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PART V11 Summary: Prospectives and Future Directions

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Prospective Predictions and Validations in Anticancer Therapy Jerry M. Collins I NTRODUCTION At first glance, the processes of anticancer drug development and en- vironmental risk assessment may not seem to have much conceptual over- lap. However, there is a strong common thread based upon the need to make decisions regarding allowable human exposure limits. In both cases, heavy reliance is placed upon interspecies toxicological comparisons. Risk assessment is based upon both mathematical models and experi- mental data. For example, the data might be the incidence of tumor formation in rodents following controlled laboratory exposures to a toxin. The role of the model is to predict the incidence of carcinogenesis in humans under a variety of occupational and/or environmental exposure conditions. The weakest link in this process is model validation. Due to ethical considerations, it is not usually possible to administer precise amounts of toxic chemicals to humans. If a human population develops an unusual form of cancer, epidemiologic detectives might be able to trace the source to a particular chemical. The human exposure data are estimated retrospectively in whatever fashion possible, but the uncertainty in these calculations is a major hurdle in quantitative analyses. Once a specific chemical becomes suspect, it would be possible to do a set of quantitative experiments in animals. Even if we accept these examples with their imprecise estimates of human exposure, the total data base for model validation is very small. Yet a variety of needs forces us to accept these models as the basis for 431

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432 JERRY M. COLLINS major prospective decisions that have an impact upon the health of citizens and the economic well-being of corporations and communities. The preclinical toxicology phase of drug development shares some of the same facets as the safety testing of industrial pollutants or other po- tential environmental contaminants. For example, animals are used to determine a lethal dose, such as the lethal dose for 10% of the animals tested (LD~o). That estimate is then used to determine safety in humans. Perhaps the single largest difference between the development of anti- cancer drugs and the assessment of risks from environmental contaminants is that direct experimental evidence is obtained in humans that can be (rapidly) compared with data from animals. The treatment of a life-threatening disease requires a rather different set of risk-to-benefit decisions than considerations of maximally allowed pollutants. The drugs used for the treatment of cancer have narrower safety margins than those used for most other diseases. In general, the ratio of a therapeutic dose to a toxic dose approaches unity. DRUG DEVELOPMENT Drug development consists of a progression of steps (Table 1) that starts with the discovery of a new compound and ends with a clinical deter- mination of therapeutic utility. To begin human testing, a safe starting dose is needed. Establishment of a safe starting dose is one of the chief functions of preclinical toxicology studies. As reviewed by Grieshaber and Marsoni (1986), the current preclinical toxicology protocol for anti- cancer drugs provides the basis for a safe starting dose, tailored to potency in rodents. The human starting dose is 1/10 of the mouse ODD, expressed on a milligrams/square meter basis. Prior to human testing, this dose is confirmed in a second species. After the starting dose has been evaluated in patients, subsequent doses are escalated. Although there is always therapeutic intent when an anti- cancer drug is given to patients, the major scientific goal of initial clinical trials is to determine the acute, reversible toxicity. The endpoint of these phase I trials is called the maximum tolerated dose, or MTD. The MTD TABLE 1 Stages of Drug Development Name Function Preclinical Discovery Random or planned Screening Bioactivity Toxicology LD,o; organ sites Clinical Phase I Safety Phase II Activity Phase III Efficacy

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Predictions and Validations in Anticancer Therapy 433 is used to establish the dose for more detailed efficacy studies in phase II testing. The procedure used for dose escalation must achieve a balance between the desire to escalate slowly enough to be safe and the desire to escalate fast enough to be efficient. The most commonly used procedure is known as the modified Fibonacci scheme (Goldsmith et al., 19751. The initial escalation is rapid (100%, or doubling of the dose); subsequent escalations narrow down until the 30-35% range is reached (Figure 11. In summary, there are two areas of risk assessment that are encountered in these early clinical trials: (1) selection of a safe starting dose, and (2) choosing the rate of dose escalation. A_ In O 3 _.' ~ O _ ~ _ ~ ~ a) Q ~ _' 2 - 0.7 - 0.5 - 0 0.1 O O 0 07 0.05 _ 0.03 10 - Doxorubicin 5 - 6-MP Daunomyctn Thalicarpine Acitnomycin D Vincristine AZQ - AMSA Teroxlrone x5 ~ Teroxirone Dlhydro-AC Carbo-Plat NMethylFor Hon~oHar ThioTEPA Triciribine - AnguidTne Triciribine x5 (I ~ F-Ara-AMP Entry - F-AraAMP x5 30-352; 30-35% 30 - 35~; 30 - 357 30-352; 30-35% 30 - 35% 30 - 357 30-35% 40% 50% 67~; 1 00% FIGURE 1 Interspecies toxicity comparison. For these 17 anticancer drugs, the median MTD in humans was equal to the mouse LD~o, when both doses were expressed on a milligram/square meter basis. To compare toxicity on a milligram/kilogram basis, the ordinate was multiplied by 0.083. All drugs were given as single doses ( x 1) or as five daily doses ( x 5). Data in the second column are from Grieshaber and Marsoni (1986). Data in the first column were collected from information in the literature or on file in the Toxicology and Investigational Drug Branches, Division of Cancer Treatment, National Cancer Institute. As a reference, the modified Fibonacci escalation steps are shown in the third column. Adapted from Collins et al. (1986).

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434 ~ ERRY M. COLLl NS COMPARISON OF HUMAN AND MURINE TOXICITY How well does this strategy work? In Figure 1, the ratio of (human MTD)/(mouse Log) is presented for a series of anticancer drugs (Collins et al., 19861. First, it is worth noting that this particular collection of interspecies toxicology data, although not exhaustive, probably exceeds any comparable compilation for environmental contaminants or other hu- man toxins. Rather than focusing on specific drugs at this stage, it is helpful to get some appreciation of the range of variation. It could be argued that there is considerable variation, even though the average is quite reasonable. It might also be reasonably argued, however, that this level of agreement is adequate for comparative purposes. A number of factors provide motivation to probe further. For example, patient safety might be improved by a better understanding of the sources of this vari- ation. Also, the efficiency of early clinical testing might be raised if the toxicologic variation could be related to measurable determinants, such as plasma levels. What are possible explanations for this variation in toxicity between mouse and man? Table 2 lists three possibilities: (1) differences in drug metabolism, elimination, and binding; (2) exposure time differences; and (3) target cell sensitivity differences. Elimination rates determine the drug exposure, or C x T. the area under the concentration versus time curve. The concept of C x T with regard to drug toxicity originated during World War I (Prentiss, 19371. German pharmacologists observed that mustard agents are equally toxic whether a high concentration is inhaled for a short time or a low concentration is inhaled for a long time. The essential feature is that the CxT is the determinant of effect rather than the absolute concentration itself. Most toxicologists have presented their dosing information in terms of milligrams/kilogram. Based upon the relationships between body surface area and body weight (Freireich et al., 1966), it is possible to interconvert dosing data between milligrams/square meter and milligrams/kilogram. For mice, the relationship is 1 m2 = 3 kg. For humans, it is 1 m2 = 37 kg. Empirically, either set of units can be used to present raw data. The use of body surface area has a distinct advantage, however, when toxicity TABLE 2 Potential Explanations for Variation in Toxicity Between Mouse and Man 1. Species differences in drug metabolism, elimination, and binding 2. Schedule dependency due to exposure time differences 3. Species differences in target cell sensitivity

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Predictions and Validations in Anticancer Therapy 435 comparisons are made across species. The physiological determinants of elimination rates (such as glomerular filtration rate or organ blood flow) tend to be highly correlated with body surface area. Thus, if the dose is expressed in milligrams/square meter and elimination rates (milliliter/min- ute/square meter) are identical in mice and men, then the drug exposure (C x T) will be the same in both species at the same dose. On the other hand, if the dose is expressed in milligrams/kilogram, the dose in humans that produces equal C x T will be 1/12th the mouse dose, because a correction must be made for body surface area differences. The factor of 12 is simply the ratio of body surface area constants, 37/3. Freireich et al. (1966), Skipper et al. (1971), and Schabel et al. (1983) have reported that with many anticancer drugs, toxicity observations carry across species on a milligram/square meter basis, as long as schedules are similar. They also were aware, however, that there are exceptions and that more complete exposure parameters such as C x T or plasma phar- macokinetics allow more useful comparisons of toxic or therapeutic re- sponses from experimental and clinical studies. Doxorubicin appears to be an example of metabolism/elimination dif- ferences. The MTD in man is fivefold greater than the LD~o in mice, on a milligram/square meter basis. Yet, as shown in Figure 2, there is con- siderable agreement between blood levels measured at equitoxic doses. It appears that humans are more tolerant than mice due to a higher clearance (milliliters/minute/square meter) for doxorubicin. FACTORS OTHER THAN C x T The second factor of possible importance is a difference in exposure times. For some drugs, there are threshold concentrations or time depen- dencies that are related to toxicity and/or mechanisms of action. For drugs with equal clearance values in mice and humans (milliliters/minute/square meter), Skipper and colleagues (1971) have made the point that a bolus dose of equal milligrams/square meter generally produces rather different time courses in mice and man (Figure 3~. If there is a threshold for action and a critical exposure time, where the threshold lies can give major differences in species response. For example, if the threshold in Figure 3 is set at 10-6 M, there is no effect in man. If the threshold is set at 10-7 M, however, the duration of effect is much longer in man than in mice. Note that the time course for doxorubicin (Figure 2) is an exception to the generalized pattern. In a classic study by Quinn et al. (1958) 29 years ago, the threshold effect was first demonstrated for the barbiturate hexobarbital. After a standard dose of 50 to 100 mg/kg was given to mice, rats, and rabbits,

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436 JERRY M. COLLINS 10-5 o _' o _ 10-6 mu o c 10-7 r ~ At 10-8 - 7 - t O Mouse LD1 0 (1 8 mg/sq.m) t Human MID (90 mg/sq.m) . _ _ . . .. . . l l 24 6 12 TIME (hours) FIGURE 2 Doxorubicin plasma concentrations in mice and humans at equitoxic doses. Human data were scaled from a 75-mg/m2 intravenous (i.v.) dose. Mouse data were scaled from a 75- mg/m2 dose given i.v. to CDFl mice. Reprinted with permission from Collins et al. (1986). there was substantial variation in the drug effectiveness. The times to awakening were 12, 90, and 49 min in mice, rats, and rabbits, respectively. When the plasma pharmacokinetics of hexobarbital were investigated, it was found that the three species exhibited rather different elimination rates, or plasma half-times. At the time of awakening, however, the plasma drug concentration was similar in all three species. Thus, this is an example of a species difference in drug effect that is determined by pharmacokinetic changes in exposure patterns. Studies in dogs did not give as clear a pattern as for the other three species. The first two reasons for the species variation in toxicology have been oriented toward plasma pha~acokinetics. The third factor essentially covers all explanations that are not related to the delivery of the drug to the site of action. There can be differences at the cellular level that de- termine species sensitivity. For example, if the drug needs to be activated

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Predictions and Validations in Anticancer Therapy 437 inside the cell, there may be a species difference in activation capabilities. Fludarabine phosphate (F-Ara-AMP) has been found to have the largest difference in dose (10- to 30-fold) between the mouse LD~o and the human MID. This discrepancy is apparently an example of species differences in target cell sensitivity. The phosphate group on F-Ara-AMP makes the drug readily soluble, but it is rapidly cleaved to F-Ara-A in viva. Within 5 min following administration, only the F-Ara-A form can be detected in plasma. As shown in the plasma profiles following single doses of F-Ara-AMP (Figure 4), there is no obvious plasma pharmacokinetic ex- planation for the species difference in toxicity. In contrast to the situation for doxorubicin (in which equitoxic doses produced similar plasma drug concentrations), it can be seen from these data that the plasma concen- trations of the circulating species F-Ara-A are considerably different. Studies with bone marrow cultures in vitro indicate that human bone 10 ~5 ~ ~ Mouse-Man sample plot Skipper Concept 10 -6 S: o _ O 10-7 o \ \ \ \ \ Mouse \\ ~~i-------- Human .. \ \ \ . . 10-8 0 3 6 12 .. - , . . 24 TIME (hours) FIGURE 3 Idealized plasma concentrations in mice and humans following equal bolus doses (milligrams/square meter). Assume that volume of distribution (liters/kilogram) and clearance (milliliters/minute/square meter) are similar in both species. Adapted from Skipper et al. (1971).

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438 ~ ERRY M. COLLI NS 1000 ~ lo: 100 o ._ Cat o ~ 10 of: 1 1 Ah\ - 452\ \ - titmouse LD10, 2600 mg/sq.m ~ ~` ` `^ - ~_, Human MTD, 260 mg/sq.m 1 ~ , . 0 240 480 720 TIME (minutes) FIGURE 4 F-Ara-A plasma concentrations in mice and humans at equitoxic doses. Mouse data are from Noker et al. (1983). Human data are from Malspeis (Minutes of the Phase I Working Group, Bethesda, Md., June 13-14, 1983). Reprinted with permission from Collins et al. (1986). marrow cells are intrinsically more sensitive to this particular compound than are mouse marrow cells (C. Poston et al., unpublished data). Because bone marrow suppression is the principal acute toxicity in viva, it appears that the species differences are due to target cell differences for this drug. SUMMARY OF DATA C x T information is listed for 12 anticancer drugs in Table 3. For the first nine of these drugs, the C x T ratio is a useful predictor of the relative toxicity in mice and humans. For S-azacytidine, doxorubicin (as already discussed), and teroxirone, the C x T ratio is far better than the dose ratio. For the next five drugs on this list, the C x T ratio was also a reasonable predictor, although it was about the same as the dose ratio. For thio- TEPA, the C x T ratio was also an improvement over the dose ratio.

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Predictions and Validations in Anticancer Therapy 439 TABLE 3 The Mouse as a Quantitative Predictor of Human Toxicity: Comparison of Dose Ratio (milligram/square meter basis) and C x T Ratio for Human MID to Mouse LD1o Dose C x T Drug ratio ratio 1. 5-Azacytidine 6.5 (1.1) 2. Doxorubicin 5.0 0.8 3. Teroxirone 4.3 0.8 4. Diaziquone (AZQ) l.O (0-7) 5. Indicine-N-oxide 0.9 0.6 6. Amsacrine (AMSA) 0.8 1.3 7. Deoxycoformycin 0.7 1.1 8. Tiazofurin 0.7 0.9 9. Thio-TEPA 0.4 1.0 10. PALA 2.8 3.3 11. F-Ara-AMP 0.1 0.1 12. Dihydroazacytidine 1.2 0.3 There are also some drugs for which the C x T ratio was not an effective predictor of toxicity. For PALA, both the dose ratio and the C x T ratio were overly conservative; i.e., humans were threefold more tolerant than mice. A more serious case arises when man is less tolerant than mice. Two such cases were found in our survey. F-Ara-AMP was discussed above. Dihydroazacytidine was also a case in which man was less tolerant than mice, due to severe chest pain. As pointed out by Grieshaber and Marsoni (1986), it is not easy to pick up some toxicities in a mouse toxicology study. Thus, the use of C x T seems to be a useful starting point for under- standing differences in toxicity between mouse and man, but it is not completely accurate. Further work is ongoing at the National Cancer Institute that is exploring the use of C x T data to adjust escalation rates in phase I trials (Collins et al., 19861. CONCLUSIONS The development of new anticancer drugs generates a unique quanti- tative data base that can be used for interspecies comparisons of toxicity. In addition to serving as a collection of empirical toxicity data, the data base can be used for the testing of hypotheses regarding the fundamental determinants of toxicity. For example, the role of pharmacokinetics can be probed. Finally, the insights gained from analyses of past experience can be put to practical use in the form of improvements to the drug development process.

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460 DAN ~ EL KREWSK' ET AL. I.:. _ Gas Exchange 1 Lung Metabolism . . . ~ . .. . .; ... ......... . .. . .. ._ .... . ..... .% .... ...... .... .. . ....... .................... ..... - ............. ;;; ........ .... .. . ..,... .; ... ,., x ~ ... ~~ .. N. -., A---,, %, ~ ~~ RICHLY PERFUSED ~ : ~ . . . .. ... ... r ~ . . ' ~ Y. -::: ~ ~ ~ .~.; -: .~::$:'~ ::: ~ -: :: :: .: :: ::-: t:::':::: :- ~ :.:: :.: :: :~ SLOWLY PERFUSED :: ~ ~ ~ I G. 1. TRACT FIGURE 9 A physiologic phaImacokinetic model for methylene chloride (Andersen et al., 1987). of the GST path. Nonetheless, on the basis of other biochemical consid- erations, Andersen et al. (1987) concluded that the GST surrogate is the most appropriate predictor of tumor incidence. Based on the GST path, the delivered dose in the high-dose groups is approximately 100 times higher in the inhalation study than in the drinking

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PK Data in Carcinogenic Risk Assessment 461 water study, as compared with the tenfold difference indicated by using the administered doses. This is due to the fact that the doses in the inhalation study were all well above the level necessary to saturate the MFO path, leading to a high rate of activity in the GST path (figure 10), whereas those in the drinking water study were not. An upper confidence limit on the risk at low doses for female mice can be calculated by using robust linear extrapolation based on the delivered dose data from the inhalation study in Table 4 to be 0.56 (g/liter/day) - I. At low doses, the rate of the GST path is approximately 0.036 mg/liter/ day/ppm, so that the low-dose slope on the administered dose scale is 2.0 x 1o-s Pam-. Working directly on the administered dose scale, the low-dose slope value would be 2.4 x 1O-4 ppm-~, which is 12 times higher. To extrapolate to humans, we follow the results of Andersen et al. (1987) and assume that the GST surrogate has the same potency across species on a body weight scale. Calculation of the amount of GST surrogate formed in humans requires determination of the human values of the model parameters by allometric scaling or, preferably, by experimental mea- surement. In the present example, Andersen et al. (1987) calculated many of the physiological constants and the rates of the GST path allometrically, but determined the metabolic constants involved in the saturable MFO pathway expenmentally. The calculation also requires specification of the dosing regimen. At low doses, inhalation of methylene chloride for 6 h 150 as - J _ ~ 100 - a) - ce o 50 3 CO CO C, o / / / - / 100 200 300 400 Administered Dose (ppm) FIGURE 10 GST activity in the liver in mice due to 6-in/day exposure to methylene chloride.

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462 DAN ~ EL KREWSK! ET AL. daily results in GST rate per part per million of about 0.012 mg/liter/day/ ppm, one-third of the rate for mice. Thus, the 95% upper confidence limit on the low-dose slope for humans is 6.7 x 10-6 ppm-i, which is 36 times less than the corresponding value for mice calculated on the basis of the administered dose. It is worth noting that this ratio does not apply to all dosing routes. For example, when drinking water exposure is modeled as continuous infusion to the liver, human GST activity per unit dose is 0.16 (mg/liter/day)/(mg/ kg/day). This is about 3 times higher than that of mice, rather than 3 times lower as calculated above for inhalation exposure. C. Chen and J. N. Blancato (this volume) used a similar physiological pharmacokinetic model to assess the risks of exposure to perchloroethylene (PCE). Their model had no lung metabolism compartment, because one path in the liver was assumed to account for all metabolism and to produce the active metabolite. Its rate was used as the dose surrogate. Species equivalence on surface area, body weight, liver volume, and air concen- tration scales were all considered. In each case, the use of the metabolized dose produced estimates of human risks 5-10 times lower than calculations based on the administered dose. SUMMARY AND CONCLUSIONS The process of carcinogenic risk assessment based on the results of toxicological experiments conducted in the laboratory involves certain assumptions, such as that of low-dose linearity when extrapolating from high to low doses. By using a simple mathematical pharmacokinetic model for metabolic activation in which the probability of tumor induction is proportional to the delivered dose, it was shown with a computer simu- lation that saturation effects in metabolic activation resulting in a curvi- linear dose response can have an impact on estimates of low-dose risk obtained by linear extrapolation. In particular, saturation of detoxification processes can result in an appreciable overestimation of risk, whereas saturation of activation processes can lead to some underestimation of risk. The most accurate estimates of risk are obtained with a linear dose response. These effects were further evaluated by using existing data on formal- dehyde and vinyl chloride monomer, using covalent binding to DNA in the nasal mucosa and the level of metabolism in the liver as possible measures of delivered dose, respectively. With formaldehyde, low-dose risks predicted on the basis of delivered dose were a factor of 4 lower than those obtained by using the administered dose level, because of the nonlinear relationship between the delivered and administered doses within the experimental dose range. Because VCM metabolism is nearly pro- portional to the level of exposure at low to moderate doses, estimates of

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PK Data in Carcinogenic Risk Assessment 463 low-dose risk based on either the delivered or administered dose scale were virtually identical. The dose delivered to the target tissue may vary with time, depending on both the exposure regimen and metabolic activation. By using a simple mathematical compartmental model based on linear kinetics, it was dem- onstrated that exposure regimens with different dosing intervals having the same systemic availability lead to different peak concentrations in the target tissue. In the absence of bioaccumulation, however, it was noted that under the multistage model of carcinogenesis, the area under the concentration-time curve is a better predictor of carcinogenic risk than are peak concentrations. Carcinogenic risk assessment can also require extrapolations between different routes of exposure and from the animal model used to humans. This can be done with PB-PK models. With methylene chloride and perchloroethylene, it was noted that estimates of low-dose risks in humans using predictions of dose delivered to the target tissue based on such models can be substantially lower than traditional estimates based on the use of the administered dose level. In conclusion, pharmacokinetic models can be used to obtain more accurate estimates of risk at low doses through the use of the dose delivered to the target tissue as a surrogate for the administered dose in toxicological studies, particularly when the response of interest is roughly proportional to the delivered dose. Predictions of the internal tissue dose for other routes of exposure can be obtained by using PB-PK models, provided that measurements of the physiological and biochemical constants associated with the different routes are available. Extrapolation between species can also be facilitated by using physiological models to predict the delivered dose in the species of interest. In those cases in which all of the relevant model parameters cannot be measured directly in humans, however, these must be obtained by scaling the corresponding values in animals. This approach to interspecies extrapolation is of most use when the dose- response curves for animals and humans are comparable when expressed in tees of delivered dose. ACKNOWLEDGM ENTS We thank Dr. Richard Reitz for kindly providing the data shown in Figure 10, and for helpful comments on the original draft of this article. REFERENCES Adolph, E. F. 1949. Quantitative relations in the physiological constitutions of mammals. Science 109:579-585. Albert, R., A. Sellakumar, S. Laskin, M. Kuschner, N. Nelson, and C. Snyder. 1982. Gaseous formaldehyde and hydrogen chloride induction of nasal cancer in the rat. J. Nat. Cancer Inst. 68:597-603.

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464 DAN ~ EL KREWSK! ET AL. Andersen, M. E., R. L. Archer, H. J. Clewell, and M. G. MacNaughton. 1984. A physiological model of the intravenous and inhalation pharmacokinetics of three dihalo- methanes CH2Cl2, CH2BrCl, CH2Br2 in the rat. Toxicologist 4:111. Andersen, M. E., H. J. Clewell III, M. L. Gargas, F. A. Smith, and R. H. Reitz. 1987. Physiologically based pharmacokinetics and the risk assessment process for methylene chloride. Toxicol. App. Pharmacol. 87:185-205. Anderson, E. L., and the Carcinogen Assessment Group of the U.S. Environmental Pro- tection Agency. 1983. Quantitative approaches in use to assess cancer risk. Risk Analysis 3:277-295. Armitage, P. 1985. Multistage models of carcinogenesis. Environ. Health Perspect. 63: 195- 201. Bickis, M., and D. Krewski. 1985. Statistical design and analysis of the long-term car- cinogenicity bioassay. Pp. 125-147 in Toxicological Risk Assessment, Vol. I, Biological and Statistical Criteria, D. B. Clayson, D. Krewski, and I. C. Munro, eds. Boca Raton, Fla.: CRC Press. Brown, C. C., T. R. Fears, M. H. Gail, M. Schneiderman, R. E. Tarone, and N. Mantel. 1978. Letter to the editor and reply by J. Cornfield. Science 202:1105-1108. Casanova-Schmitz, M., T. B. Starr, and H. d'A. Heck. 1984. Differentiation between metabolic incorporation and covalent binding in the labeling of macromolecules in the rat nasal mucosa and bone marrow by inhaled 14C- and 3H-formaldehyde. Toxicol. Appl. Pharmacol. 76:26 4~1. Cornfield, J. 1977. Carcinogenic risk assessment. Science 198:693-699. Crump K. S., and R. B. Howe. 1984. The multi-stage model with a time-dependent dose pattern: Applications to carcinogenic risk assessment. Risk Analysis 4:163-176. Crump, K. S., D. G. Hoel, C. H. Langley, and R. Peto. 1976. Fundamental carcinogenic processes and their implications for low dose risk assessment. Cancer Res. 36:2973- 2979. Davis, N. R., and W. W. Mapleson. 1981. Structure and quantification of a physiological model of the distribution of injected agents and inhaled anesthetics. Br. J. Anesthesiol. 53:399-405. Day, N. E. 1985. Epidemiological methods for the assessment of human cancer risk. Pp. 3- 15 in Toxicological Risk Assessment, Vol. II, General Criteria and Case Studies, D. B. Clayson, D. Krewski, and I. C. Munro, eds. Boca Raton, Fla.: CRC Press. Day, N. E., and C. C. Brown. 1980. Multistage models and the primary prevention of cancer. J. Nat. Cancer Inst. 64:977-989. Dittert, L. W. 1977. Pharmacokinetic prediction of tissue residues. J. Toxicol. Environ. Health 2:735-756. EPA (U.S. Environmental Protection Agency). 1985. Health assessment document for dichloromethane (methylene chloride). Final Report. EPA/600/8-82/004F. Washington, D.C.: U.S. Environmental Protection Agency. Evans, C. L. 1967. The toxicity of hydrogen sulphide and other sulphides. Q. J. Exp. Physiol. 52:231-248. Fiserova-Bergerova, V. 1983. Physiological models for pulmonary administration of inert vapors and gases. In Modeling of Inhalation Exposure to Vapors: Uptake, Distribution and Elimination, Vol. 1, V. Fiserova-Bergerova, ed. Boca Raton, Fla.: CRC Press. Gehring, P. J. 1978. Chemobiokinetics and metabolism. In Principles and Methods for Evaluating the Toxicity of Chemicals, Part I. Geneva: World Health Organization. Gehring, P. J., and G. E. Blau. 1977. Mechanisms of carcinogenesis: Dose response. J Environ. Pathol. Toxicol. 1 :163-179

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PK Data in Carcinogenic Risk Assessment 465 Gehring, P. J., P. G. Watanabe, and C. N. Park. 1978. Resolution of dose-response toxicity data for chemicals requiring metabolic activation: Example vinyl chloride. Toxicol. Appl. Pharmacol. 44:581-591. Gibaldi, M., and D. Perrier. 1975. Pharmacokinetics. New York: Marcel Dekker. Gillette, J. R. 1976. Application of pharmacokinetic principles in the extrapolation of animal data to human. Clin. Toxicol. 9:709-721. Hammer, R., and G. Bozler. 1977. Pharmacokinetics as an aid in the interpretation of toxicity tests. Arzneim. Forsch. 27:555-557. Himmelstein, K. J., and R. J. Lutz. 1979. A review of the applications of physiologically based pharmacokinetic modeling. J. Pharmacokinet. Biopharm. 7:127-145. Hoel, D. G. 1985. Incorporation of pharmacokinetics in low-dose risk estimation. Pp. 205- 214 in Toxicological Risk Assessment, Vol. I, Biological and Statistical Criteria, D. B. Clayson, D. Krewski, and I. C. Munro, eds. Boca Raton, Fla.: CRC Press. Hoel, D. G., N. L. Kaplan, and M. W. Anderson. 1983. Implication of nonlinear kinetics on risk estimation in carcinogenesis. Science 291:1032-1037. Krewski, D., and C. Brown. 1981. Carcinogenic risk assessment: A guide to the literature. Biometrics 37:353-366. Krewski, D., and J. Van Ryzin. 1981. Dose response models for quantal response toxicity data. Pp. 201-231 in Statistics and Related Topics, M. Csorgo, D. Dawson, J. N. K. Rao, and E. Saleh, eds. Amsterdam: North-Holland. Krewski, D., C. Brown, and D. Murdoch. 1984. Determining "safe" levels of exposure: Safety factors or mathematical models? Fund. Appl. Toxicol. 4:S383-S394. Krewski, D., D. Murdoch, and A. Dewanji..1986. Statistical modelling and extrapolation of carcinogenesis data. Pp. 259-282 in Modern Statistical Methods in Chronic Disease Epidemiology, S. H. Moolgavkar and R. L. Prentice, eds. New York: Wiley-Interscience. Maltoni, C., G. Lefemine, A. Ciliberti, G. Cotti, and D. Carretti. 1981. Carcinogenicity bioassays of vinyl chloride monomer: A model of risk assessment on an experimental basis. Environ. Health Perspect. 41:3-29. Mantel, N., and M. A. Schneiderman. 1975. Estimating safe levels, a hazardous under- taking. Cancer Res. 35: 1379-1386. McDougal, J. N., G. W. Jepson, H. J. Clewell, M. G. MacNaughton, and M. E. Andersen. 1986. A physiological pharmacokinetic model for dermal absorption of vapours in the rat. Toxicol. Appl. Pharmacol. 85:286-294. Moolgavkar, S. H., and A. G. Knudson, Jr. 1981. Mutation and cancer: A model for human carcinogenesis. J. Natl. Cancer Inst. 66:1037-1052. Moolgavkar, S. H., and D. J. Venzon. 1979. Two-event models for carcinogenesis. In- cidence curves for childhood and adult tumors. Math. Biosci. 47:55-77. Murdoch, D., and D. Krewski. 1987. Carcinogenic Risk Assessment with Time-Dependent Exposure. Technical Report No. 106. Laboratory for Research on Statistics and Prob- ability. Ottawa: Carleton University. Murdoch, D. J., D. Krewski, and K. S. Crump. In press. Mathematical models of car- cinogenesis. Pp. 61-89 in Cancer Modelling, J. R. Thompson and B. W. Brown, eds. New York: Marcel Dekker. NTP (National Toxicology Program). 1984. Report of the NTP Ad Hoc Panel on Chemical Carcinogenesis Testing and Evaluation. Washington, D;C.: U.S. Department of Health and Human Services. NTP (National Toxicology Program). 1986. Toxicology and Carcinogenesis Studies of Dichloromethane (Methylene Chloride) in F344/N Rats and B6C3F, Mice. CAS No. 75- 09-2. Bethesda, Md.: National Institutes of Health.

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466 DAN ~ EL KREWSK' ET AL. OSTP (Office of Science and Technology Policy). 1985. Chemical carcinogens: A review of the science and its associated principles. Fed. Regist. 50:10372-10442. Rall, D. P. 1969. Difficulties in extrapolating the results of toxicity studies in laboratory animals to man. Environ. Res. 2:360-367. Ramsey, J. C., and M. E. Andersen. 1984. A physiologically based description of inhalation Pharmacokinetics of styrene in rats and humans. Toxicol. Appl. Pharmacol. 73:159- 175. Reitz, R. H., P. J. Gehring, and C. N. Park. 1978. Carcinogenic risk estimation for chloroform: An alternative to EPA's procedure. Food Cosmet. Toxicol. 16:511-514. Sato, A., and T. Nakajima. 1979. Partition coefficients of some aromatic hydrocarbons and ketones in water, blood and oil. Br. J. Ind. Med. 36:231-234. Starr, T. B., and R. B. Buck. 1984. The importance of delivered dose in estimating low- dose cancer risk from inhalation exposure to formaldehyde. Fund. Appl. Toxicol. 4:740- 753. Swenberg, J. A., W. D. Kerns, R. E. Mitchell, E. J. Gralla, and K. L. Pavkov. 1980. Induction of squamous cell carcinomas of the rat nasal cavity by inhalation exposure to formaldehyde vapor. Cancer Res. 40:3398-3402. Wagner, J. G. 1971. Pp. 239-241 in Biopharmaceutics and Relevant Pharmacokinetics, 1st ed. Hamilton, Ill.: Drug Intelligence Publications. Whittemore, A. S., S. C. Grosser, and A. Silvers. 1986. Pharmacokinetics in low dose extrapolation using animal cancer data. Fund. Appl. Toxicol. 7:183-190. Widmark, E. M. P. 1919. Studies in the concentration of indifferent narcotics in blood and tissues. Acta. Med. Scand. 52:87-164. Widmark, E. M. P., and J. Tandberg. 1924. The limitations for the accumulation of indifferent narcotics. Theoretical calculation. Biochem. J. 147:358-369. Withey, J. R. 1984. Pharmacokinetics and metabolism. Chapt. IV., pp. 36-45 in Current Issues in Toxicology: Interpretation and Extrapolation of Chemical and Biological Carcino- genicity Data to Establish Human Safety Standards. New York: Springer-Verlag. Withey, J. R., and D. Murdoch. 1987. Application of pharmacokinetics in risk assessment for pesticides. Pp. 569-572 in R. Greenhalgh and T. R. Roberts, eds. Pesticide Science and Biotechnology. Philadelphia: Blackwell Scientific.

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PK Data in Carcinogenic Risk Assessment 467 APPENDIX: THE MULTISTAGE MODEL AND TIME-DEPENDENT DOSING Under the multistage model, the probability of a tumor occurring by . . . ~ time t Is given by: where H(t) = f O f ok P(t) = 1 expEH(t)l, . . (A-1) fo2 II Ai~t~dul . . . duk (A-2) i=1 denotes the cumulative hazard function and Lift) is the transition intensity function for stage i = 1, . . . k (Crump and Howe, 1984~. To accom- modate exposure to a particular xenobiotic, the intensity functions are often assumed to be linearly related to the dose date at time t, with mitt) = al + bidets, (A-3) where (ai, bi > 04. For constant exposure data = d, this reduces to the usual form of the multistage model with: tk k H(t) = II (ai + bid) k! id (A-4) To explore the effects of time-dependent dosing under the multistage model, consider the simplest case in which only the rth stage is dose dependent. Because bi = 0 for i ~ r, we have: H(t) = aLt) + beta do, where (A-S) ante = tweak= iai~lk!, bate = (brlar~aft), and do = ELd(Urk)] = To dLu~wfu; r, k r + 1, t~du. (A-6) Here, Mu; r, kr + 1, t) represents the marginal density of Urk, the rth order statistic in a sample of size k from the uniform distribution on to, tl. This density is given by: ur-"tu~k-~ (A-7) (O < u < t), with B(, ~ denoting the beta function (see Murdoch and Krewski, 1987, for further details). It follows from Equation A-S that do represents that fixed dose which, if given continuously from time O to

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468 DAN ~ EL KREWSK! ET AL. time t, would produce the same cumulative hazard at time t as the variable dosing regimen date. It follows from Equation A-6 that the use of a constant time-weighted average dose d, = Orb dfu~dult (A-8) will be valid when k = 1, because Mu; 1, 1, t) = 1/t for O < u < t. When k > 1, however, the use of do in place of d, does not in general lead to the same cumulative hazard at time t as that which accrues under the variable dosing regimen data. When only one stage is dose dependent, it follows from Equation A-S that the excess risk is proportional to d i. Because this function is a weighted average of the values of dfu) over O < u < t, the ratio R of the excess risk under variable dosing as compared with that based on a constant average dose is at most the maximum value of the density Mu; r, kr + 1, tJ divided by its average value lit. This ratio can be written as: R = ~ ~ leak ~ '(! OCR for page 429
PART V111 Perspectives

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