concentration of the experiment .
   If  b12  -  b121  -  b122  - 0,  then the joint
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 b1  -
                      - b22 - 0, then
      (b,x1 + b2x2); the lines in Figure 2 are

    coincident,  the chemical concentration has no
    effect  on  the  response.
2) If
                               then R(XI,XZ;T)
    (bj^  + b2x2) + b11T 4-  bj2!2;  the  lines in

    Figure  2 are parallel, the response increases

    by  a   constant  amount   as  concentration
    increases .
3) If b
             b2  -  b11
                             - 0, then
                                                                    +  b21x1 4-
                                                                                          the  lines  in
                                                          Figure 2 are not parallel,  the  response
                                                          increases     proportionally     with
                                                          concentration .
                                                          Equation  (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  muta-
                                                       genesis data,  Snee  and Irr (1981)  suggested using
                                                       the Box-Cox (1964)  power transformation  model
                                                                             4- e  for
0;    (10)
                                                       log  y   -  log  [R(x1(x2)] 4- e  for  X  - 0  ,

                                                       where  A 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-NBP  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 Maron  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-NBI

Revertants per Plate




   The Box-Cox power  transformation  was  used to
ensure  that  the  assumptions  of  normality  and
homogeneous variance  of  experimental error were
satisfied.   Using the 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  '  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)


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,  b1   -  147 and b.  -  435,  and
the nonlinear term, b.._   4190,  in the mixture

components.   Moreover,  it can  be shown  that  a
synergistic  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.

Ames, B.,  MaCann,  J., and Yamasaki, E.  (1975).
   Methods for detecting  carcinogens  and mutagens
   with  the  Salomella/mammalian  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.H.,  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.G. (1980).   Quantita-
    tive  methods  for  describing  interactive
    effects in toxicology.  Technical Report  No.
    1-6-80,  Montana   State  University,   Bozeman,
Irr, J.D. and  Snee,  R.D.  (1982).  A  statistical
    method  for the  analysis of mouse  lymphoma
    L5178Y cell TK locus 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  mononltrobenzo(a)pyrenes:
    synthesis, identification and mutagenic
    activities, Mutation Research,  140, 81-85.
Reif, A.E. (1984).    Synergism in Carcinogenesls,
    Journal  of National  Cancer Institute,  73,
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 hypoxanChine-guanlne  phos-
    phoribosyl transferase locus of  cultured
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    Research,  85, 77-98.
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    synergism in  antinioplastic chemotherapy,
    Advance Chemotherapy,  1, 397-498.

                                      Dose of
                                                                                  Dose of





               5. O
               O O
               3 o>





                      Elizabeth H. Margosches, U.  S.  Environmental Protection Agency
   I am pleased to have the opportunity  to  comment
on this paper.  When Dr. Chen first sent me the
paper, several directions for comments came to
mind.  At this conference we have already heard
many speakers refer to the properties of response
additivity.  Nevertheless , there are some special
points here.
   Chen et 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
endpoint, mutagenicity.
   Chen et 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 et_ al. appears to be on the latter  and,  as
we've heard from several speakers, this  is  an
important 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
   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
   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 come  to  mind have 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 pairwise isoboles:   again,  we're
bound by the paper plane.   What about colors,
faces, perspective, etc.  It's  almost ten years
since Gnanadesikan published his book on ways to
look at multivariate events.  Let's consider
other graphic 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) - x^jtT)  + X2F2(T)  + E(x1,x2,T),

where E(xi,x2,T) - 0 for any xj, 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


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

  Purpose    provide risk estimates
           from Joint exposure

  Situation  assume components are
           predict curve at dose
           noc studied

  Methods    procedures robust
  need      against misspecifica-
elucidate mechanisms
of joint toxicity

assume components are
decide If joint action
at dose studied

tests of full v
reduced models

                           Ronald E. Wyzga,  Electric  Power Research Institute

   The 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 is likely.
This can help assess mixtures toxicity 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.


Joint Action Models
Complex Mixtures
Combined Toxicant Effects

                 1.   INTRODUCTION

   This paper attempts to summarize the use 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 analyze more complex mixtures,  which  realis-
tically reflect exposure.  Environments  are
complex; pure 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 assume a different role here  as  the
experimental agents may 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.


   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
   The most commonly asked questions probably
relate to the three given below.

   1.  Under ambient conditions,  Is the  mixture
      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 addltlvlty 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

(1986) address the toxlclty of mixtures over  dose
ranges where extrapolation models are 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 less are of policy concern.
   The collection of papers suggests that
question la can be answered for simple mixtures
of two to three substances.  A response to this
question for more complex mixtures is hampered by
unwieldy experimental designs and unrealistic
data requirements.  This situation can be alle-
viated somewhat by fractional 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, Levin and coworkers (1986) demonstrate a
relatively complex "interactive" effect of CO and
CO2 on the mortality of rats.  Over a part of the
dose range, mortality response appears to
Increase with Increasing C02 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.


3.1  Information Availability

   The nature of available Information will
obviously influence the approach for addressing
the mixture's toxicity.  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
tn the next section.

3.2  Pharmacoklnetlcs

   Another Important information question is  that
of pharmacokinetlcs.  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" is 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 were to change as 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 pharmacokinetic 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-
cokinetic 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
pharmacokinetics is clearly  warranted  in
assessing the toxicity of mixtures.  The develop-
ment of both pharmacokinetic 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), yet  would still allow
estimation of the toxicity of all 15 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

results, mixtures of several known components can
be easily addressed by adding the toxicity of the
components.  This requires, however,  that the
toxicity of the components be known.
   When the components of a mixture are  unknown,
two approaches are possible.  A mixture  with
unknown components can be fractionated  into
mutually exclusive mixtures; the  resulting
mixtures then can be analyzed as  if they were
single substances to estimate any "Interaction"
of the resulting mixtures.  Such  an approach has
been considered to address the toxicity  of
unleaded gasoline, a very complex mixture whose
constituents are not completely specified.
(Feder et  al.  1984).
   When the components of the mixture are not
known, a second approach  is to study  the mixture
directly as has been done with cigarette smoke.
If the mixture toxicity  is of interest,  it  may
not matter whether or not there  is  interaction
among the  mixture's components.   The  toxicity
could be assessed  for several mixtures in  the
same class (e.g.,  different brands  of cigarettes,
vapors  from different gasolines  or  exhaust  fumes
from different dlesel 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 term large
enough  to double the risk over that  predicted by
additivlty at  low doses.  Under that design, for
x,  at  a level of 1.05415 x 10"5 the  risk Is about
 1 x  10~5.   For x, at 2.10828 x 10  ,  the risk is
 also  about 1 x 10  .   Under an additive model,
 the  risk of a mixture  of x^ and ^ would be
 2 x 10" ,  whereas the true model gives  the risk
 of 4  x 10  .   Now If only a mixture  of Xj and
 *2 " X3 were tested ln a bioassay design,
 extrapolation from the high dose levels In
 Table 1 (4.8713 x 10~J for Xj and 9.7486 x  10~J
 for x,) would yield a risk estimate  of  about
 3.9 x 10   for the mixture at the low  dose  level
 with true risk 4 x 10  , I.e., we would over-
 predict the mixture's toxicity by an order  of
 magnitude.  This result should be placed in
 perspective, however.  Table 1 reflects an
 extreme example and a factor of  ten  may be
 reasonable given some of the other uncertainties
 Inherent  In similar risk assessment  exercises.

                5.  MODEL DEPENDENCE

    Models are a  major topic of this  conference.
 All of the papers assume some model  in addressing
 mixture toxicity, although the complexity  of
 models varies considerably  from  response  and
  concentration additive  models to Hewlett-
  Plackett, Ashford-Cobbey and  multistage models.
  In some papers,  the models are  tested to  deter-
  mine  If  they  are consistent  with data.  It Is
  noteworthy  that  the data are not always consis-
  tent with a  given model.   In the case of  the
  multistage  model,  there Is  no  way  to test  the  fit
of the model in the  "low"  dose  range.   A model
may not be appropriate and  assumption  of the
wrong model can lead  to  Incorrect  Inferences.
Slemiatycki and Thomas (1981),  as  Kodell (1986)
has pointed out,  show that  "data  can be consis-
tent with a particular model  even  though the
underlying conditions...are not met."   As a
result of this, a fitted model  may be  incorrect
and lead to incorrect Inferences  about inter-
active effects.   Slemlatycki  and  Thomas (1981)
Illustrate this point well.
   There are three alternatives to this
problem.  One  Is  to  apply  several models and to
place greatest confidence  in  those results where
several models converge.  Christenson  (1986)
applies several models to  the same data.  The
models agree over a  fairly wide range, but
diverge considerably in  the tails yielding
considerable uncertainty about what happens
   A  second approach to  this  problem Is to use
the data to generate a dose-response surface.
Chen  et al.  (1986) gives one  approach to this
problem.  An alternative Is that  applied by
0*Sullivan  to  the fire  toxicology data of Levin
et al.  (1986).   Using generalized linear models
to estimate  the  toxicity of Individual components
and  their combination from the experimental
data.  Given  the  availability of  recent codes
such  as GLIM,  these  methods are relatively  easy
to  apply,  and  require relatively  few underlying
assumptions.   The principal drawback of this
approach  Is  the  requirement of a  large  number  of
data  points,  considerably  more than usually
available  from experimental data.   Also,  for  this
method it  can  be dangerous to extrapolate  outside
 the  range of tie observed  data because  Inter-
actions  among  the mixtures components  may  be
 dose-dependent in some  poorly  understood  manner.
    Another way to avoid the use of  a  specific
 model relating toxicity to dose  is  to  apply
 Bayesian  methods  to  extrapolate between mixtures.
 The work of Harris  (1983)  and  DuMouchel and
 Harris (1983)  Is  instrumental  here.   They  see the
 problem as one In combining  experimental  results.
    Consider a collection  of  mixtures  with  yi
 denoting the experimentally  derived toxicity  or
 some other property  of  mixture 1; 9^  is the true
 measure of y^ for mixture  i.   The problem Is  to
 ascertain 9. for another  mixture  j, using all
 available evidence.  DuMouchel and Harris  (1983)
 define y " 9* + *  where  et Is  a measure  of
 "within-experlment   error.  Xj^ is a vector of
 characteristics  for mixture  1, such as physical-
 chemical characteristics,  component data,  or
 selective toxicity  results.   The authors then
 define a hypothetical common mechanism, f, that
 relates the 9's  to  Xt,  namely, /i " 9i + ei *
 f (Xt, p) +6,,  where p Is a set of hyper-
 parameters and 6t Is the  "error  of imperfect
 relevance" between  studies.   For example, 6^,
 could represent  nonlinear Interactions between
 elements In the  mixture 1, if f  were  a linear
 model.  DuMouchel and Harris (1983) then develop
 and  use prior  distributions  on the 6t, the e^,
 and  P, to estimate  the  posterior distribution of
 9^ given  data y.
    An example of the above would be the estimate
 y, of  the  carclnogenlclty of a mixture i,  such as
 unleaded  gasoline:

         ?i " "I + ei " f  (XI' B) + 6i  '

where 9^ is the true carcinogeniclty of the
mixture, e^ is some error associated with  the
measure of yt such as the error due to
extrapolating from rats to humans or the error
associated with a short-term test.  The p  could
be a vector of the toxicities of the major
components of gasoline and X^ is the vector  of
concentratigns of the components.  For example,
f(X1,8) - XjB, the model could be Interpreted as
an additive model under which the toxicity of the
mixture is the sum of the toxicities of its
constituents.  In this case, 6^ is a measure of
Interactions among the mixture constituents.
Given prior distributions on 6^, e^, and 8,  one
can estimate the posterior distribution of the
mixture toxicity given the data y.  One can
extend the context here by defining CL  such  that
y. "9? + ej, where 9 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 may 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 de'lve  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 as 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.  Weber et al.  (1985),  for
example,  help  Identify  greater needs  by following
their  intuition to  illustrate  the poor  behavior
of  zinc-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 one 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 use statistics to move
   away  from  this  approach towards one that is
   consistent with biology.


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  May 5-6, Washington, D.C.

  "Concentration and Response Addition of
  Mixtures of Toxicants Using Lethality, Growth,
  and Organ System Studies," presented at  the
  ASA/EPA Conference on Current Assessment of
  Combined Toxicant Effects, May  5-6, 1986,
  Washington, D.C.

                                                                                      ASA/EPA   CONFERENCE

                                                                                ON  CURRENT   ASSESSMENT   OF

                                                                               COMBINED  TOXICANT  EFFECTS
                                                                                                CAPITOL  HOLIDAY  INN

                                                                                                 WASHINGTON, D.  C.




                                                                                                   MAY  5-6,  1986




                                                     CAPITOL HOLIDAY  INN,  WASHINGTON,- D.C.
                                                                   MAY  5-6,  1986
                                                   Conference Chair:  Emanuel Landau
                                                                     American Public Healch Association
                             Monday. Hay 5
                                                                                                      Tuesday. May 6




 9:00 AM




:30 -
:00 -
:15 -
:45 -
:15 -
:30 -
:45 -





Ralph L. Kodell, National Center
                  for lexicological Research
Keynote:  Modeling the Joint Action of
 Toxicants:  Basic Concepts & Approaches



Todd Thorslund, ICF/Clement
Use of the Multistage Model to Predict the
 Carcinogenic Response Associated with Time-
 Dependent Exposures to Multiple Agents

Discussant:   Paul I. Feder, Battelle Columbus Labs


Stella G. Machado, Science Applications International
Assessment of Interaction in Long-Tern Experiments

Discussant:  Chao Chen, Carcinogen Assessment Group,  EPA



Lavern J. Weber, Mark Hatfleld Marine Science Center
Concentration and Response Addition of Mixtures of
 Toxicants Using Lethality, Growth, and Organ System

Discussant:  Bertram D. Lltt, Office of Pesticides, EPA


 9:00 -  9:30 AM

 9:30 - 10:00

10:00 - 10:15

10:15 - 10:30

10:30 - 11:00

11:00 - 11:30

11:30 - 11:45

11:45 -  1:15 PM

 1:15 -  1:45

 1:45 -  2:15

 2:15 -  2:30

 2:30 -  3:30

 3:30 -  4:00
Steven J. Broderluc, EPA Environmental Research
                      Laboratory, Duluth
Joint Aquatic Toxlclty of Chemical Mixtures and
 Structure-Toxiclty Relationships

Discussant:  G. P. Pa til, Center for Statistical
              Ecology and Environmental Statistics,
              Penn State University



Eric R. Chrlstenien, University of Wisconsin-
Development of Models for Combined Toxicant

Discussant:  Richard C. Hertzberg, EPA



James J. Chen, National Center for Toxlcological
                Research, FDA
 A Response-Additive Model for Assessing the
  Joint Action of Mixtures

Discussant:  Elizabeth H. Hargoschea, EPA


Summary of Conference:  Ronald Wyzga, Electric
                         Power Research Inat'itute


        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.  20460

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
401 M Street, S. W.
Washington, D. C.  20460

Judith S. Bellin
ORD RD 681
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C.  20460

Hiranmay Biswas
7702 Middle Valley Drive
Springfield, Virginia  22153

Steven J. Broderius
Energy Research Laboratory
Environmental Protection Agency
Duluth, Minnesota  55804

Mary J. Camp
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
                                  Environmental Protection Agency
                                  401 M Street, S. W.
                                  Washington, D. C.  20460

                                  Kurt Enslein
                                  Health Designs, Inc.
                                  183 Main Street
                                  East Rochester, New York  14604

Linda S. Erdreich
26 West St. Glair Street
Cincinnati, Ohio 45268

Thomas R. Fears
National Cancer Institute
7910 Woodmont Avenue
Landow Building, Rm. 3B04
Bethesda, Maryland 20892

Paul I. Feder
Battelle Columbus Laboratories
Applied Statistics and
 Computer Application Section
505 King Avenue, Room 11-9082
Columbus, Ohio  43201

Bernice T. Fisher
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C.  20460

Mary J. Frankenberry
Environmental Protection Agency
401 M Street, S.W.
Washington, D. C.  20460

Paul H. Friedman
OSW - WH-562B
Environmental Protection Agency
401 M 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
Union Carbide Corporation
PO Box  8361, 770-203A
South Charleston, West Virginia 25526
Richard C. Hertzberg
Environmental Criteria and
 Assessment Office
Environmental Protection Agency
Cincinnati, Ohio  45268

Joseph F. Heyse
Merck Sharp & Dohme Res. Labs
West Point, Pennsylvania  19486

Stephanie Irene
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C.  20460

W. Barnes Johnson
Stat. Pol. Branch, PM 223, 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  72079

Aparna M. Koppikar
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

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

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
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. Margosch.es
Office of Toxic Substances
Environmental Protection Agency
401 M Street, S. W.
Washington, D. C.  20460

Margaret McCarthy
Div. of Public Health
University of Massachusetts
Amherst, 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
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  16802

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
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
112Q4 Schuylkill Road
Rockville, Maryland  20852

Ms. Judy A. Stober
Health Effects Research Lab.
26 West St. Glair 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 Potfer 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