Comparison of cancer slope factors using different statistical approaches.

The U.S. Environmental Protection Agency's cancer guidelines ( USEPA, 2005 ) present the default approach for the cancer slope factor (denoted here as s*) as the slope of the linear extrapolation to the origin, generally drawn from the 95% lower confidence limit on dose at the lowest prescribed risk level supported by the data. In the past, the cancer slope factor has been calculated as the upper 95% confidence limit on the coefficient (q*₁) of the linear term of the multistage model for the extra cancer risk over background. To what extent do the two approaches differ in practice? We addressed this issue by calculating s* and q*₁ for 102 data sets for 60 carcinogens using the constrained multistage model to fit the dose‐response data. We also examined how frequently the fitted dose‐response curves departed appreciably from linearity at low dose by comparing q₁, the coefficient of the linear term in the multistage polynomial, with a slope factor, s_c, derived from a point of departure based on the maximum liklihood estimate of the dose‐response. Another question we addressed is the extent to which s* exceeded s_c for various levels of extra risk. For the vast majority of chemicals, the prescribed default EPA methodology for the cancer slope factor provides values very similar to that obtained with the traditionally estimated q*₁. At 10% extra risk, q*₁/s* is greater than 0.3 for all except one data set; for 82% of the data sets, q*₁ is within 0.9 to 1.1 of s*. At the 10% response level, the interquartile range of the ratio, s*/s_c, is 1.4 to 2.0.     

Assessing Cancer Risks from Short-Term Exposures in Children

For the vast majority of chemicals that have cancer potency estimates on IRIS, the underlying database is deficient with respect to early-life exposures. This data gap has prevented derivation of cancer potency factors that are relevant to this time period, and so assessments may not fully address children's risks. This article provides a review of juvenile animal bioassay data in comparison to adult animal data for a broad array of carcinogens. This comparison indicates that short-term exposures in early life are likely to yield a greater tumor response than short-term exposures in adults, but similar tumor response when compared to long-term exposures in adults. This evidence is brought into a risk assessment context by proposing an approach that: (1) does not prorate children's exposures over the entire life span or mix them with exposures that occur at other ages; (2) applies the cancer slope factor from adult animal or human epidemiology studies to the children's exposure dose to calculate the cancer risk associated with the early-life period; and (3) adds the cancer risk for young children to that for older children/adults to yield a total lifetime cancer risk. The proposed approach allows for the unique exposure and pharmacokinetic factors associated with young children to be fully weighted in the cancer risk assessment. It is very similar to the approach currently used by U.S. EPA for vinyl chloride. The current analysis finds that the database of early life and adult cancer bioassays supports extension of this approach from vinyl chloride to other carcinogens of diverse mode of action. This approach should be enhanced by early-life data specific to the particular carcinogen under analysis whenever possible.     

The Benefits of Probabilistic Exposure Assessment: Three Case Studies Involving Contaminated Air,Water, and Soil1

Probabilistic risk assessments are enjoying increasing popularity as a tool to characterize the health hazards associated with exposure to chemicals in the environment. Because probabilistic analyses provide much more information to the risk manager than standard “point” risk estimates, this approach has generally been heralded as one which could significantly improve the conduct of health risk assessments. The primary obstacles to replacing point estimates with probabilistic techniques include a general lack of familiarity with the approach and a lack of regulatory policy and guidance. This paper discusses some of the advantages and disadvantages of the point estimate vs. probabilistic approach. Three case studies are presented which contrast and compare the results of each. The first addresses the risks associated with household exposure to volatile chemicals in tapwater. The second evaluates airborne dioxin emissions which can enter the food-chain. The third illustrates how to derive health-based cleanup levels for dioxin in soil. It is shown that, based on the results of Monte Carlo analyses of probability density functions (PDFs), the point estimate approach required by most regulatory agencies will nearly always overpredict the risk for the 95^th percentile person by a factor of up to 5. When the assessment requires consideration of 10 or more exposure variables, the point estimate approach will often predict risks representative of the 99.9^th percentile person rather than the 50^th or 95^th percentile person. This paper recommends a number of data distributions for various exposure variables that we believe are now sufficiently well understood to be used with confidence in most exposure assessments. A list of exposure variables that may require additional research before adequate data distributions can be developed are also discussed.     

Reducing Conservatism in Risk Estimation for Mixtures of Carcinogens

The excess cancer risk that might result from exposure to a mixture of chemical carcinogens usually must be estimated using data from experiments conducted with individual chemicals. In estimating such risk, it is commonly assumed that the total risk due to the mixture is the sum of the risks of the individual components, provided that the risks associated with individual chemicals at levels present in the mixture are low. This assumption, while itself not necessarily conservative, has led to the conservative practice of summing individual upper-bound risk estimates in order to obtain an upper bound on the total excess cancer risk for a mixture. Less conservative procedures are described here and are illustrated for the case of a mixture of four carcinogens.     

The Role of Cancer Risk in the Regulation of Industrial Pollution

The extent of carcinogen regulation under existing U.S. environmental statutes is assessed by developing measures of the scope and stringency of regulation. While concern about cancer risk has played an important political role in obtaining support for pollution control programs, it has not provided the predominant rationale for most regulatory actions taken to date. Less than 20% of all standards established to limit concentrations of chemicals in various media address carcinogens. Restrictions on chemical use are more frequently based on concerns about noncancer human health or ecological effects. Of the chemicals in commercial use which have been identified as potential human carcinogens on the basis of rodent bioassays, only a small proportion are regulated. There is an inverse relationship between the scope of regulatory coverage and the stringency of regulatory requirements: the largest percentages of identified carcinogens are affected by the least stringent requirements, such as information disclosure. Standards based on de minimis cancer risk levels have been established for only 10% of identified carcinogens and are restricted to one medium: water. Complete bans on use have affected very few chemicals. The general role that carcinogenicity now plays in the regulatory process is not dramatically different from that of other adverse human health effects: if a substance is identified as a hazard, it may eventually be subject to economically achievable and technically feasible restrictions.     

Potency Factors for Risk Assessment at Libby,Montana

We reanalyzed the Libby vermiculite miners’ cohort assembled by Sullivan to estimate potency factors for lung cancer, mesothelioma, nonmalignant respiratory disease (NMRD), and all‐cause mortality associated with exposure to Libby fibers. Our principal statistical tool for analyses of lung cancer, NMRD, and total mortality in the cohort was the time‐dependent proportional hazards model. For mesothelioma, we used an extension of the Peto formula. For a cumulative exposure to Libby fiber of 100 f/mL‐yr, our estimates of relative risk (RR) are as follows: lung cancer, RR = 1.12, 95% confidence interval (CI) =[1.06, 1.17]; NMRD, RR = 1.14, 95% CI =[1.09, 1.18]; total mortality, RR = 1.06, 95% CI =[1.04, 1.08]. These estimates were virtually identical when analyses were restricted to the subcohort of workers who were employed for at least one year. For mesothelioma, our estimate of potency is K_M = 0.5 × 10^?8, 95% CI =[0.3 × 10^?8, 0.8 × 10^?8]. Finally, we estimated the mortality ratios standardized against the U.S. population for lung cancer, NMRD, and total mortality and obtained estimates that were in good agreement with those reported by Sullivan. The estimated potency factors form the basis for a quantitative risk assessment at Libby.     

Bounding Analysis of Drinking Water Health Risks from a Spill of Hydraulic Fracturing Flowback Water

A bounding risk assessment is presented that evaluates possible human health risk from a hypothetical scenario involving a 10,000‐gallon release of flowback water from horizontal fracturing of Marcellus Shale. The water is assumed to be spilled on the ground, infiltrates into groundwater that is a source of drinking water, and an adult and child located downgradient drink the groundwater. Key uncertainties in estimating risk are given explicit quantitative treatment using Monte Carlo analysis. Chemicals that contribute significantly to estimated health risks are identified, as are key uncertainties and variables to which risk estimates are sensitive. The results show that hypothetical exposure via drinking water impacted by chemicals in Marcellus Shale flowback water, assumed to be spilled onto the ground surface, results in predicted bounds between 10⁻¹⁰ and 10⁻⁶ (for both adult and child receptors) for excess lifetime cancer risk. Cumulative hazard indices (HI_CUMULATIVE) resulting from these hypothetical exposures have predicted bounds (5th to 95th percentile) between 0.02 and 35 for assumed adult receptors and 0.1 and 146 for assumed child receptors. Predicted health risks are dominated by noncancer endpoints related to ingestion of barium and lithium in impacted groundwater. Hazard indices above unity are largely related to exposure to lithium. Salinity taste thresholds are likely to be exceeded before drinking water exposures result in adverse health effects. The findings provide focus for policy discussions concerning flowback water risk management. They also indicate ways to improve the ability to estimate health risks from drinking water impacted by a flowback water spill (i.e., reducing uncertainty).     

Comparative Potency Method for Cancer Risk Assessment: Application to Diesel Particulate Emissions1

An estimation of the human lung cancer “unit risk” from diesel engine particulate emissions has been made using a comparative potency approach. This approach involves evaluating the tumorigenic and mutagenic potencies of the particulates from four diesel and one gasoline engine in relation to other combustion and pyrolysis products (coke oven, roofing tar, and cigarette smoke) that cause lung cancer in humans. The unit cancer risk is predicated on the linear nonthreshold extrapolation model and is the individual lifetime excess lung cancer risk from continuous exposure to 1 μg carcinogen per m³ inhaled air. The human lung cancer unit risks obtained from the epidemiologic data for coke oven workers, roofing tar applicators, and cigarette smokers were, respectively, 9.3 × 10^?4, 3.6 × 10^?4, and 2.2 × 10^?6 per μg particulate organics per m³ air. The comparative potencies of these three materials and the diesel and gasoline engine exhaust particulates (as organic extracts) were evaluated by in vivo tumorigenicity bioassays involving skin initiation and skin carcinogenicity in SENCAR mice and by the in vitro bioassays that proved suitable for this analysis: Ames Salmonella microsome bioassay, L5178Y mouse lymphoma cell mutagenesis bioassay, and sister chromatid exchange bioassay in Chinese hamster ovary cells. The relative potencies of the coke oven, roofing tar, and cigarette smoke emissions, as determined by the mouse skin initiation assay, were within a factor of 2 of those determined using the epidemiologic data. The relative potencies, from the in vitro bioassays as compared to the human data, were similar for coke oven and roofing tar, but for the cigarette smoke condensate the in vitro tests predicted a higher relative potency. The mouse skin initiation bioassay was used to determine the unit lung cancer risk for the most potent of the diesel emissions. Based on comparisons with coke oven, roofing tar, and cigarette smoke, the unit cancer risk averaged 4.4 × 10^?4. The unit lung cancer risks for the other, less potent motor-vehicle emissions were determined from their comparative potencies relative to the most potent diesel using three in vitro bioassays. There was a high correlation between the in vitro and in vivo bioassays in their responses to the engine exhaust particulate extracts. The unit lung cancer risk per μg particulates per m³ for the automotive diesel and gasoline exhaust particulates ranged from 0.20 × 10^?4 to 0.60 × 10^?4; that for the heavy-duty diesel engine was 0.02 × 10^?4. These unit risks provide the basis for a future assessment of human lung cancer risks when combined with human population exposure to automotive emissions.     

Experimental Design of Bioassays for Screening and Low Dose Extrapolation

Relatively high doses of chemicals generally are employed in animal bioassays to detect potential carcinogens with relatively small numbers of animals. The problem investigated here is the development of experimental designs which are effective for high to low dose extrapolation for tumor incidence as well as for screening (detecting) carcinogens. Several experimental designs are compared over a wide range of different dose response curves. Linear extrapolation is used below the experimental data range to establish an upper bound on carcinogenic risk at low doses. The goal is to find experimental designs which minimize the upper bound on low dose risk estimates (i.e., maximize the allowable dose for a given level of risk). The maximum tolerated dose (MTD) is employed for screening purposes. Among the designs investigated, experiments with doses at the MTD, 1/2 MTD, 1/4 MTD, and controls generally provide relatively good data for low dose extrapolation with relatively good power for detecting carcinogens. For this design, equal numbers of animals per dose level perform as well as unequal allocations.     

Extrapolation of Carcinogenicity Between Species: Qualitative and Quantitative Factors

Prediction of human cancer risk from the results of rodent bioassays requires two types of extrapolation: a qualitative extrapolation from short-lived rodent species to long-lived humans, and a quantitative extrapolation from near-toxic doses in the bioassay to low-level human exposures. Experimental evidence on the accuracy of prediction between closely related species tested under similar experimental conditions (rats, mice, and hamsters) indicates that: (1) if a chemical is positive in one species, it will be positive in the second species about 75% of the time; however, since about 50% of test chemicals are positive in each species, by chance alone one would expect a predictive value between species of about 50%. (2) If a chemical induces tumors in a particular target organ in one species, it will induce tumors in the same organ in the second species about 50% of the time. Similar predictive values are obtained in an analysis of prediction from humans to rats or from humans to mice for known human carcinogens. Limitations of bioassay data for use in quantitative extrapolation are discussed, including constraints on both estimates of carcinogenic potency and of the dose-response in experiments with only two doses and a control. Quantitative extrapolation should be based on an understanding of mechanisms of carcinogenesis, particularly mitogenic effects that are present at high and not low doses.     

Use of Acute Toxicity to Estimate Carcinogenic Risk

Data on the effects of human exposure to carcinogens are limited, so that estimation of the risks of carcinogens must be obtained indirectly. Current risk estimates are generally based on lifetime animal bioassays which are expensive and which take more than two years to complete. We here show how data on acute toxicity can be used to make a preliminary estimate of carcinogenic risk and give an idea of the uncertainty in that risk estimate. The estimates obtained are biased upwards, and so are useful for setting interim standards and determining whether further study is worthwhile. A general scheme which incorporates the use of such estimates is outlined, and it is shown by example how adoption of the procedures suggested could have prevented regulatory hiatus in the past.     

Extended Analysis and Evidence Integration of Chloroprene as a Human Carcinogen

β-Chloroprene is used in the production of polychloroprene, a synthetic rubber. In 2010, Environmental Protection Agency (EPA) published the Integrated Risk Information System “Toxicological Review of Chloroprene,” concluding that chloroprene was “likely to be carcinogenic to humans.” This was based on findings from a 1998 National Toxicology Program (NTP) study showing multiple tumors within and across animal species; results from occupational epidemiological studies; a proposed mutagenic mode of action; and structural similarities with 1,3-butadiene and vinyl chloride. Using mouse data from the NTP study and assuming a mutagenic mode of action, EPA calculated an inhalation unit risk (IUR) for chloroprene of 5 × 10⁻⁴ per µg/m³. This is among the highest IURs for chemicals classified by IARC or EPA as known or probable human carcinogens and orders of magnitude higher than the IURs for carcinogens such as vinyl chloride, benzene, and 1,3-butadiene. Due to differences in pharmacokinetics, mice appear to be uniquely responsive to chloroprene exposure compared to other animals, including humans, which is consistent with the lack of evidence of carcinogenicity in robust occupational epidemiological studies. We evaluated and integrated all lines of evidence for chloroprene carcinogenicity to assess whether the 2010 EPA IUR could be scientifically substantiated. Due to clear interspecies differences in carcinogenic response to chloroprene, we applied a physiologically based pharmacokinetic model for chloroprene to calculate a species-specific internal dose (amount metabolized/gram of lung tissue) and derived an IUR that is over 100-fold lower than the 2010 EPA IUR. Therefore, we recommend that EPA's IUR be updated.     

Using Average Lifetime Dose Rate for Intermittent Exposures to Carcinogens

The effect of using the average dose rate over a lifetime as a representative measure of exposure to carcinogens is investigated by comparing the true theoretical multistage intermittent-dosing lifetime low-dose excess risk to the theoretical multistage continuous-dosing lifetime risk corresponding to the average lifetime dose rate. It is concluded that low-dose risk estimates based on the average lifetime dose rate may overestimate the true risk by several orders of magnitude, but that they never underestimate the true risk by more than a factor of k/r, where k is the total number of stages in the multistage model and r is the number of stages that are dose-related.     

Improving Cancer Dose–Response Characterization by Using Physiologically Based Pharmacokinetic Modeling: An Analysis of Pooled Data for Acrylonitrile-Induced Brain Tumors to Assess Cancer Potency in the Rat

Historically, U.S. regulators have derived cancer slope factors by using applied dose and tumor response data from a single key bioassay or by averaging the cancer slope factors of several key bioassays. Recent changes in U.S. Environmental Protection Agency (EPA) guidelines for cancer risk assessment have acknowledged the value of better use of mechanistic data and better dose–response characterization. However, agency guidelines may benefit from additional considerations presented in this paper. An exploratory study was conducted by using rat brain tumor data for acrylonitrile (AN) to investigate the use of physiologically based pharmacokinetic (PBPK) modeling along with pooling of dose–response data across routes of exposure as a means for improving carcinogen risk assessment methods. In this study, two contrasting assessments were conducted for AN-induced brain tumors in the rat on the basis of (1) the EPA's approach, the dose–response relationship was characterized by using administered dose/concentration for each of the key studies assessed individually; and (2) an analysis of the pooled data, the dose–response relationship was characterized by using PBPK-derived internal dose measures for a combined database of ten bioassays. The cancer potencies predicted for AN by the contrasting assessments are remarkably different (i.e., risk-specific doses differ by as much as two to four orders of magnitude), with the pooled data assessments yielding lower values. This result suggests that current carcinogen risk assessment practices overestimate AN cancer potency. This methodology should be equally applicable to other data-rich chemicals in identifying (1) a useful dose measure, (2) an appropriate dose–response model, (3) an acceptable point of departure, and (4) an appropriate method of extrapolation from the range of observation to the range of prediction when a chemical's mode of action remains uncertain.     

Estimation of the Joint Risk from Multiple-Compound Exposure Based on Single-Compound Experiments

In the absence of data from multiple-compound exposure experiments, the health risk from exposure to a mixture of chemical carcinogens is generally based on the results of the individual single-compound experiments. A procedure to obtain an upper confidence limit on the total risk is proposed under the assumption that total risk for the mixture is additive. It is shown that the current practice of simply summing the individual upper-confidence-limit risk estimates as the upper-confidence-limit estimate on the total excess risk of the mixture may overestimate the true upper bound. In general, if the individual upper-confidence-limit risk estimates are on the same order of magnitude, the proposed method gives a smaller upper-confidence-limit risk estimate than the estimate based on summing the individual upper-confidence-limit estimates; the difference increases as the number of carcinogenic components increases.     

Improving cancer dose-response characterization by using physiologically based pharmacokinetic modeling: an analysis of pooled data for acrylonitrile-induced brain tumors to assess cancer potency in the rat.

Historically, U.S. regulators have derived cancer slope factors by using applied dose and tumor response data from a single key bioassay or by averaging the cancer slope factors of several key bioassays. Recent changes in U.S. Environmental Protection Agency (EPA) guidelines for cancer risk assessment have acknowledged the value of better use of mechanistic data and better dose-response characterization. However, agency guidelines may benefit from additional considerations presented in this paper. An exploratory study was conducted by using rat brain tumor data for acrylonitrile (AN) to investigate the use of physiologically based pharmacokinetic (PBPK) modeling along with pooling of dose-response data across routes of exposure as a means for improving carcinogen risk assessment methods. In this study, two contrasting assessments were conducted for AN-induced brain tumors in the rat on the basis of (1) the EPA's approach, the dose-response relationship was characterized by using administered dose/concentration for each of the key studies assessed individually; and (2) an analysis of the pooled data, the dose-response relationship was characterized by using PBPK-derived internal dose measures for a combined database of ten bioassays. The cancer potencies predicted for AN by the contrasting assessments are remarkably different (i.e., risk-specific doses differ by as much as two to four orders of magnitude), with the pooled data assessments yielding lower values. This result suggests that current carcinogen risk assessment practices overestimate AN cancer potency. This methodology should be equally applicable to other data-rich chemicals in identifying (1) a useful dose measure, (2) an appropriate dose-response model, (3) an acceptable point of departure, and (4) an appropriate method of extrapolation from the range of observation to the range of prediction when a chemical's mode of action remains uncertain.     

Point Estimates of Cancer Risk at Low Doses

There has been considerable discussion regarding the conservativeness of low-dose cancer risk estimates based upon linear extrapolation from upper confidence limits. Various groups have expressed a need for best (point) estimates of cancer risk in order to improve risk/benefit decisions. Point estimates of carcinogenic potency obtained from maximum likelihood estimates of low-dose slope may be highly unstable, being sensitive both to the choice of the dose–response model and possibly to minimal perturbations of the data. For carcinogens that augment background carcinogenic processes and/or for mutagenic carcinogens, at low doses the tumor incidence versus target tissue dose is expected to be linear. Pharmacokinetic data may be needed to identify and adjust for exposure-dose nonlinearities. Based on the assumption that the dose response is linear over low doses, a stable point estimate for low-dose cancer risk is proposed. Since various models give similar estimates of risk down to levels of 1%, a stable estimate of the low-dose cancer slope is provided by ŝ = 0.01/ED01, where ED01 is the dose corresponding to an excess cancer risk of 1%. Thus, low-dose estimates of cancer risk are obtained by, risk = ŝ × dose. The proposed procedure is similar to one which has been utilized in the past by the Center for Food Safety and Applied Nutrition, Food and Drug Administration. The upper confidence limit, s , corresponding to this point estimate of low-dose slope is similar to the upper limit, q ₁ obtained from the generalized multistage model. The advantage of the proposed procedure is that ŝ provides stable estimates of low-dose carcinogenic potency, which are not unduly influenced by small perturbations of the tumor incidence rates, unlike ₁.     

Exposure to Persistent Organochlorines in Canadian Breast Milk: A Probabilistic Assessment

Exposure to persistent organochlorines in breast milk was estimated probabilistically for Canadian infants. Noncancer health effects were evaluated by comparing the predicted exposure distributions to published guidance values. For chemicals identified as potential human carcinogens, cancer risks were evaluated using standard methodology typically applied in Canada, as well as an alternative method developed under the Canadian Environmental Protection Act. Potential health risks associated with exposure to persistent organochlorines were quantitatively and qualitatively weighed against the benefits of breast-feeding. Current levels of the majority of contaminants identified in Canadian breast milk do not pose unacceptable risks to infants. Benefits of breast-feeding are well documented and qualitatively appear to outweigh potential health concerns associated with organochlorine exposure. Furthermore, the risks of mortality from not breast-feeding estimated by Rogan and colleagues exceed the theoretical cancer risks estimated for infant exposure to potential carcinogens in Canadian breast milk. Although levels of persistent compounds have been declining in Canadian breast milk, potentially significant risks were estimated for exposure to polychlorinated biphenyls, dibenzo-p-dioxins, and dibenzofurans. Follow-up work is suggested that would involve the use of a physiologically based toxicokinetic model with probabilistic inputs to predict dioxin exposure to the infant. A more detailed risk analysis could be carried out by coupling the exposure estimates with a dose–response analysis that accounts for uncertainty.     

The Cancer Risk Associated with Residential Exposure to Soil Containing Radioactive Coal Combustion Residuals

Coal combustion residuals (CCRs) are composed of various constituents, including radioactive materials. The objective of this study was to utilize methodology on radionuclide risk assessment from the Environmental Protection Agency (EPA) to estimate the potential cancer risks associated with residential exposure to CCR‐containing soil. We evaluated potential radionuclide exposure via soil ingestion, inhalation of soil particulates, and external exposure to ionizing radiation using published CCR radioactivity values for ²³²Th, ²²⁸Ra, ²³⁸U, and ²²⁶Ra from the Appalachia, Illinois, and Powder River coal basins. Mean and upper‐bound cancer risks were estimated individually for each radionuclide, exposure pathway, and coal basin. For each radionuclide at each coal basin, external exposure to ionizing radiation contributed the greatest to the overall risk estimate, followed by incidental ingestion of soil and inhalation of soil particulates. The mean cancer risks by route of exposure were 2.01 × 10⁻⁶ (ingestion), 6.80 × 10⁻⁹ (inhalation), and 3.66 × 10⁻⁵ (external), while the upper bound cancer risks were 3.70 × 10⁻⁶ (ingestion), 1.18 × 10⁻⁸ (inhalation), and 6.15 × 10⁻⁵ (external), using summed radionuclide‐specific data from all locations. The upper bound cancer risk from all routes of exposure was 6.52 × 10⁻⁵. These estimated cancer risks were within the EPA's acceptable cancer risk range of 1 × 10⁻⁶ to 1 × 10⁻⁴. If the CCR radioactivity values used in this analysis are generally representative of CCR waste streams, then our findings suggest that CCRs would not be expected to pose a significant radiological risk to residents living in areas where contact with CCR‐containing soils might occur.     

Estimates of the Number of Liver Carcinogens in Bioassays Conducted by the National Toxicology Program

Estimates were made of the numbers of liver carcinogens in 390 long-term bioassays conducted by the National Toxicology Program (NTP). These estimates were obtained from examination of the global pattern of p-values obtained from statistical tests applied to individual bioassays. Representative estimates of the number of liver carcinogens (90% confidence interval in parentheses) obtained in our analysis compared to NTP's determination are as follows: female rats—49 (23, 76), NTP = 30; male rats—88 (59, 116), NTP = 35; female mice—131 (105, 157), NTP = 81; male mice—100 (73, 126), NTP = 61; overall—166 (135, 197), NTP = 108. The estimator from which these estimates were obtained is biased low by an unknown amount. Consequently, this study provides persuasive evidence of the existence of more rodent liver carcinogens than were identified by the NTP.