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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

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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;

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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

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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

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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

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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

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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

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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

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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~) 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

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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,

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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,

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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

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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.

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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.

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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.

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Problems of Risk Estimation 65 Selikoff, I.J., E.C. Hammond, and J. Churg. 1968. Asbestos exposure, smoking and neoplasia. J. Am. Med. Assoc. 204: 106 112. Shortley, G. 1965. A stochastic model for distributions of biological response tunes. Biometrics 21 :562-582. Smyth, ELF., Jr., C.S. Weill, J.S. West, and C.P. Carpenter. 1969. An exploration of joint toxic action: twenty-seven industrial chemicals intubated in rats in all possible pairs. Toxicol. Appl. Pharmacol. 14:34~347. Turner, M.E. 1975. Some classes of hit-theory models. Math. Biosci. 23:219-235. U.S. Environmental Protection Agency. 1975. Preliminary assessment of suspected carcinogens in drinking water. Report to Congress. U.S. Environmental Protection Agency, Washington, D.C. 52 pp. Vos, ].G., J.A. Moore, and J.G. Zinkle. 1974. Toxicity of 2,3,7,8-tetrachlorodibenzop- dioxin (TCDD) in C57B1/6 mice. Toxicol. Appl. Pharmacol. 39:229-241. Wagner, J.G. 1974. A modern view of pharmacokinetics. Pp. 27-67 in T. Teorell, R.L. Dedrick, and P.G. Condliffe, eds., Pharmacology and Pharmacokinetics. Plenum, New York. Walker, A.I.T., D.E. Stevenson' J. Robinson, E. Tho~pe, and M. Roberts. 1969. The toxicology and pharmacodynamics of dieldrin (HEOD): two-year oral exposure of rats and dogs. Toxicol. Appl. Pharmacol. 15 :345-373. Walters, hI.A., and F.J.C. Roe. 1964. The effect of dietary casein on the induction of lung tumors by the injection of 9,10-dimethyl-1,2-benzanthracene (DMBA) into newborn mice. Br. J. Cancer 18:312-316. Werkheiser, W.C. 1971. Mathematical simulation in chemotherapy. Ann. N.Y. Acad. Sci. 186:343-358. Whittemore, A., and J.B. Keller. 1978. Quantitative theories of carcinogenesis. SAIAM Review 20(1): 1-30. Williams, R.T. 1974. Inter-species variations in the metabolism of xenobiotics. Biochem. Soc. Trans. 2:359-377.

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