&EPA United States Environmental Protection Agency Office of Policy, Planning and Evaluation Washington, DC 20460 EPA-230-03-87-027 Statistical Policy ASA/EPA Conferences on Interpretation of Environmental Data I. Current Assessment of Combined Toxicant Effects May 5-6, 1986 ------- DISCLAIMER This document has not undergone final review within EPA and should not be used to infer EPA approval of the views expressed. ------- Statistical Policy vvEPA ASA/EPA Conferences on Interpretation of Environmental Data I. Current Assessment of Combined Toxicant Effects May 5-6, 1986 ------- PREFACE This volume is a compendium of the papers and commentaries that were presented at the first of a series of conferences on interpretation of environmental data conducted by the American Statistical Association and the U. S. Environmental Protection Agency's Statistical Policy Branch of the Office of Standards and Regulations/Office of Policy, Planning, and Evaluation. The purpose of these conferences is to provide a forum in which professionals from the academic, private, and public sectors can exchange ideas on statistical problems that confront EPA in its charge to protect the public and the environment through regulation of toxic exposures. They provide a unique opportunity for Agency statisticians and scientists to interact with their counterparts in the private sector. The holding of a research conference and preparation of papers for publication requires the efforts of many people. Gratitude is expressed to the ASA Committee on Statistics and the Environment which was instrumental in developing this series of conferences. Thanks are also owed to members of the ASA staff and, particularly, Ede Denenberg, who supported the entire effort. Although there was no provision for a formal peer review, thanks are also due to the reviewers who assessed the articles for their scientific merit and raised questions which were submitted to the authors for their consideration. The views presented in this conference are those of the individual writers and should not be construed as reflecting the official position of any agency or organization. Following the first conference on "Current Assessment of Combined Toxicant Effects," in May 1986, a second was held in October 1986 on "Statistical Issues in Combining Environmental Studies," from which a proceedings volume will also be published. The subject of the next conference, scheduled for May 1987, will be "Sampling and Site Selection for Environmental Studies." Emanuel Landau, Editor American Public Health Association Dorothy G. Wellington, Co-Editor Environmental Protection Agency iii ------- 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 IV ------- 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 ANDERSON, CARL MUSKA, ELIZABETH YINGER, DENNIS SHELTON, Oregon State University 30 Discussion. BERTRAM D. LITT, Office of Pesticides, U.S. Environmental Protection Agency 44 Joint Aquatic Toxicity of Chemical Mixtures and Structure-Toxicity Relationships. STEVEN J. BRODERIUS, U.S. Environmental Protection Agency, Environmental Research Laboratory, Duluth 45 Discussion. G.P. PATIL, C. TAILLIE, Center for Statistical Ecology and Environmental Statistics, Pennsylvania State University 63 Development of Models for Combined Toxicant Effects. ERIK R. 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 ------- MODELING THE JOINT ACTION OF TOXICANTS: BASIC CONCEPTS AND APPROACHES Ralph L. Kodell, National Center for lexicological Research Introduction 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 epidemiology. Joint Action Nomenclature In looking into the problem of investigating the joint action of toxicants, one Immediately senses a lack of consistency among investigators with respect to the nomenclature used to characterize various types of joint action. For example, some authors use the term "synergism" very loosely to describe any enhanced joint effect, while others use a term "potentiation" to describe certain types of enhancement and synergism to describe others. The term "additivity" implies the absence of synergism to some, but is a special case of synergism to others. Berenbaum (1977) has described the inconsistent terminology surrounding synergism quite succinctly, although a bit harshly: "Synergy, however, is a topic on which confusion reigns. The relevant pharmacological literature is often obscure (some papers, indeed, are models of incomprehensibility) and is profusely littered with technical terms that are not always clearly defined. Several different terms are used to 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. Addition Noninteragtive_Action Independence Concentration Response Response Addition Multiplication Similar Action Response Independence Interactive Action Synergism Potentiation Enhancemen t Supra-Addition • Antagonism—' Inhibition Attenuation Infra-Addition 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. Null Discipli Toxicology/ Pharmacology Epidemiology Biostatistics Concentra- tion Addition Response Addition Response Multipli- catlon Additivity Summation Additivity Multipli- cation 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 hypo-multiplication. 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 hetero-additivity. Concentration^Additivity 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« 1°8 d., ls "*•* (Finney, 1971). Setting ^ - B2 yi*W« P " exp[(a,-a.)/B ]. Another simple method is the -1 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(d1+d2) 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 additivity. The biostatistical approach to assessing response additivity has involved the fitting of dose-response models. For example, a simple procedure has been to formulate P(d.+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 Additivity 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 needed. Let D., and D, denote exposure levels of toxicants 1 and 2, respectively, that correspond individually to an acceptable level of risk, R. To insure an acceptable level of risk, R, to a combination, dj+d,, of toxicants 1 and 2 under concentration additlvity, then d1 and d, must satisfy (Finney, 1971) dl d2 — + — < 1 . Equivalently, 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 response, 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. Interaction As indicated earlier, there is no clear consensus as to what constitutes "interaction" of drugs or toxicants. In a broad sense, several authors have expressed the concept that interaction is characterized by one agent's influencing the biological action of the other (Bliss, 1939; Hewlett and Plackett, 1959; Ashford, 1981). However, there is disagreement when this broad concept is made more specific. Plackett and Hewlett (1967) pointed out differences between their concept of interaction and that of Ashford and Smith (1965), quoting their definition of Interaction 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 antagonistic. Hamilton (1979) reviewed various measures of synergism that are employed with two-by-two tables of cohort data from epidemiology studies. All have been designed to detect departures from the additive and multiplicative models of relative risk. Investigators who have discussed or used both the additive and multiplicative models of relative risk are Kupper and Hogan (1978), Koopman (1981), Thomas (1981), Siemiatycki and Thomas (1981), 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 factors. Discussion The study of the joint action of agents administered in combination is a very difficult undertaking both conceptually and practically. Even though there is common ground among investigators of joint toxic action, there 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 made. Dose- Response Convex Convex Concave Concave True Situation Concentration Addition Response Addition Concentration Addition Response Addition Null Hypothesis Response Addition Concentration Addition Response Addition Concentration Addition Incorrect Conclusion Synergism Antagonism Antagonism Synergism References Ashford, J. R. (1958). Quantal responses to mixtures of poisons under conditions of simple similar action - the analysis of uncontrolled data. Biometrika 45; 74-88. Ashford, J. R. (1981). 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D. and Holford, T. R. (1978). Additive, multiplicative and other models of disease risks. American Journal of Epidemiology 108: 341-346. Webb, J. L. (1963). Effect of more than one inhibitor. In: Enzymes and Metabolic Inhibitors 1: 66-79, 487-512. Academic Press, New York. Joint Action Studies Type of Agent 1 Drug 1 Type of Effect 1 Pesticide 1 Type of Effect I I Intended Adverse Nature of Effect Adverse Intended I Nature of Effect Therapeutic Toxic Optl Mix Objective mal S« ture Mix 1 Concerns 1 Health fe Ss ture Mix Safety Assessment Objective ife Opt ture Mix mal ture 1 Scientific Disciplines 1 Pharmacology Environment Toxicology Bio statistics Epidemiology Figure 1. Schematic representation of opposing objectives in joint action studies, along with concerns that motivate assessment of combined toxicant effects, and scientific discipline involved. ------- d- 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 "Antagonism" Isobole for "AddJtivity" Isobole for "Synergism" Figure 3. Isobologram depicting some commonly accepted, but not universally accepted, representations of concentration additivity, synergism, and antagonism. Isoboles for response additivity can lie anywhere within the square, depending upon the underlying dose-response curves. ------- USE OF THE MULTISTAGE MODEL TO PREDICT THE CARCINOGENIC RESPONSE ASSOCIATED WITH TIME-DEPENDENT EXPOSURES TO MULTIPLE AGENTS Todd W. Thorslund and Gail Charnley, ICF Clement Associates Introduction In a review of multiple agent dose-response experiments, Filov et al. (1979) notes that the observed interaction effects are usually highly dose-dependent. As a result, such empirical tests of interaction as proposed by Hamilton and Hoel (1979), Machado et al. (1983), and Chen and Kodell (1986) performed at one set of dose levels may give very little information about interac- tions at another set of dose levels. The "high" dose levels for joint effects are defined as the exposure values where statisti- cally 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 agent. 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 variable. Multistage Model The most utilized quantitative model of the carcinogenic process is the simple multistage model described by Armitage and Doll (1954). This multistage model provides a satisfactory explanation of the power law for the age Inci- dence of many forms of epithelial carcinoma. It also explains the time-dependent effects of vari- able exposures, including cigarette smoking (Armitage 1985). The multistage model is based upon the assumption that the carcinogenic process is a series of ordered, irreversible transforma- tions in a single cell. After going through a fixed number of transformations, a cell is con- sidered to be a tumor that will grow and be ob- served some time in the future. If these transformations occur at the molec- ular level, it is reasonable to assume that a single molecule of an agent, if it enters the critical reaction, can cause the transformation from one stage to the next. Under this assump- tion, the probability of a transformation is ------- linearly related 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 (1) where 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 k-1 h(x,t) - n (a 1-0 (t-w)fc /(k-1)!, (2) where 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 |