National Academies Press: OpenBook

Drinking Water and Health,: Volume 3 (1980)

Chapter: III Problems of Risk Estimation

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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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Suggested Citation:"III Problems of Risk Estimation." National Research Council. 1980. Drinking Water and Health,: Volume 3. Washington, DC: The National Academies Press. doi: 10.17226/324.
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111 Problems of Risk Estimation Historically, two approaches have been taken to estimate acceptable levels of exposure to various agents. One approach is based on the application of "safety factors" to levels of the chemical that did not produce an observed effect in animal studies. This approach gives rise to acceptable daily intakes (ADI's) for humans. The other, which has been used to estimate the risk to the population as a whole from low doses of radiation, is based on extrapolation of experimental dose-effect curves to lower dose levels where no data existed. This is called the "risk estimate" approach. The risk estimate approach generally assumes that at all doses some organ, or targets within the organ, will be affected and that there is a finite probability for the occurrence of damage that can lead to ill health, i.e., there is no threshold. This probabilistic approach has been used not only for radiation but also to estimate the risks from carcinogens in drinking water (National Academy of Sciences, 1977~. To estimate risk, adequate dose-response curves must exist for the purpose of extrapolation. However, such data do not exist for the majority of chemicals that are found in drinking water. In these cases the Committee on Risk Estimation continued the ADI approach for noncarcinogens with the belief that it should be used until sufficient data accrue to make risk estimation feasible. The rational determination of a permissible exposure to a toxic chemical in drinking water requires the ability to specify the quantitative nature of the exposure. Thus, the biological factors, such as absorption, distribution, metabolism, and excretion, that determine the toxic ejects both in the animals used for testing and in humans should be assessed. 25

infants, the infirm, or the aged. 26 DRINKING WATER AND H"LTH ACUTE EXPOSURE While considerable attention has been paid to chronic exposure from chemicals in drinking water, the problem of acute exposures from accidental spills and discharges needs consideration. To protect exposed populations, health officials must be able to respond quickly following such occurrences. Observations on humans have provided some of the data on toxicity from acute exposures of I week or less. Clinical observations on the effects of both low concentrations and accidental high exposures, epidemiological observations on various segments of the population, and deliberately planned experiments provide a body of knowledge on dose-response relationships from which one can estimate risk. When such evidence is not available, recourse is often made to experimental exposures in various subprimate animal species. Although information derived from data on the most sensitive species may be desirable, the only data available often pertain to acute oral toxicities in rodents. How the available data base is to be used in the assessment of acute risk is, of course? a matter of great concern. A wide range of"safety factors'' (from 10 to 5,000) has been considered for use with chronic oral toxicity data to estimate an acceptable risk to the exposed population. Unfortunately, none of these safety factors, including the most conserva- tive, has any relevant experimental verification in heterogeneous popula- tions that are analogous to humans likely to be exposed acutely to contaminants in drinking water. The presumed absence of toxic effects at any particular level in an experimental system may not be adequate to protect especially sensitive population subgroups such as the fetus, To determine the safety factor to be applied to the acute toxicity data for a given situation, the following should be carefully evaluated: · quality and quantity of data; · most sensitive target organist or body systems to be affected; · interspecies and intraspecies variations; · nature of the dose-response curve and the time-concentration relationships; · nature and degree of severity of injury at which the effect of the exposure ceases to be reversible; · potential interactions with other environmental chemicals or thera- peutic drugs; · identification of potential cumulative effects;

Problems of Risk Estimation 27 · known chronic or subchronic elects of similar or related com- pounds; · identification of physiologic or pathologic states and functional abnormalities among the potentially exposed population; and · possibility of chronic effects from repeated acute short-term exposure. Because acute exposures to chemical contaminants have no demon- strable beneficial effect on health and because of the desirability of protecting sensitive members of our society, a conservative approach is advisable when establishing permissible levels of acute intake to insure an adequate supply of"safe" drinking water. When compounds in drinking water appear in combination, as they often do, their joint effect may be additive, synergistic, or antagonistic. Some biochemical modeling has been done by Werkheiser (1971), who simulated the effect of antimetabolites on de-novo DNA synthesis, and observed considerable joint action ranging from potentiation through additivity to antagonism. In general, there is not likely to be sufficient information on mixtures of environmental contaminants. Consequently, estimates will out of necessity have to be based on a nonconservative assumption of additivity. The work of Smyth et al. (1969) on the joint action of 27 industrial chemicals is pertinent. They administered doses containing all possible pairs of the chemicals to rats by oral intubation. Comparison of the predicted LI)50 to that observed in the rats that had received the 350 pairs of equivolume mixtures indicated the utility of a harmonic mean formula for estimation of relative hazard: Pa Pb ~ LD50 of component A LD50 of component B predicted LD50 = where Pa' Pb are the fractions of components A and B in the mixture. The ratio of predicted LD50 to observed LD50 covered a range from 0.23 to 5.09. The majority of the time, the observed LD50 was well estimated by the formula (median range of 0.58 to 1.50 in predicted to observed LD50~. Comparable results were achieved for a selected subset of equitoxic mixtures. Data to extend the harmonic mean formula to multicomponent mixtures, predicted LD50 = N i= LD50 of component i Pi

28 DRINKING WATER AND H"LTH where.IP, = 1, are generally lacking, and any attempt to predict acute toxicities of mixtures on this basis must allow for the possibility that a larger number of interactions is possible, and greater uncertainty should be anticipated. However, the use of such formulas for predictive purposes in the event of a spill of two or more agents into the drinking water may be the only way of estimating the toxicity of the mixture. QUANTITATIVE EXTRAPOLATION OF TOXICITY FROM LABORATORY ANIMALS TO HUMANS Reliable information on the toxicity of most chemicals to humans is very diffiluit to obtain. Usually, it must be based on accidental or occupation- al exposures which, by their very nature, are uncontrolled. Assembling information on the degree of exposure is difficult and those who exhibit symptoms are much more likely to be studied than those who do not. ~ nils section summarizes some of the available information on the quantitative aspects of interspecies toxicology. Ironically, the best quantitative data on interspecies toxicology, including humans, have been obtained from work on developing and evaluating anticancer drugs. These are usually cytotoxic agents that involve a variety of mechanisms of action. They are screened against experimental tumor systems in mice and, if sufficient activity is observed, subjected to extensive preclinical toxicology. Then, because of their generally low therapeutic indices, they must be used at or near maximally tolerated doses in the clinic. Thus, it is possible to obtain in ethical well-controlled, and documented studies the toxic levels in several mammalian species including humans. Pinkel ( 1958) examined appropriate therapeutic doses of several anticancer drugs in animals and humans and suggested that cancer ~_ _ =,= cllemotneraplsts consider bony surface area as a criterion tor dosage in both laboratory and clinical studies. Freireich en al. (1966) extended the observations of Pinkel to a group of 18 anticancer drugs. They generally confirmed Pinkel's hypothesis that the body surface area is a suitable normalizing factor for dose. They based their quantitation on the following toxicologic end points: the LD50's for rats or hamsters and the maximum tolerated dose for dogs, monkeys, and humans. Dixor~ (1976) has questioned the usefulness of the mg/m2 extrapola- tion if the clinical estimate is based on data from dogs and monkeys. In fact, when the more sensitive of these two species was used and the dose was expressed on a mg/kg basis. the correlation was excellent. Dixon

Problems of Risk Estimation 29 also observed that introduction of a new anticancer drug at one-tenth of the maximum tolerated dose (MTD) in the more sensitive species would be expected to be associated with a risk exceeding the human MTD of approximately 3%. Goldsmith et al. (1975) argued that the mouse is a reasonably good predictor of human toxicity. The dog would have underpredicted human toxicity in 6 of 28 drugs, whereas the mouse would have underpredicted only 2 of 29. Overpredictions would have been approximately the same for dog and mouse. They did not argue that dose estimation should be based on rodent data alone but concluded that mouse data can be a useful addition to large animal data in estimation of the initial human dose for Phase I clinical trials. The adequacy of quantitation can be observed by comparing the ratio of the human dose (mg/m2) arrived at in a clinical setting to the optimum dose in leukemic mice. The median ratio (for 30 drugs) was 1.5 with a range of 0.08 to 26. In summary, the common practice among cancer chemotherapists of basing dose on body surface area is useful, particularly for extrapolation from small animals to humans, and is supported by a sizeable body of experimental evidence. Since body surface area is approximately proportional to the two-thirds power of body weight, the anticancer drugs are relatively more toxic to the larger animals than to the smaller ones. For example, by the Freireich criterion, the drug dosage given to a mouse (on a mg/kg basis) must be 12-fold greater than that given to a human. CHRONIC EXPOSURE Acceptable Daily Intake The acceptable daily intake (ADI) of a chemical is defined as the dose that is anticipated to be without lifetime risk to humans when taken daily. It is not assumed that this dose guarantees absolute safety. Deter nination of the ADI is often based on the application of laboratory animal toxicity data concerning chronic (long-term repeated) doses to the environmental doses to which humans are exposed. The use of safety (or uncertainty) factors in extrapolating animal toxicity data to acceptable exposure levels for humans has been the cornerstone of regulatory toxicology. The concept of a safety factor arose in the early days of food additive legislation when it became apparent that there was

30 DRINKING WATER AND H"LTH no universally acceptable quantitative method for extrapolating from animals to humans. The originators of the safety factor approach, Lehman and Fitzhugh (1954), founded the concept of the "100-fold safety factor" as a practical means of handling the uncertainties involved in extrapolation. They considered that animals might be more resistant to the toxic ejects of chemicals than are humans. Hence, they applied a factor of 10 when extrapolating from animals to humans. They incorporated another factor of 10 to account for differential sensitivities within the human popula- tion. This concept of the 100-fold safety factor in regulatory toxicology pertaining to food additives has been endorsed by such international organizations as the World Health Organization (FAD/WHO Expert Committee on Food Additives, 19581. The 100-fold factor is usually applied to the highest no-adverse-effect dose measured in animal studies to establish the ADI for humans. ADI's were first applied to food additives Subsequently, the Joint FAD/WHO Expert Committee on Pesticide Residues (FAD/WHO, 1965) used the term ADI in its recommendations. In connection with environmental contaminants, the FAD/WHO Expert Committee on Food Additives (1972) specifically noted that the ADI concept is not applicable to heavy metals and lipophilic substances. These substances tend to accumulate in the body tissues after prolonged exposure. In some instances, different chemical forms of such metals as mercury are difficult to differentiate and may have vastly different toxicological properties. For contaminants, the WHO recommended use of"tolera- ble" intakes to signify permissibility rather than acceptability. "Tolera- bility" is applied only to those situations in which intake of a contaminant is unavoidably associated with consumption of otherwise nutritious food or with inhalation of air. The FAD/WHO Expert Committee on Food Additives (1962) pointed out limitations and expressed reservations regarding use of the ADI. They recognized that animal species, strain, and sex differences, variations in susceptibility among exposed individuals, insufficient laboratory animal data, and a number of other matters must be considered when arriving at the ADI. Food additives or other er~viron- mental contaminants may be ingested by people of all ages throughout their lives. They are consumed by the sick as well as the healthy, and there may be wide variations among individual exposure patterns. Thus, it is not surprising to find that expert committees of the FAD/WHO do not steadfastly use the 100-fold factor, but at times modify the safety factor when there is a lack of available information regarding the particular substance under question. Thus, in 1962 the FAD/WHO

Problems of Risk Estimation 31 Expert Committee on Food Additives (FAD/WHO, 1962) introduced the terms "conditional" and "unconditional" ADI's. The "conditional" ADI's require a larger than 100-fold safety factor due to limitations or uncertainties regarding the available animal data or specifications with respect to the purity and identity of the chemical under consideration. The ADI based on laboratory animal data is also dependent upon the interpretation of a no-adverse-e~ect level. For example, Edson and Noakes (1960), in their investigation of Diazinon, defined an adverse effect to be an important inhibition of red-cell cholinesterase (CHE) activity, where important meant at least a 20% reduction over the control values. This resulted in the determination by Edson and Noakes of a 5 mg/liter no-effect level since it produced only a 19% reduction of CHE activity in red cells. The meaning of a difference between 19% and 20% is questionable. This experimental determination of a no-e~ect level is also dependent upon the number of animals used in the bioassay. The likelihood of observing a no adverse effect at a given dose is statistically greater for experiments with few animals than for larger experiments. (This is due to the fact that statistical tests of hypothesis have increasing power with increasing sample sizes.) Therefore, small studies are likely to produce higher no-effect levels than large studies; yet the ADI concept does not explicitly take this into account. Because of the uncertainties in this method of determining the ADI level, it is desirable to examine the feasibility of improving the use of the animal toxicity data for low exposure noncarcinogenic risk assessment. One approach is extrapolation to low doses from high dose animal toxicity data that show a dose response. The subcommittee has examined the potential of such extrapolation for providing estimates of noncarci- nogenic toxic effects of drinking water contaminants at the low exposure levels that were determined by the ADI calculations in Drinking Water and Health (National Academy of Sciences, 19771. Each of the studies upon which those ADI's were based was reviewed to determine whether the data were of sufficient quality for the dose-response extrapolation. The utility of dose-response extrapolation for noncarcinogenic toxic effects is subject to a number of limitations. Many of the experimental bioassays were conducted at dose levels that were too low to show any adverse effect. For example, Table VI-6 on the toxicity of Amiben and Table VI-54 on the toxicity of methyl methacrylate in Drinking Water and Health (National Academy of Sciences, 1977, pp. 520 and 748) show that the highest dose tested in all the bioassays of these chemicals did not produce any toxic ejects. Therefore, no dose-response extrapolation could be used since no dose-response was observed. Another limitation is the lack of detail in the data reported in some of the published studies

32 DRINKING WATER AND H"LTH of these contaminants. In many instances the numbers of animals tested were not given, the toxic effect was not quantified arithmetically (e.g., the effects were ranked by +, + +, or + + +), or the published report simply stated a no-observed-effect level without supporting data. An additional problem encountered when measuring noncarcinogenic effects is that the toxic response is often difficult to quantify. Behavioral ejects are an example of such responses. Even with quantifiable dose-response information, the results of extrapolation methodology are difficult to interpret, as illustrated by the two examples presented below. One is an example of a quantitative response; the other is an example of a dichotomous (yes-no) response. These two studies are among the best, in the sense of usable published data, for illustrating dose-response methodology The first example deals with the toxicity of hexachlorophene (HCP). Gaines et al. (1973) reported on a bioassay in rats. Ten rats of each sex (Fo generation) were fed HCP in their diets at levels of 0, 1.16, and 5.8 mg/kg/day beginning at the age of 4 to 5 weeks. After treatment for 166 days, the Fo rats were pair-mated to produce the Fit generation. Ten rats of each sex of this Fit generation were continued on the same treatment as their parents. The Fo rats were sacrificed at 258 days and the Fat rats at 145 days. The occurrence of brain lesions was found to be associated with high dietary levels of this chemical and the no-adverse-effect level was found to be 1.16 mg/kg. The combined subchronic toxicity results for both sexes of rats are shown in Table III-1. Because there was no apparent difference in sensitivities between the sexes, they were com- bined for this analysis. For illustrative purposes only, the data for the two generations were combined by using a crude measure of total exposure based on the product of the concentration in the diet and length of exposure. The following dose-response extrapolation is not necessarily meant to be meaningful. These assumptions, the combining of sexes and generations, along with this measure of total exposure, were made in order to construct a usable example of the extrapolation methodology. A log-logistic dose-response model was fitted to these data; the dose was the total dose and the response was the occurrence of a brain lesion. It was assumed that the spontaneous occurrence of such lesions was nil. The fitted dose-response curve was then used to estimate the probability of a dose-induced brain lesion at the ADI level of 0.00116 mg/kg/dlay. This ADI was translated to a total lifetime dose in mg/kg-days for humans based on an assumption of a total population dietary intake of 666 kg/yr (Lehman, 1962) for a 70-kg human over a 70-year lifetime, producing 57 mg/kg-days of exposure. The estimated probability of brain lesion occurrence is 3.3 x 10-5. However, this extrapolation is

Problems of Risk Estimation 33 TABLE III- 1 Brain Lesions Observed in Ten Female and Ten Male Rats That Had Been Fed Hexachiorophenea Number of DietaryTotal Animals with Days on Level,Dose, Brain Lesions/ Generation Diet mg/kgrng/kg x days Total Treated Fo 258 00 0/20 1258 0/20 51290 10/20 F1 145 00 0/20 1145 0/20 5725 3/20 a From Gaines et al., 1973. based on the "best fitting" log-logistic dose-response curve. Many other estimates of the parameters in the model fit these data almost as well. Therefore, to incorporate the statistical variability into this extrapola- tion, an approximate 95% confidence interval on the estimated risk was calculated. This interval indicates that the extrapolated risk lies between 3 x 10-8 and 0.095, an interval so wide as to suggest that little is known quantitatively about the level of risk. This example shows that applying dose-response extrapolation techniques when the data are limited in experimental dose levels and sample sizes will not yield precise risk estimates. The second example deals with the toxicity of 2,3,7,8-tetrachlorodi- benzo-p-dioxin (TCDD) in rats and mice (Kociba et al., 1976; Vos et al., 19741. The ADI in Drinking Water and Health (National Academy of Sciences, 1977) for TCDD of 0.0001 ~g/kg/day was calculated from the results of the Kociba study by applying a safety factor of 100 to the no- adverse-e~ect level of 0.01 ,ug/kgJday. The subchronic toxicity effect of TCDD upon the thymus weights of the rats and mice in the two studies is shown in Table III-2. A general dose-response model relating dose, d, to thymus weight, W. is W(d) = Wo (l-F(a)), where WO represents the weight for unexposed animals and F(a, is a dose-response curve for which F(O) = 0 and is monotonically increasing to a limit of unity. Therefore, W(O) = WO and W(d~) < W(d2) when d' > d2. A log-normal model and a log-logistic model, both of which have the commonly observed sigmoid appearance but have different extrapolation characteristics, were used for F(a0. These

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Problems of Risk Estimation 35 TABLE IlI-3 Estimated Reduction in Thymus Weight at a Continuous Daily Exposure to TCDD of 0.0001 ,ug/kg Estimated Reduction in Thymus Weight, % Model Male Rats Female Rats Male Mice Log normal 0.0004 0.19 Log logistic 0.02 0.87 0.00001 o.oOs models were fitted by the weighted least squares method to each of the three sets of data in Table III-2. The fitted models were then used to estimate the decrease in thymus weight at the ADI level of 0.0001 ,ug/kg/day. These estimated reductions are shown in Table III-3. The variability of the extrapolations is illustrated in Table III-3. Although the female rat appears to be the most sensitive of these three groups, the two dose-response models give quite different results. At a daily exposure level of 0.0001 ~g/kg, the average thymus weight of the most sensitive animal, the female rat, is estimated to be either 99.81% or 99.13% that of the unexposed animals. On the basis of average values, a reduction of this magnitude is much too small to be serious; however, one should be concerned with the effect of this difference in average values upon the proportion of the population at risk that would have seriously low thymus weights. For example. the female rat has an average thymus weight of 0.4 g, and the standard deviation of the distribution of thymus weights is approximately 0.04 g. To illustrate, we shall assume that a thymus weight of 0.25 g is small enough to cause physiological difficulties. Assuming a normal distribution of thymus weights in the population, then the proportion of animals with thymus weights of 0.25 g or less would be 0.0088% in the unexposed population and either 0.0092% or 0.0125970 in a population exposed to the ADI based on the log-normal or log-logistic extrapolation model, respectively. Depending on the extrapolation model used, this implies that 0.0004% or 0.004% of the population would be affected by exposure to TCDD at the ADI value. These calcluations serve as an example of the potential of what may be gained by the application of dose-response methodology to . . . noncarc~nogen~c toxic responses. The potential utility of dose-response extrapolation methodology for noncarcinogenic human risk assessment does exist but has been found to be of limited value for contaminants in drinking water. The models used to estimate risk require lifetime feeding studies which use appropriate numbers of animals of each sex and demonstrate some dose response. As noted above, this type of information is not now available for many of

36 DR]NKING WATER AND H"LTH the contaminants of drinking water. While both the risk estimate and ADI approach require some degree of value judgment, it is the belief of this subcommittee that the ADI methodology is the most useful for noncarcinogenic hazards given the general deficiencies in available data. In situations for which high-quality toxicological data are available, the risk estimate approach would be appropriate for the assessment of noncarcinogenic hazards. Consequently, in the absence of such data the application of safety factors to no-observed-effect levels that have been derived from laboratory animal toxicity data is the most feasible and currently acceptable method for the determination of human exposure limits to noncarcinogenic environmental contaminants. To incorporate differential measures of uncertainty in these ADI calculations, the Safe Drinking Water Committee (National Academy of Sciences, 1977) used the following uncertainty factors: a factor of 10 when chronic human exposure data were available and were supported by chronic oral toxicity data in animal species; a factor of 100 when good chronic oral toxicity data were available in some animal species but not in humans; and a factor of l,OOO with limited chronic animal toxicity data. It should be cautioned that even when complete toxicological data are available, including those from long-term tests, the ADI represents only a judgment regarding acceptable levels of human exposure, and is not an estimate of risk nor a guarantee of absolute safety. Furthermore, the ADI methodology does nothing to correct the deficiencies in mathemati- cal extrapolation methods. The subcommittee has recommended that the ADI concept should not be applied to carcinogens. The reasons for this recommendation are illustrated by the following examples. A theoretical ADI may be computed for the known or suspected carcinogens that appear in Table VI-60 of Drinking Water and Health (National Academy of Sciences, 1977, p. 7941. The calculations in Table III-4 were based on the lowest dose that showed a statistically significant increase over background, whereas a true ADI is always based on the highest no-observed-adverse-e~ect level. Furthermore, in every instance the minimum effect used for computation was cancer. While other kinds of minimum elects have been observed for a few of these compounds, carcinogenicity was the end point used to calculate the risk estimates. Therefore, to achieve consistency, it was used in all cases. If a "safety factor" is applied to this dose, then the risk at this value (mg/kg/day) can be determined by using the upper 95% confidence estimate of lifetime cancer risk per ,ug/liter from Table VI-60. (Although the selection of the 95% confidence interval can be considered to be arbitrary

Problems of Risk Estimation 37 and/or traditional, the need for working with a confidence interval is necessary for a conservative approach to public health.) Using this approach, the estimated risks range from a low of 0.0737c for DDT to a high of 1037O for b-BHC (Lindane) (see Table III-4~. To demonstrate further the variability that would be associated with the ADI approach, an arbitrary risk value of 1 x 10-6 was chosen, and the daily dose (mg/kg/day) that would theoretically produce this level of risk was calculated. The doses (mg/kg/day) required to produce a risk of 1 x 10-6 range from 5.5 x 10-8 (Dieldrin) to 1.3 x 10-4 (carbon tetra- chloride). These examples show the potentially great variability in risk calculated at supposedly equivalent levels of safety using the safety factor. Thus, applying ADI methods to carcinogens instead of risk estimates may very well be misleading with regard to regulatory actions. MODELS FOR LOW DOSE CARCINOGENIC RISK ESTIMATION Dichotomous Response Models In many quantitative theories of carcinogenesis it is assumed that the process consists of one or more stages at the cellular level beginning with a single cell somatic mutation at which point the cancer is initiated. These stages may be cell mutations or other biochemical events that are either monocellular or multicellular in origin. Whittemore and Keller (1978) reviewed all these theories. Many of these theories lead to a mathematical model relating dose, d, to the probability of response, P(a), by P(d) = 1 -exp (-~NO + Aid + A2d2 + ... +\kdk)~. This model was used by the Safe Drinking Water Committee (National Academy of Sciences, 19774. Its background and its application to experimental animal data are discussed in more detail in the committee's 1977 report. In addition to this particular mathematical dose-response model, a number of other models have been proposed for the assessment of low exposure human risk. The most commonly used extrapolation models are described in the following section. Linear, No-Threshold Model Conceptually, the simplest modes for high to low dose risk extrapolation is based on the assumption that risk is directly proportional to the environmental exposure level. In mathematical terms, the probability of

38 Cal . _ V' a: on o ._ C) a) c U) as V) so o a: 3 o ._ 3 Ct ._ o Cal V) m o 3 Ct Cal . ~ . Ct v Cal Cal :;s ° ._ ~ ~4 ~ o 1 ~ _ ~ ~ ~ m ~ _ Cal C ~ a a., ~ ._ c,) 1 C> AL X tb-= .£ o ~ ~ _ o o o_ ._ ~ ~n oN LU ~: ~ C,) ·- _ o . _ S~ o =: . > ,, C) C. cn CQ ,~ o ~: ~L 3 ·- ~ ~ 5 . _ C~ ~ '= ~ X X X V, . . . ~ ~ _ X X X . . . _ _ r~ r~ ~ _ ~ ~ ~ ~O O O O O O 3 X X X X X X O ~ 0 r~ ~4 ~_ ~ _ _ _ _ C~ O oo ~o ~ _ _ o _ ~ _ o O O O O O O O O O O O ~ - ._ X ~ o O =: ~ O `:: ~ E ~ ~ ~ ~ ~ ~ ~ ° ~ ~V

39 ~ ~ x ~ ~ ~ ~o ~ ~ 1 1 1 1 1 1 1 1 1 o o o o o o o o o ~ - - - - - - - - x x x x x x x x x ~ ~ ~ ~ ~ ~ ~ ~ o . . . ~ . . . . . oo ~ ~ ~ ~ ~ ~ - ~ 1 ~ 1 1 1 1 1 1 1 o o o o o o o o o - - - - - - - - - x x x x x x x x x ~ ~ ~ ~ ~ oo ~) oo - . . . . . . . .. t x o ~ ~ o o ~ ~ ~ o o ~ o o - c~ - o o ~ o o o ~ o o o o o o o o ~i o c~ v~ '= . . . . . o o o v) ~ - ~ cy' '= ~- ~ - c ~- - o ·, o ~ ~ - ~ ~ - ~ 'e o . - s c) ~: s o ~ s ~ ~ o _ CL ~ ~ a' a, ~ - o r~ c' - ~ ~ c) s s ~ c~ - c: o ~ o ~ 2 :e ~ o ~ ~ ~ s c~o x 8 ~° t) ~ ~ ~ ~ ~ X o ~ ~ o U~ C ~o ~o _ _ ° ') s ''' ~ X _ ~ ~ ° ~ X C~ ~O ~ ~ .E ~, ~ ~=~ ~ o '_ ~ ~ s ~ ~ ~ om °O a' ~ ~ ~ = ~C) ~.St ,u s ~O.= - C) C~0 ~ ~.~ ,=- o E o ~c o O = _ ~ ~ 8 s o `,, ° E s a, ~ ~ ~ S ~ ~ 3 ,,, ° s3 .£ o _ s t> _ ~ 0 ~ ~ ~ 0 0 ~o ~ °8 ~ ° ° s E 8 ~ ~ ° s ~ ~ ~o ~ ~ `_ s U) ~ ~ ~ .= s 3 ~ ~ O CL 8 3 s g s ~ E E 9 _ _ s ~ ~ , ~, a ,_ e U) ._ ~0 o - x - o ~: .= g £ ._ - C~ . - 3 Ct ·C) o u Ct C~ ao .= o s x t_, o ;> o s U' - o C) ~o s - .= V, a' o C) 3 et r~ o - x o 11 o X

40 DRINKING WATER AND HEATH a carcinogenic response, ideal, is related to the daily dose level, d, by the equation P(a) = old. This simple extrapolation model and the models described below assume the impossibility of proof of a population threshold level, i.e., a level of the carcinogen below which exposure will produce no response in any member of the population at risk. Under the assumption that the true dose-response relationship is convex (positive second derivative with the dose on the abscissa) in the low dose region, linear extrapolation from an experimental dose in this region of convexity will provide an overestimate to the true low dose risk. However, it is often not known whether the experimental dose is in this convex region. Tolerance Distribution Models The hypothesis of tolerance distribution, which was originally proposed for toxic responses other than carcinogenesis, is based on the assumption that each member of the population at risk has an individual tolerance for the toxic agent below which a dose will produce no response, whereas a dose as great or greater will certainly produce the response. Further- more, it is assumed that these tolerances vary among the population members according to some probability distribution, F. The frequency distribution of tolerances, as measured on a linear scale, is seldom symmetrical since a few individuals with extremely high tolerances will provide the distribution with an extended "tail." However, a simple transformation of the scale of measurement, such as a logarithmic transformation, will often convert the distribution to near symmetry. This probability distribution of tolerances is also commonly assumed to involve two parameters, one of location, a, and one of scale, ,l? 2 0 Therefore, this distribution can be generally denoted by F(a + Flog z), where z denotes the tolerance level to a particular toxic agent. This probability distribution produces a dose-response relationship in the following manner. Assume that an individual from the population is selected at random and is given a dose of size d. Then the probability for this randomly selected individual response, P(d), is the probability that his tolerance is less than d, i.e., a +,Elogd P(d) = F(a ~ ~ log d) = ~ dF(x). -X Therefore, the proportion of the population expected to respond to a specific dose of the toxic agent is indicated by the proportion of individuals having tolerances less than this dose level. These assumptions imply that the probability of response at a zero dose is equal to zero, i.e.,

Problems of Risk Estimation 41 P(0) = 0, and that the probability of response at an infinite dose is equal toone,i.e.,P(x)=l. The incorporation into these models of spontaneous response, i.e., a response in the absence of exposure to the specific toxic agent, is discussed in a later section. The results of many toxicity experiments have shown that the proportion of responders increases monotonically with dose and often shows an approximately sigmoid relationship with the logarithm of dose. This led to the development of the log-normal, or log-probit, model of dose response. This model assumes that the distribution of tolerances, F. is Gaussian (normal) against the logarithm of dose. This assumption of normality is not based on strong biological theory, but in the absence of evidence favoring a specific alternative tolerance distribution, the fact that the normal distribution accords fairly well with historical observa- tion has made the assumption attractive. A history of the development of this model is given by Finney (1952~. Mantel and Bryan (1961) have suggested that a modified version of this model be used for extrapolation of carcinogenesis bioassays from high to low doses. They stated that since the normal probability model is not usually true at the extremes, i.e., there is often more probability mass in the tails of the distribution than the normal model would predict, then the slope of the relationship between the log dose and the probit of response will flatten out and become less steep as the dose level decreases. They proposed that high dose to low dose extrapolation be based on the observed data but with the use of a slope that is shallower than that observed. They suggested that the slope selected be no greater than the average true slope over the extrapolation range. A slope of one probit per 10-fold change in dose is commonly used for this Mantel- Bryan extrapolation. Logistic Models Another mathematical dose-response function, which was originally derived from chemical kinetic theory, is the logistic function P(d) = F(a + ,B log d) = [1 + exp (a + ,8 log Alibi, ,8 < 0. This dose-response model is based on the assumption of a logistic distribution of the logarithms of the individual tolerances in the population and a theoretical description of certain chemical reactions. Reed and Berkson (1929) demonstrated the utility of this type of function to describe the time behavior of a number of different chemucal reactions. One of its primary uses has been to describe autocatalytic

42 DRINKING WATER AND H"LTH reactions. Berkson (1944) proposed its use as a dose-response model due to its theoretical basis in chemical kinetic theory and its sigmoid appearance which is similar to that of the integrated normal curve. If the response under consideration is measured in terms of this type of physicochemical reaction in a biological assay, then the logistic function does have a theoretical basis. However, in terms of a tolerance distribution, there is no theoretical justification for preferring either the logistic or normal distribution. The normal and logistic models are the most attractive to the biologist since each is applicable in many contexts. Other tolerance distribution models have been suggested but have received little support and use because of their lack of a theoretical basis (Finney, 19711. All tolerance distribution models have little theoretical justification for a carcinogenic response. "Hitness" Models Dose-response models for radiation-induced carcinogenesis have been proposed on the basis of what is called the "target theory." This theory assumes that the site of action has some number (N ~ 1) of critical "targets" and that an event occurs if some number (n ~ N) of them are "hit" by k, or more, radiation particles. In addition, the probability of a hit is assumed to be proportional to the radiation dose. For this class of models, the probability of a response increases with increasing dosage, presumably due to an increased chance of a critical target being "hit" rather than to a variation among individual tolerances to the effect of such a dosage. Therefore, the proportion of the population expected to respond to a specific dose of the toxic agent is determined by the probability that the dose produces the required number of"hits" on the critical "targets." The most commonly used models in this class are the single-hit model by= 1, k = 1) in which a single hit on a single critical target is necessary for the response, the two-hit model (N = 1, k-2) in which either of two hits on a single target is responsible for the effect, and the two-target model (N = 2, k = 1) in which one hit on each of two targets is required. The single-hit theory has been used to describe high linear energy transfer (LET) radiation, while the two-target models describe low LET radiation (Kellerer and Rossi, 1971; Rossi and Kellerer, 19741. Brown (1976) argued in favor of a multievent theory of radiation-induced carcinogenesis which involves both a linear and quadratic dependence upon dose. He also suggested that the possibility of cell killing at high dose levels be included in the model. Other generalizations of this theory include variations among the targets in the'

Problems of Risk Estimation 43 probability of a hit and variations in tolerance among the subjects at risk. These models are all summarized by Turner (1975~. All of these models assume the nonexistence of a population threshold, i.e., a level below which exposure will not produce a response in any member of the population at risk. A more complete discussion of this assumption can be found in Drinking Water and Health (National Academy of Sciences, 1977, Ch. II). Models of Time to Tumor Occurrence The dose-response models discussed in the previous section are based quantal (yes-no) observational data. However, for many experimental or observational studies, there is an additional piece of information that these quantal response models ignore. These data concern the distribu- tion of times from initiation of exposure to response or, in cases of no response, the total length of time the subjects were observed without a response. Among others, Armitage and Doll (1961) defined this time between initial exposure and clinical appearance of the disease as the latent period. These data add information that aids the determination of the dose-response relationship, especially in experimental situations in which the response rates at the high dose levels are close to lOO~o. Experiments in which most dose levels produce 100% or nearly lOO~o response will not provide much information on the dose-response relationship; however, examination of the times to response will often show a monotonic relation between their means, or medians, and the dose levels. In addition, the actual times to tumor occurrence are meaningful in the sense that tumors that appear early may be more biologically important and a greater potential hazard than the later tumors. Moreover, these response times pet licit the formulation of mathematical models that relate the dose level to the probability distribution of times to response. These models may then be used to estimate the expected numbers of responders in the population at risk at any time. Gail (1975) proposed three measures of the effect of dose upon life expectancy that could be used in place of its effect on cancer nclc ence. The formulation of a mathematical time to response model consists of two parts. The first is the mathematical for ~ for the probability distribution of the random variable of response time, T: probability (T < t) = F(t;~, where F(~) is some cumulative probability distribution function indexed by a vector of parameters, 8. It is assumed that the mathematical form of

44 DRINKING WATER AND H"LTH F is the same for each dose level and that one or more of the parameters are functions of dose. It is also assumed that all subjects will eventually respond, i.e., F(x)= 1; however, because of competing risks such as death without evidence of the disease, the subject may be removed from observation before the response occurs. This assumption is probably more valid for chronic exposure than for acute exposure. The second assumption concerns the relation between the dose level, d, and one of the parameters, 8. A general empirical relation that has been proposed by Busvine (1938), among others, is Bi = add, or log(8)) = log~a) + ,8 logjam, although there is no presumed biological basis for this relationship. However, when pi is the median time to response, an approximate linear relation between the logarithm of 8; and the logarithm of dose has often . i, been observed. A number of mathematical time to response models have been proposed. All of them have corresponded directly with dichotomous dose-response models (Chand and Hoel, 1974~. One of the first models was proposed by Druckrey (19764. He assumed that the probability distribution of the response times was log normal, that the median response time was related to dose as above, and that the standard deviation was independent of dose. It can be shown that this model is related to the normal, or probit, quantal response model. A Weibull model for the response time distribution was proposed by Pike (1966) and Peto et al. (1972~. In this model the scale parameter is related to dose while the shape parameter is independent of dose. This model corresponds to an extreme value quantal response model in general, and when the parameter ,B in the above relationship is assumed to be unity, this model corresponds to a single-hit quantal response model. These and other models have also been studied by Shortley ( 1965) and Gart (19651. Armitage and Doll (1961), Armitage (1974), and Peto (1974) have proposed that when exposure to a carcinogenic agent is at a constant rate continuously over time, there is a general model in which the hazard rate, i.e., the age-specific incidence rate, can be factored into the product of a function of dose, d, and a function of time, I: H(t,d;~i,82) = f~t;~)g~d;82) The Weibull distribution, where; = 8~ t At, is a member of this general class. Hartley and Sielken (1977) developed the analysis of dose- response data using this model and applied it to some experimental results. They used the polynomial form of the multistage model for the

Problems of Risk Estimation 45 function of dose g~d;82) and a general polynomial for the function of time Oft;. Crump (1978) also assumed this factorable hazard model with a polynomial for the function of dose and applied marginal likelihood analysis techniques which require~no assumption on the form of the time function. The utility of these time to response models requires additional research. They appear to provide improved estimates of the relation between dose and response. Their utility will depend upon the number of tumors found in the animal bioassay: high incidence tumors and their times to occurrence will provide substantially more information than low incidence tumors. In addition, the actual times to tumor occurrence are unavailable for many animal bioassays, either because the records were not kept or the tumor was of a type found only upon sacrifice at the termination of an experiment, e.g., after 2 years of exposure. These restrictions reduce the usefulness of such approaches for high to low dose extrapolation. When using a model that is fit to the experimental result and then used for extrapolation, it is assumed that the dose-response relationship observed at these high dose levels will continue to hold throughout the entire spectrum of exposure levels. This assumption has been questioned by some toxicologists and other health scientists. The effective exposure level the amount of the carcinogen actually reaching the target cells and molecules may well be some complex function of the absorption, distribution, biotransformation, and excretion characteristics of the dose, each of which may depend upon and influence the level of the carcinogen to which the animals are environmentally exposed. The following section contains discussions of some pharmacokinetic consid- erations that are relevant to both low dose extrapolation and quantita- tion of differences between species. PHARMACOKI NETIC CONSIDERATIONS A pharmacodynamic hypothesis for toxicity from foreign chemicals states that biological effects are manifestations of biochemical interac- tions between the foreign substances (or materials derived from them) and components of the body. It follows that these interactions result from the presence of a toxic material at the site of action and that the fundamental biochemical interaction depends in some way on the concentration of the toxic material and the length of time that it is present. Actual mechanisms of toxicity are many and varied, and the kinetics

46 DRINKING WATER AND H"LTH relating concentration with eject depend on the mechanism. It is commonly assumed in pharmacology that the biochemical effect of a reversible inhibitor depends on the existing free concentration of drug at the site of action. Irreversible biochemical reactions require joint consideration of concentration and duration of exposure. Whether or not any interaction at the biochemical level will be observable as a biological eject and the time course of that effect also depend on the nature of the interaction. An inhibitor may have to react with a significant fraction of receptor sites before any gross effect will be observed. The effect, then, may correlate directly with concentration, e.g., in certain central nervous system responses, or it may be delayed, e.g., if protein or DNA synthesis is involved. Irreversible reactions with DNA are of particular concern because, in principle, a single defective molecule that is not repaired or eliminated from the pool could lead to a mutation or to cancer. Furthermore, clinical expression could be delayed many years. Dose Effects A critical problem in the application of pharmacokinetic principles to risk assessment is the potential change in metabolism as concentrations decrease. Linear models are most frequently used for drug disposition; however, there are numerous examples of nonlinear behavior in a therapeutic range. While the potential of these models to predict both therapy and toxicity is generally recognized, relatively few models completely elucidate a complex reaction scheme. One of these is the model of Levy et al. (1972), who developed a detailed kinetic description of the elimination of salicylic acid and its metabolites. Two of the several steps (formation of salicyl phenolic glucuronide and salicylurate) exhibit . . . . saturation . kinetics. The presence of saturation kinetics, particularly as they affect various reaction paths differentially, has significant implications to the testing of environmental chemicals. Gehring and Blau (1977) have stressed the existence of nonlinear elimination of a variety of chemicals such as 2,4,5- trichlorophenoxyacetic acid 1,4-dioxane and its implication to toxicity testing. Nonlinear kinetics pose significant problems in quantitative extrapolation from "high" doses to "low" doses if the kinetic parameters are not measured. Many of the physiological processes, e.g., biliary or urinary secretion, which underlie pharmacokinetics, have limited capacities. Similarly, various -relevant biochemical interactions, such as protein binding, membrane transport, and metabolism, may exhibit nonlinear behavior at

Problems of Risk Estimation 47 sufficiently high concentrations. Some of these have been reviewed by Wagner (1974~. The nonlinearities are most often expressed in the form of a Langmuir or Michaelis-Menten expression, kC/(K ~ C)' where k is the capacity of the process for binding, transport, chemical reaction, etc., and K is the value of the concentration, C, at which the rate or binding is half maximal. Quite clearly, the concentration is "high" or "low" when compared with the constant, k. All processes that follow a Langmuir or Michaelis-Menten expression approach linearity with a constant or proportionality equal to k/K as C becomes small compared with K. It is now well established that a foreign chemical may undergo metabolism to a more (or less) toxic form. The kinetic implications and consequences for extrapolation of animal data to humans were discussed by Gillette (1976, 19771. Most of the emphasis has been placed on organic chemicals since comparable concepts relating to precise chemi- cal species of inorganic complexes in biological systems are not well studied. The diagram shows a simplified reaction scheme following the approach of Gillette (19761: Absorption - A - B - C. |r ~Ire The parent chemical is represented by A, and the reactive intermediate is represented by B. Both are assumed to be at steady state with a constant rate of absorption of A. The steady-state analysis is instructive; more complex transient analysis would not lead to a different result. The various reaction rates are indicated by r as follows: rA and rB represent the summation of all processes that may be involved in the elimination of A and B or chemical conversion to nontoxic products; rAB is the reaction rate for conversion of A to the reactive intermediate; rBC represents the rate of irreversible reaction of the reactive intermediate with the site of toxicity, e.g., by covalent binding to protein molecules. Many of the various rates may be enzymatically mediated and kinetically saturable. Although a one-compartment description of the body is implied by the diagram, the various chemical reactions and excretory processes do not necessarily occur at the same site. B may be formed in the liver and' if sufficiently stable, could produce toxicity in other organs. Similarly, B might be conjugated in the liver and eliminated by the kidneys. Quite clearly, if all of the processes are linear, the concentration of the reactive intermediate B (and thus exposure to toxicity) will be propor- tional to the rate of absorption of A. Saturation phenomena and enzyme

48 DRINKING WATER AND H"LTH induction or inhibition produce quite variable results depending upon the steps where they act. If the pathways of rA or rB leading to nontoxic products and elimination start to saturate, then the production of C will increase more rapidly than the dose. However, if the pathways of ran leading to C start to saturate, then the production of C may increase less rapidly than dose. In a similar way, induction or inhibition of enzymatic or excretory processes may increase or decrease C. Thus, it appears impossible to make generalizations concerning the effect of dose on the formation of toxic intermediates over a wide range of doses; however, since all processes that follow Michaelis-Menten kinetics approach linearity at sufficiently low concentrations, exposure to B should be proportional to dose. It is unlikely that totally new biochemical pathways are invoked as concentrations increase; only the relative quantitative importance of the various pathways is at issue. A slight variant of the reaction scheme shown above was considered by Cornfield (1977) to support the possibility of a threshold level for a . . carcinogenic compounc .: D + S k AX k* D + T >Y. In the above scheme, D represents a toxic substance that combines reversibly with a free substrate, S. to form an activated complex, X. D can also react irreversibly with a deactivator, T. to form a toxin- deactivator complex, Y. It was assumed that the probability of a toxic reaction is proportional to the amount of X and argued that as long as T is present in excess of D there would be no toxic reaction. That conclusion could not be valid for any finite values of the rate constants in a transient or steady-state analysis. If D is much less than S and T. both forward reactions are pseudo-first-order reactions, and exposure to X is proportional to the dose of D. Species Considerations Chemicals must be tested for toxicity in experimental systems and the results extrapolated to humans. The methodology for making this extrapolation rests, in part, on pharmacokinetic considerations of species similarities in absorption, distribution, binding, metabolism, and elimi- nation. It is generally conceded that no animal mimics "man" in all respects that are relevant to pharmacokinetics. Studies in humans themselves can be quite variable, reflecting intraspecies variations. Even if there were an

Problems of Risk Estimation 49 animal in which the pharmacokinetics of a particular substance mimicked an average human, there is no certainty that the mimicry would extend to another substance. Species differences do not obviate the value of model systems; they do make interpretation of results more difficult and arbitrary. Models are used extensively in engineering. These may be physical or purely mathematical. They may be designed to simulate only a part of a complex system. In any event, the model is never the same as the prototype. Successful use of the results of a model rests on a knowledge, often largely empirical, of the similarities among species. Therefore, it is appropriate to consider both similarities and differences among species when examining pharmacokinetics that are relevant to risk assessment. Adolph (1949) correlated a large number of quantitative properties of mammals with body weight. His correlation equation took the following form: property = anybody weighty. In most cases the exponent was not unity, i.e., these properties were not linearly proportional to body weight. In all cases when the "property" was a physiologic or metabolic function, the exponent was less than unity. Representative values of k include: urine outputs 0.82; creatinine clearance, 0.69; basal oxygen consumption, 0.734; nitrogen output, 0 735; oxygen consumption by liver slices, 0.77. This observation indicates that the function per unit of body weight goes down as body weight increases. For example, a 20-g mouse consumes approximately 9 time~more oxygen per unit of body weight than does a 70-kg human. Some similar variation has been observed among tissue perfusion rates (Bischoffet al., 1971), which are important to pharmacokinetics. Some of these concepts have been applied to correlate the history of plasma concentrations of methotrexate, an anticancer drug, among several mammalian species that eliminate the drug predominantly unchanged (Dedrick et al. 1970~. Purely physical interactions of environmental contaminants with biological tissues and fluids might not be expected to show great variation among species; however, much work needs to be done to establish an experimental basis for that hypothesis. For example, a heavy metal ion that reacts very strongly with a free sulfhydryl group may not discriminate greatly between species. Hughes (1957) reported less than a fourfold difference between the association constants of methylmercury iodide with human and bovine serum albumin. The ratio of the concentration of dieldrin in the adipose tissue to that in the blood has been reported to be 104 in rats and 169 in dogs (Walker et al., 1969~. The

50 DRINKING WATER AND H"LTH corresponding ratio in humans is 136 (Hunter et al., 1969~. Physiologic modeling of dieldrin pharmacokinetics by Lindstrom et al. (1974) is based on the idea that equilibrium distribution into a tissue is proportional to the lipid content of that tissue. The interspecies differences that may confound pharmacokinetic predictability most significantly are those concerning metabolism. Quinn et al. (1958) stated that humans usually metabolize drugs less rapidly than other animals. There are numerous exceptions to that ge;~eraliza- tion. Furthermore, as discussed above, toxicity may be related to the concentration of an active inte~ediate, and there are extraordinarily large qualitative and quantitative differences in metabolism. As discussed by Williams (1974), foreign organic compounds tend to be metabolized in two phases. Phase I reactions lead to oxidation, reduction, and hydrolysis products. Phase II reactions lead to synthetic or corrugation products that are relatively polar and, thus, more easily excreted by the kidney and, in some cases, by the liver. Within this general framework, however, there are large interspecific variations. Williams points out that such variations in Phase I reactions are very common and often appear to be unpredictable. If an interspecific difference is found for a particular compound, similar compounds may have similar variations. Phase II reactions are much more limited in number than Phase I reactions. Eight principal conjugation reactions are common to humans and most other mammals. It may be possible to identify patterns in these reactions. In part, because of the complexity of metabolism studies in whole animals and variables introduced by factors other than metabolism, a large number of studies have been conducted on tissue extracts. Some of the studies of hepatic and extrahepatic mixed-function oxidase have been reviewed by Bend and Hook (19771. They observed that most microsomes used in metabolism studies have come from rodent livers and that the cytochrome P-450 content of human microsomes has generally been reported to be lower than P-450 from rats, but with considerable variation Cytochrome P-450 appears to have a role in most microsomal mixed-function oxidase reactions. Nelson et al. (1976) observed that levels (per milligram of protein) of cytochrome P-450, NADPH-cytochrome P-450 reductase, and NADPH cytochrome-c reductase were lower in human microsomes than in those from the male rat and female pig. Kuntzman et al. ( 1966) determined that 3,~ benzpyrene, pentobarbital, and 3-methyl-4-monomethylaminoazoben- zene are metabolized more slowly by human liver enzymes than by preparations from male rats; dealkylation of acetophenetidin was more rapid with human liver preparations. Krasovskii (1976) examined

Problems of Risk Estimation 51 mammalian hepatic enzyme activities (per kilogram of body weight) and showed that the activity of 15 of 16 enzymes tended to decrease as body weight increased. Biological knowledge is still too limited to permit confident extrapola- tion of pharmacokinetics of many metabolized substances from labora- tory animals to humans. Both the qualitative and quantitative aspects of metabolism should be studied further. It may be possible to obtain adequate information from in-vitro studies on isolated cells (such as hepatocytes) or cell-free extracts and to use this information in conjunction with pharmacokinetic models that incorporate physiological and anatomical differences. A philosophy of"scale-up" design has been discussed by Dedrick (1973~. Early work attempting to relate in-vitro to in-viYo metabolism has met with at least semiquantitative success for cytosine arabinoside (Dedrick et al., 1973) and phenytoin (Collins et al. 19781. In summary, no laboratory animal is fully equivalent to humans pharmacokinetically. There are, however, many similarities as well as differences. Pharmacokinetic analysis of appropriate experiments, in- cluding in-vitro studies, can considerably strengthen our ability to assess the risk to humans posed by foreign substances in the environment. The incorporation of pharmacokinetic models into the estimation of dose- response relationships is worthwhile. The practical business concerning which techniques to use and their quantitative impact on the low dose estimation process has not yet been resolved unanimously. INTERACTION IN RISK ESTIMATION Most toxicological studies of the effects of chemicals on mammals are performed using one chemical at a time as the toxicant. However, the joint action of chemicals in the environment must also be addressed. There have been many experiments on cocarcinogenesis and initiation- promotion. Cocarcinogenesis involves the simultaneous administration of more than one chemical or the influence of modifying factors upon the carcinogenic process. Initiation-promotion involves a prior, often very low exposure to a carcinogenic agent, an initiator that induces an irreversible change in some of the cells in the target tissue. But the initiator produces little or no evidence of cancer without subsequent exposure to a promoter, an agent that is generally incapable of initiating the carcinogenic process but increases the cancer response when applied after initiation. Some chemicals are complete carcinogens, capable of

52 DRINKING WATER AND H"LTH both initiation arid promotion, whereas other chemicals produce only initiating action and still others, only promotion. Dietary components (Carroll and Khor, 1970; Walters and Roe, 1964) and combinations of known carcinogens (Diechmann et al., 1967) have been studied as modifying factors of carcinogenesis. Schmahl (1976) reported his results on a number of different studies in which animals were exposed either to two carcinogens having the same or different target organs or to one carcinogen and one noncarcinogenic stimulus. The joint elects of these agents interacted only with carcinogens having the same target site. Some epidemiological observations illustrate joint action in humans. Selikoff et al. (1968) found a greater than additive elect of cigarette smoking and exposure to asbestos dust on lung cancer mortality. Lundin e! al. (1969) reported a possibly similar elect of cigarette smoking and exposure to uranium. On the other hand, for oral cancer Rothman and Keller (1972) concluded that the joint effect of cigarette smoking and alcohol consumption upon the risk could be described by a simple additive model. Theoretical Models for the Joint Actions of Two or More Agents Bliss (1939) formulated one of the first theoretical developments of the joint action of two toxic ingredients. He defined three types of joint action: (1) independent joint action in which the toxicants act indepen- dently and have different modes of action; (2) similar joint action in which the toxicants have the same mode of action but act independently so that one component can be substituted at a constant proportion for the other; and (3) synergistic or antagonistic action in which one component either synergizes or antagonizes-the action of the other toxica-nt. Bliss also used the probit dose-response model to relate the dose levels of the two toxicants to the probability of response. Plackett and Hewlett, in a series of papers (Plackett and Hewlett, 1952; Hewlett and Plackett, 1959, 1964), proposed biological models for combinations of toxic agents, derived mathematical models from them, and tested their fit to experimental data. Their models were based on the existence of tolerances in biological systems, where the amount of the toxicant acting upon the system is the amount transmitted to the site o action. Plackett and Hewlett (1967) and Ashford and Colby (1974) have also developed a system of mathematical models for joint action based upon the concepts of routes of administration, sites of action, and physiological systems that may be affected. The action of a toxicant is assumed to take place as a result of the occupation of receptors, which is;

Problems of Risk Estimation 53 governed by the laws of mass action dependent upon the concentrations of the toxicants at the sited of action. The utility of another model for independent action, the application of harmonic mean calculation, is discussed in the section on acute exposure. These theoretical models were all derived for noncarcinogenic re- sponses and may not apply to carcinogenesis. For carcinogenic re- sponses, Whittemore and Keller (1978) have proposed a mathematical model to describe the observed initiation-promotion phenomenon of some carcinogenesis in which tumors regress after termination of exposure to the promoting agent. They applied their model to data from experiments of Burns et al. (1976) on mouse skin papillomas and obtained excellent agreement between the model and the data. Initiation-promotion and cocarcinogenesis may have regulatory impli- cations different from those for complete carcinogens, i.e., when exposure to another factor is not required. A prolonged period of exposure to a promoter is often required before cancer appears. During this period, if the application of the promoter is stopped soon enough, the incidence of cancer can often be substantially reduced. In animal studies, this time sequence has been studied by Roe and Clack (1964~. In humans, similar conclusions might be drawn from a study of lung cancer among British doctors who gave up smoking (Doll and Hill, 1964~. The effects of promoting agents in the environment upon the total cancer burden of the population may be greater than the effects of initiating agents that induce mutations by interacting directly with cellular DNA. These initiating agents or complete carcinogens may be discovered through experimental in-vitro mutagenesis tests or through animal bioassays, while promoting agents whose mechanism of action may be nonmutagenic in nature, e.g., an agent that increases cell proliferation, may not be mutagenic in vitro and will often not be carcinogenic in a single agent animal bioassay. Hamilton and Hoel ( 1978) proposed a modification of the multistage carcinogenesis model of Armitage and Doll to take into account multifactor exposures. For exposure to two agents, they assumed that no more than two stages in the process are affected. Their most general model allowed each agent to affect each of the two stages and allowed for modification of effect by one agent upon the other. They showed that the meaning of the term "interaction" is dependent upon the model of dose and response. The estimation of low exposure risk in a multifactor situation will be highly dependent upon the mechanisms of action by the joint agents. The models of joint toxic action could be of benefit in the risk

54 DRINKING WATER AND H"LTH assessment of low exposures; however, none has been adequately studied for this purpose. Their theoretical and practical implications need to be studied further before their utility can be assessed. High dose to low dose extrapolation for individual agents is an unresolved problem filled with many unknowns, and extrapolation of the actions of joint agents contains an additional major source of uncertainty. Epidemiological Risk Assessment Two major problems are encountered in the assessment of human risk based on the results of experimental animal bioassays: (1) the extrapola- tion from the observed risks at relatively high exposure levels, which are commonly used in animal bioassays, to low exposure levels that are comparable to human environmental exposure and (2) the extrapolation of estimated risks from laboratory animals to humans. The current methodologies that are used for these extrapolations super from a lack of basic knowledge concerning the disease process in animals and humans and from a paucity of relevant data. Although epidemiological studies on human populations that have been exposed to low levels of environmen- tal contaminants are not faced with either of these problems, they are beset with difficulties of their own. To measure the effects of factors that are related to specific human diseases, two general epidemiological approaches are available-descrip- tive and analytic. Descriptive studies are mainly observational. They can suggest possible relationships but seldom prove them. Analytic studies may also be used to test specific hypotheses or to measure specific effects. Two commonly used types of analytic studies are: (1) prospective cohort studies in which populations exposed to various levels of a suspect agent are followed and their future disease incidence is compared, and (2) case-control studies in which the past exposure to a suspect agent is measured in a sample of individuals with and without the disease in question. Mathematical models of dose-response relationships can be fit to the results from either type of study to estimate the quantitative relation between exposure level and disease incidence. However, these studies also super from a number of limitations and difficulties. Both prospective cohort and case-control studies may produce biased results when confounding from other factors related to disease risk is not considered. Moreover, these studies lack the desirable experimental control of extraneous factors, which is found in animal bioassays, since many of the relevant risk factors are either unknown or cannot be adequately measured or controlled. Therefore, the quantitative results of such studies are always open to question. In addition, practical

Problems of Risk Estimation 55 limitations of prospective cohort studies are the long period between initiation of the study and the collection of statistically adequate numbers of disease cases, and the correspondingly high cost of such a long study. An important limitation of case-control studies is the questionable validity of retrospective information concerning exposure that may have occurred over a long period in the past. Even with their inherent limitations and difficulties, these types of analytic epidemiological studies provide useful information for assessing the risk from environmental contaminants. However, there are no adequate analytic studies of this nature on the relationship between cancer incidence and exposure to drinking water contaminants. There are a number of epidemiological studies of the relationship between cancer incidence and organic contaminants in drinking water. These studies are discussed in some detail in Chapter II. Three of the studies (Cantor e! al., 1977; Hogan et al., 1979; McCabe, 1975) compared cancer mortality rates among counties across the United States in which trihalomethane (THM) concentrations in the drinking water supplies had been measured during two surveys conducted by the U.S. Environmental Protection Agency (1975~. Multiple regression techniques were used to analyze the variability among counties in the sex-specific, age-adjusted mortality rates for each site of cancer. This methodology related the cancer mortality rate in the county, M, to a number of explanatory variables, X, i = 1, . . ., k, and THM concen- tration, in the drinking water, W. by the following equation: M = a + ~ ,BiXi+ yW, i - ~ where the parameters a, ,B (i= 1, . . ., k), and y are to be estimated from the data. The effect of one unit of THM concentration was measured by the parameter y, which represented the dirt erence in cancer mortality between an unexposed county (W = 0) and a county with one unit ofexposure(W= 14. These studies, although useful for suggesting future analytic studies, are deficient in the quantification of cause-and-effect relationships. Hogan et al. (1979) discussed in some detail both the biological and statistical limitations of this methodology. The outcome, or dependent variable, cancer mortality, is an average aggregate rate for a heterogene- ous collection of individuals from 1950 to 1969. Individual exposure patterns were unknown, and any secular changes might have been concealed by the aggregation. In 1975 the THM exposure data were collected for only one sample site in each county. Any quantitative conclusions from such a study would require the assumptions that the ~,

56 DRINKING WATER AND H"LTH relative sampled TIlM concentrations have been basically unchanged for up to 50 years and that the single site is representative of an entire county's drinking water supply Another problem is that THM concen- tration may be correlated with those of other water contaminants. Thus, any estimated THM effect may represent the eject of some other causative agent. In addition to the epidemiological limitations, there are other inferential validity problems with the statistical methodology. These problems include the exclusion of important cancer risk factors such as cigarette smoking, the erroneous inclusion of factors that are not related to cancer but are related to THM concentrations, and the assumption that THM concentrations are measured with small error. (Hogan et al. showed that there was considerable variation in the THM measurements between the two EPA surveys.) Quantitative indications produced by a multiple regression analysis of observational data on groups of individu- als will provide necessary but insufficient data, and will suggest the need for confirmation by more controlled analytic epidemiological studies. Summarizing their opinion on these limitations, Hogan et al. stated: " . . . the quantitative, causal interpretation of results generated by an indirect study would appear to be a very tenuous and questionable practice in most instances." Reliability of Quantitative Risk Estimates As noted earlier, there is a paucity of data for the toxicological effects of many chemicals that could be found as contaminants in drinking water. This is true even at the high dose levels at which effects could be measured. At the low dose levels corresponding to expected human exposures, the attendant number of responses are so small that the performance of experiments with adequate statistical precision would require an inordinate number of laboratory animals. Furthermore, such studies would be confounded by the potential differences in response between the controlled test animal and the highly variable human population living in a complex environment. Consequently, to estimate effects obtained at low levels of a given agent, an extrapolation must be made from the data that were obtained at higher doses. Unfortunately, the extrapolated risk for a given low dose is highly dependent upon the mathematical model chosen for such an enterprise. To illustrate, consider the three common dose-response models: log normal, log logistic, and single hit. These three models give similar values over the range of doses that can be measured, i.e., 5970 to 95370 response,

Problems of Risk Estimation 57 TABLE III-S Expected Response Rates for Different Dose-Response Models as a Function of Dosea Percent Response Relative Log Log Single Dose Normal Logistic Hit 16 98 96 99+ 8 93 92 92 4 84 84 94 2 69 70 75 1 50 50 50 1/2 31 30 29 1/4 16 16 16 1/8 7 8 8 1/16 2 4 4 0.01 0.5 0.4 0.7 0.001 0.00035 0.026 0.07 0.0001 0.0000001 0.0016 0.007 a From Food and Drug Administration Advisory Committee on Pro- tocols for Safety Evaluation, 1971. rates. However, upon extrapolation to very low dose ranges, they would give very dissimilar estimates. This can be seen in Table III-5. Although the three models differ very little over a 256-fold dose range, they lead to increasingly divergent estimates upon extrapolation to very low levels. At a dose that is one-thousandth of the 50~o response dose, the single-hit model gives an estimated response rate 200 times as large as that given by the log-normal model. A limited animal bioassay conducted at dose levels high enough to give observable response rates cannot discriminate among these various models, and these same models are substantively divergent at lower dose levels. These factors present major difficulties for high to low dose extrapolations. Therefore, the model must be selected on the basis of biological considerations. This decision may greatly affect an estimated risk at a low dose level and, hence, a resulting regulatory standard. There is no unanimity concerning the proper way to incorporate the spontaneous, or background, response, i.e., responses that do not result from exposure to the chemical. One approach, which is used for carcinogens, assumes independent action between the chemical and the background. This is known as '`Abbott's correction." The other method,

58 DRINKING WATER AND H"LTH TABLE III-6 Extrapolated Dose-Induced Response Rates for a Log-Normal Model with Two Different Corrections for Background Dose Independent Additive to Level Action Background 1.0 0.47 0.45 0.1 0.14 0.13 0.01 0.019 0.018 0.001 0.13 x 10-2 0.19 x 10-2 0.00(~1 0.30 x 10-4 0.19 x 10-3 0.00001 0.20 x 10-6 0.19 x 10-4 which was proposed by Albert and Altshuler (1973), assumes that the dose of the carcinogen is additive to the background. These two approaches can give substantially different results when extrapolating outside of the observed dose range. Table III-6 shows an example of this difference for a log-normal dose-response model with a slope of unity and an overall 50970 response rate at a dose of one unit which includes a spontaneous, or background, rate of 5%. As the mathematical theory predicts (Crump et al., 1976), the model, assuming background additivity, approaches linearity at low dose levels. When fitting dose-response models to carcinogenesis data, the effective exposure level, which is the amount of the carcinogen actually reaching the target cells and molecules, is likely to be some complex function of the absorption, distribution, biotransformation, and excre- tion characteristics of the host. Each characteristic may depend upon and influence the level of the carcinogen to which the animals are environmentally exposed. With the current state of knowledge, the in- vivo mechanisms that relate environmental chemical exposure levels to the levels that reach the target cells are usually not adequately quantified. Consequently, assumptions of proportionality between the environmental exposure level and the effective exposure level may be wrong. The proportionality assumption is doubtlessly an oversim- plification of the true relationship in the absence of information on metabolic pathways, activation and deactivation systems, biological repair, and other pharmacokinetic considerations. However, this as- sumption is needed in order to apply the extrapolation models that are currently available. The Safe Drinking Water Committee (National Academy of Sciences, 1977) used a probabilistic multistage model to estimate the carcinogenic

Problems of Risk Estimation 59 risk from exposure to low doses. This model was chosen over others because it is based on a plausible biological mechanism of carcinogens, i.e., a single cell somatic mutation model for the initiation of cancer. Because the other models are more empirical, they were thought to be less desirable. At low doses, the multistage model is often mathematically equivalent to the linear or single-hit model. Therefore, its use for extrapolation is consistent with the conservative linear risk estimation. If the precise mechanism of carcinogenesis is represented by a threshold or log-normal dose-response relationship, the multistage model ma, considerably overestimate the risk at low dose levels. However, this possibility cannot be reasonably quantified. In the committee's report (National Academy of Sciences, 1977) risk calculations were made for each contaminant of drinking water that had been shown to be carcinogenic in an appropriate animal bioassay. The calculations were based on available carcinogenicity data and an average value was reported. To estimate quantitatively the cumulative carcino- genic risk of several carcinogens, or multiple responses due to the same carcinogen, e.g., liver and bladder tumors induced by 2.acetylamino- fluorene (2-AAF), the individual risks might be added. This assumes that interactions are not present and that the risks are small enough so that adjustments for joint probabilities are not needed. If interactions leading to synergism or antagonism are found, then adjustments must be made when cumulative effects are estimated. Estimates obt ined from each model have wide ranges of variability. This results from the statistical variability of the observations; the biological variability among strains, sexes, and organs of the laboratory animals; and the differences within the experimental range among different species. For the various compounds considered in Drinking Water and Health (National Academy of Sciences, 1977), the statistical upper 95% confidence limit on risk was typically a factor of 2 to 10 over the actual risk estimate. Occasionally, the multistage models that are the best fit to a data set do not contain a linear term. When this is true, the upper confidence limit would be orders of magnitude greater than the estimate itself. Variability of low dose risks among strains and species of rodents has also been empirically estimated for a few compounds. Roughly, it appears as though risk estimates may be a factor of 10 higher or lower than the median risk level (e.g., see Table 6.22 on chloroform, p. 192 in Chloroform, Carbon Tetrachloride. and Other Halomethanes, National Academy ofSciences, 19781.

60 DRINKING WATER AND H"LTH Finally, for six human carcinogens considered by the NAS study on pest control (Contemporary Pest Control Practices and Prospects, National Academy of Sciences, 1975), one finds that on an equivalent daily dose rate basis, the most sensitive rodent comes within a factor of to in predicting effects in humans. This assumes the use of the most sensitive species, the appropriate sex, and the appropriate site of action. In this report, comparisons were based on total lifetime dose per unit body weight. At times, this resulted in the rodent appearing to be more sensitive than humans. In conclusion, if the estimates of risk from low doses of carcinogens are made with reasonable data and reasonable models, the variability noted above results in a precision of 1 to 2 orders of magnitude in the estimates. CONCLUSION AND SUMMARY Finished drinking water may contain small amounts of many potentially toxic chemicals. The concentration of most of them is often so low that it is very difficult to predict a potential observable effect. In these cases of noncarcinogenic toxicity, the preferred procedure is to make a risk estimate based on extrapolation to low dose levels from experimental curves obtained from much larger doses where ejects can be readily measured. When such curves are not available, the ADI approach should be used until better data are available. In this approach, safety factors are applied to the highest no-observable-effect dose found in animal studies. The subcommittee believes that the ADI approach is not applicable to carcinogenic toxicity arid that high dose to low dose extrapolation methods should be used for carcinogens. Because of the uncertainties involved in the true shapes of the dose-response curves that are used for extrapolation, a multistage model might be fitted to the data. Such a model has more biological meaning than other models, e.g., the probit or logistic model. Moreover, it tends to be conservative in that, at low doses, it will give higher estimates of the unknown risk than will many others. More confidence could be placed in mathematical models fo extrapolation if they also incorporate the principles of pharmacokinetics and time to occurrence of tumors. Procedures for doing this are being studied and might be available soon. Much more effort is required in this area. Extrapolation from animals to humans should incorporate infor- mation on comparative pharmacokinetic data between the two species.

Problems of Risk Estimation 61 In the absence of such data the subcommittee suggests that the extrapolation be based on the surface area rule. When reliable, valid human data are available, they should be used in conjunction with information from animal bioassays. The weight given to the human data in this process will depend on its quality and sensitivity. REFERENCES Adolph, E.F. 1949. Quantitative relations in the physiological constitutions of mammals. Science 109:579-585. Albert, R.E., and B. Altshuler. 1973. Considerations relating to the formulation of limits for unavoidable population exposures to environmental carcinogens. Pp. 233-253 in C.L. Sanders, R.H. Busch, J. E. Ballou, and D.D. Mahlum, eds., Radionuclide Carcinogene- sis. AEC Symposium Senes. Available from NTIS as CONF-720505, Springfield, Va. Armitage, P. 1974. Multistage carcinogenesis models. Presented at the National Institute of Environmental Health Sciences Conference on Extrapolation of Risks to Man from Environmental Toxicants on the Basis of Animal Experiments. Wrightsville Beach, N.C., October 1974. Armitage, P., and R. Doll. 1961. Stochastic models for carcinogenesis. Pp. 1~39 in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 4. University of California, Berkeley, Calif. Ashford, J.R., and J.M. Colby. 1974. A system of models for the action of drugs applies singly or jointly to biological organisms. Biometrics 30:11-31. Bend, J.R., and G.E.R. Hook. 1977. Hepatic and extrahepatic m~xed-function oxidases. Pp 419~440 in D.H.K. Lee, ea., Handbook of Physiology. Sec. 9. Reactions to Environmen- tal Agents. Amencan Physiological Society, Bethesda, Md. Berkson, J. 1944. Application of the logistic function to big-assay. J. Am. Stat. Assoc. 39:357-365. Bischoff, K.B., R.L. Dedrick, D.S. Zaharako, and J.A. Longstreth. 1971. Methotrexate pharmacokinetics. J. Pharm. Sci. 60: 1128-1133. Bliss, C.I. 1939. The to~cicity of poisons applies jointly. Ann. Appl. Biol. 26:585 615. Brown, J.M. 1976. Linearity versus non-linearity of dose response for radiation carcinogen- esis. Health Phys. 31 :231-245. Burns, F.? M. Vanderlaan? A. Sivak. and R.E. Albert. 1976. The regression kinetics of mouse skin papillomas. Cancer Res. 36:1422-1427. Busvine, J.R. 1938. The toxicity of ethylene oxide to Canadra oryzae, C. granaria, Tnbolium castaneum, and Cimex lectularis. Ann. Appl. Biol. 25:605~32. Cantor, K.P., R. Hoover. T.J. Mason, and L.J. McCabe. 1977. Association of Halometh- anes in Drinking Water with Cancer Mortality. Environmental Epidemiology Branch, National Cancer Institute, Bethesda, Md. Unpublished. 24 pp. Carroll, K.K., and H.T. Khor. 1970. Effects of dietary fat and dose level of 7, 12- dimethylbenze (a) anthracene on mammary tumor incidence in rats. Cancer Res. 30:2260 2264. Chand. N., and D.G. Hoel. 1974. A comparison of models for determining safe levels of environmental agents. Pp. 681-700 in F. Proschan, and R.J. Serfling, eds., Reliability and Biometry, Statistical Analysis of Lifelength. Society for Industrial and Applied Mathematics, Philadelphia, Pa.

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Problems of Risk Estimation 63 Freireich, E.J., E.A. Gehan, D.P. Rall, L.H. Schmidt, and H.E. Skipper. 1966. Quantitative comparison of toxicity of anticancer agents in mouse, rat, hamster, dog, monkey, and man. Cancer Chemother. Rep. 50:219-244. Gail, M. 1975. Measuring the benefit of reduced exposure to environmental carcinogens. J. Chronic Dis. 28:135-147. Gaines, T.B., R.D. Kimbrough, and R.E. Linder. 1973. The oral and dermal toxicity of hexachlorophene in rats. Toxicol. Appl. Pharmacol. 25:332-343. Gart, J.J. 1965. Some stochastic models relating time and dosage in response curves. Biometrics 21 :583-599. Gehring, P.J., and G.E. Blau. 1977. Mechanisms of carcinogenesis: dose response. J. Environ. Pathol. Toxicol. 1 :163-179. Gillette, J.R. 1976. Application of pharmacokinetic principles in the extrapolation of animal data to humans. Clin. Toxicol. 9:709-722. Gillette, J.R. 1977. Kinetics of reactive metabolites and covalent binding in viva and in vitro. Pp. 25~1 in Biologically Reactive Intermediates, P.J. Jallow, J.J. Kocsis, R. Snyder and H. Vainio (eds). Plenum Press, New York. Goldsmith, M.A., M. Slavik, and S.K. Carter. 1975. Quantitative prediction of drug toxicity in humans from toxicology in small and large animals. Cancer Res. 35: 135~1364. Hamilton, M.A., and D.G. Hoel. 1978. Detection of synergistic effects in carcinogenesis. Biometrics 34(4):733. Hartley, H.O., and R.L. Sielken, Jr. 1977. Estimation of"safe doses" in carcinogenic experiments. Biometrics 33: 1-30. Hewlett, P.S., and R.L. Plackett. 1959. A unified theory for quantal responses to mixtures of drugs: non-interactive action. Biometrics 15:591-610. Hewlett, P.S., and R.L. Plackett. 1964. A unified theory for quantal responses to mixtures of drugs: competitive action. Biometrics 20:56~575. Hoel, D.G., D.W. Gaylor, R.L. Kirschstein, U. Saffiotti, and M.A. Schneidell~an. 1975. Estimation of risks of irreversible, delayed toxicity. J. Toxicol. Environ. Health 1: 133- 151. Hogan, M.D., P.Y. Chi, T.J. Mitchell, and D.G. Hoel. 1979. Association between chloroform levels in finished drinking water supplies and various site-specific cancer mortality rates. J. Environ. Pathol. Toxacol. 2:873-887. Hughes, W.L. 1957. A physical-chemical rationale for the biological activity of mercury arid its compounds. Ann. N.Y. Acad. Sci. 65:454~60. Hunter, C.G., J. Robinson, and M. Roberts. 1969. Pharrnacodynamics of dieldnn (HEOD): ingestion by human subjects for 18 to 24 months, and postexposure for eight months. Arch. Environ. Health 18: 12-21. Kellerer, A.M., and H.H. Rossi. 1971. RBE and the primary mechanism of radiation action. Radiat. Res. 47: 15-34. Kociba, R.J., P.A. Keeler, C.N. Park, and P.J. Gehnng. i 976. 2,3,7,8-Tetra- chlorodibenzo-p-dioxin (TCDD): results of a 13-week oral toxicity study in rats. Toxicol. Appl. Phannacol. 35:553-574. Krasovskii, G.~. 1976. Extrapolation of experimental data from animals to man. Environ. Health Perspect. 13 :51 -58. Kuntzman, R., L.C. Mark, and L. Brand. 1966. Metabolism of drugs and carcinogens by human liver enzymes. J. Pharrnacol. Exp. Ther. 152: 151-156. Lehman. A.J. 1962. The annual per capita consumption of selected items of food in the United States. Assoc. Food Drug Off. U.S. Q. Bull. 26:149-151. Lehman, A.J., and O.G. Fit~hugh. 1954. 100 Fold margin of safety. Assoc. Food Drug Off. Q. Bull. 18:33-35.

64 DRlNKl~G WATER AND H"LTH Levy? G., T. Tsuchiya, and L.P. Amsel. 1972. Limited capacity for salicyl phenolic glucurorude formation and its effect on the kinetics of salicylate elimination in man. Clin. Pharmacol. Ther. 13:258-268. Lindstrom, F.T., J.W. Gillett, and S. E. Rodecap. 1 974. Distribution of HEOD (dieldrin) in mammals. I. Preliminary model. Arch. Environ. Toxicol. 2:9~2. Lundin, F.E., J.W. Lloyd, E.M. Smith, V.E. Archer, and D.A. Holaday. 1969. Mortality of uranium miners in relation to radiation exposure, hard rock mining and cigarette smoking-1950 through September 1967. Health Phys. 16:571-578. Mantel, N.. and W.R. Bean. 1961. "Safety,' testing of carcinogenic agents. J. Nat. Cancer - Inst. 27:455~70. McCabe, L.J. 1975. Association Between Halogenated Methanes in Drinking Water and Mortality (NORS Data). Water Quality Division, Environmental Protection Agency. Unpublished. 4 pp. National Academy of Sciences. 1975. Contemporary Pest Control Practices and Prospects. Environmental Studies Board, Commission on Natural Resources, National Academy of Sciences, Washington, D.C. National Academy of Sciences. 1977. Dnnking Water and Health. Safe Drinking Water Committee, National Academy of Sciences. Washington, D.C. 939 pp. National Academy of Sciences. 1978. Chloroform, Carbon Tetrachloride, and Other Halomethanes: An Environmental Assessment. Environmental Studies Board, Comis- sion on Natural Resources. National Academy of Sciences, Washington, D.C. 294 pp. Nelson, E.B.. P.P. Raj, K.J. Belfi, and B.S.S. Masters. 1976. Oxidative drug metabolism in human liver microsomes. J. Pharmacol. Exp. Ther. 178:58~588. Peto, R. 1974. Time to occurrence models. Presented at the National Institue of Environmental Health Sciences Conference on Extrapolation of Risks to Man from Environmental Toxicants on the Basis of Animal Experiments. Wrightsville Beach, N.C., October 1974. Peto, R., P.N. Lee, and W.S. Paige. 1972. Statistical analysis of the bioassay of continuous carcinogens. Br. J. Cancer 26:258-261. Pike, M C. 1966. A method of analysis of a certain class of experiments in carcinogenesis. Biometrics 22: 142-161. Pinkel, D. 1958. The use of body surface area as a criterion of drug dosage in cancer chemotherapy. Cancer Res. 18: 853-856. Plackett, R.L.' and P.S. Hewlett. 1952. Quantal responses to mixtures of poisons. J. R. Stat. Soc. Ser. B 14:141-154. Plackett. R.L.. and P.S. Hewlett. 1967. A comparison of two approaches to the construction of models for quantal responses to mixtures of drugs. Biometrics 23:27 44. Quinn, G.P.. J. A,celrod, and B.B. Brodie. 1958. Species, strain and sex differences in metabolism of hexobarbitone, amidopyrine, antipyrine and aniline. Bio^hem. Pharma- col.l:l52-159. Reed. L.J., and J. Berkson. 1929. The application of the logistic function to experimental data. J. Phys. Chem. 33:76~779. Roe. F.J.C.. and J. Clack. 1964. Two-stage carcinogenesis: effect of length of promoting treatment on the yield of benign and malignant tumors. Br. J. Cancer 17:596~04. Rossi, H.H., and A.M. Kellerer. 1974. The validity of risk estimates of leukemia incidence based on Japanese data. Radiat. Res. 58: 131-140. Rothman. K., and A. Keller. 1972. The effect of joint exposure to alcohol and tobacco on nsk of carlcer of the mouth and pharynx. J. Chronic Dis. 25:71 1-716. Schmahl, D. 1976. Combination effects in chemical carcinogenesis (experimental results). Oncology 33: 73-76.

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