Dose response problems in carcinogenesis.

The estimation of risks from exposure to carcinogens is an important problem from the viewpoint of protection of human health. It also poses some very difficult dose-response problems. Two dose-response models may fit experimental data about equally well and yet predict responses that differ by many orders of magnitude at low doses. Mechanisms of carcinogenesis are not sufficiently understood so that the shape of the dose-response curve at low doses can be satisfactorily predicted. Mathematical theories of carcinogenesis and statistical procedures can be of use with dose-reponse problems such as this and, in addition, can lead to a better understanding of the mechanisms of carcinogenesis. In this paper, mathematical dose-response models of carcinogenesis are considered as well as various proposed dose-response procedures for estimating carcinogenic risks at low doses. Areas are suggested in which further work may be useful. These areas include experimental design problems, statistical procedures for use with time-to-occurrence data, and mathematical models that incorporate such biological features as pharmacokinetics of carcinogens, synergistic effects, DNA repair, susceptible subpopulations, and immune reactions.     

Improving Risk Assessment: Priorities for Epidemiologic Research

The Epidemiology Work Group at the Workshop on Future Research for Improving Risk Assessment Methods, Of Mice, Men, and Models, held August 16 to 18, 2000, at Snowmass Village, Aspen, Colorado, concluded that in order to improve the utility of epidemiologic studies for risk assessment, methodologic research is needed in the following areas: (1) aspects of epidemiologic study designs that affect doseresponse estimation; (2) alternative methods for estimating dose in human studies; and (3) refined methods for dose-response modeling for epidemiologic data. Needed research in aspects of epidemiologic study design includes recognition and control of study biases, identification of susceptible subpopulations, choice of exposure metrics, and choice of epidemiologic risk parameters. Much of this research can be done with existing data. Research needed to improve determinants of dose in human studies includes additional individual-level data (e.g., diet, co-morbidity), development of more extensive human data for physiologically based pharmacokinetic (PBPK) dose modeling, tissue registries to increase the availability of tissue for studies of exposure/dose and susceptibility biomarkers, and biomarker data to assess exposures in humans and animals. Research needed on dose-response modeling of human studies includes more widespread application of flexible statistical methods (e.g., general additive models), development of methods to compensate for epidemiologic bias in dose-response models, improved biological models using human data, and evaluation of the benchmark dose using human data. There was consensus among the Work Group that, whereas most prior risk assessments have focused on cancer, there is a growing need for applications to other health outcomes. Developmental and reproductive effects, injuries, respiratory disease, and cardiovascular disease were identified as especially high priorities for research. It was also a consensus view that epidemiologists, industrial hygienists, and other scientists focusing on human data need to play a stronger role throughout the risk assessment process. Finally, the group agreed that there was a need to improve risk communication, particularly on uncertainty inherent in risk assessments that use epidemiologic data.     

Allowing for random errors in radiation dose estimates for the atomic bomb survivor data

The presence of random errors in the individual radiation dose estimates for the A-bomb survivors causes underestimation of radiation effects in dose-response analyses, and also distorts the shape of dose-response curves. Statistical methods are presented which will adjust for these biases, provided that a valid statistical model for the dose estimation errors is used. Emphasis is on clarifying some rather subtle statistical issues. For most of this development the distinction between radiation dose and exposure is not critical. The proposed methods involve downward adjustment of dose estimates, but this does not imply that the dosimetry system is faulty. Rather, this is a part of the dose-response analysis required to remove biases in the risk estimates. The primary focus of this report is on linear dose-response models, but methods for linear-quadratic models are also considered briefly. Some plausible models for the dose estimation errors are considered, which have typical errors in a range of 30-40% of the true values, and sensitivity analysis of the resulting bias corrections is provided. It is found that for these error models the resulting estimates of excess cancer risk based on linear models are about 6-17% greater than estimates that make no allowance for dose estimation errors. This increase in risk estimates is reduced to about 4-11% if, as has often been done recently, survivors with dose estimates above 4 Gy are eliminated from the analysis.     

International Commission for Protection against Environmental Mutagens and Carcinogens. ICPEMC publication No. 13. The need for biological risk assessment in reaching decisions about carcinogens

The prudent assumption that carcinogen bioassays in rodents predict for human carcinogenicity is examined. It is suggested that in certain cases, as for example the induction of tumors against a high incidence in controls, or in situations in which high dose toxicity may be a critical factor in the induction of cancer, the probability that animal bioassays predict for humans may be low. The term 'biological risk assessment' is introduced to describe that part of risk assessment concerned with the relevance of specific animal results to the induction of human cancer. Biological risk assessment, which is almost entirely dependent on an understanding of carcinogenesis mechanisms, is an important addition to present mathematical modeling used to predict the effects of animal carcinogens that have been demonstrated after high dose exposure, to the effects of the much smaller doses to which humans are perceived to be exposed. Evidence for the conclusions reached by biological risk assessment may sometimes be supported by a careful review of human epidemiological data.     

Statistical Dose-Response Models with Hormetic Effects

Monotonically increasing or decreasing functions are often used to model the relationship between the response of an experimental unit and the dose of a given substance. Of late, there has been an increased interest in dose-response relationships that exhibit hormetic effects. These effects may be characterized by an increase in response at low doses instead of the expected decrease in response that is observed at higher doses. Herein, we study the statistical implications of hormesis in several ways. First, we present a broad class of parametric mathematical-statistical models, constructed from standard dose-response models, that allow the incorporation of hormetic effects in such a way that the presence of hormesis can be tested statistically. Second, we consider the impact of model misspecification on effective dose estimation, such as the ED50 and the limiting dose for stimulation, when the hormetic effect is present but ignored in the dose-response model by the researcher (model underspecification) and when an hormetic effect is not present but incorporated into the dose-response model (model overspecification). Our simulation study reveals that it is more damaging to the estimation of effective dose to ignore the hormetic effect through model underspecification than to include the hormetic effect in the model through model overspecification. Third, we develop a nonpara-metric regression technique useful as an exploratory procedure to indicate hormetic effects when present. Finally, both parametric and nonparametric methods are illustrated with an example.     

Dose-response and threshold-mediated mechanisms in mutagenesis: statistical models and study design

The objective of this paper is to review the use, in mutagenesis, of various mathematical models to describe the dose-response relationship and to try to identify thresholds. It is often taken as axiomatic that genotoxic carcinogens could damage DNA at any level of exposure, leading to a mutation, and that this could ultimately result in tumour development. This has led to the assumption that for genotoxic chemicals, there is no discernible threshold. This assumption is increasingly being challenged in the case of aneugens. The distinction between 'absolute' and 'pragmatic' thresholds is made and the difficulties in determining 'absolute' thresholds using hypothesis testing approaches are described. The potential of approaches, based upon estimation rather than statistical significance for the characterization of dose-response relationships, is stressed. The achievement of a good fit of a mathematical model to experimental data is not proof that the mechanism supposedly underlying this model is operating. It has been argued, in the case of genotoxic chemicals, that any effects produced by a genotoxic chemical which augments that producing a background incidence in unexposed individuals will lead to a dose-response relationship that is non-thresholded and is linear at low doses. The assumptions underlying this presumption are explored in the context of the increasing knowledge of the mechanistic basis of mutagenicity and carcinogenicity. The possibility that exposure to low levels of genotoxic chemicals may induce and enhance defence and repair mechanisms is not easily incorporated into many of the existing mathematical models and should be an objective in the development of the next generation of biologically based dose-response (BB-DR) models. Studies aimed at detecting or characterizing non-linearities in the dose-response relationship need appropriate experimental designs with careful attention to the choice of biomarker, number and selection of dose levels, optimum allocation of experimental units and appropriate levels of replication within and repetition of experiments. The characterization of dose-response relationships with appropriate measures of uncertainty can help to identify 'pragmatic' thresholds based upon biologically relevant criteria which can help in the regulatory process.     

Variability: the common factor linking low dose-induced genomic instability, adaptation and bystander effects

The characteristics of low dose radiation-induced genomic instability, adaptive responses, and bystander effects were compared in order to probe possible underlying mechanisms, and develop models for predicting response to in vivo low dose radiation exposures. While there are some features that are common to all three (e.g., absence of a true dose-response, the multiple endpoints affected by each), other characteristics appear to distinguish one from the other (e.g., TP53 involvement, LET response, influence of DNA repair). Each of the responses is also highly variable; not all cell and tissue models show the same response and there is much interindividual variation in response. Most of these studies have employed in vitro cell culture or tissue explant models, and understanding underlying mechanisms and the biological significance of these low dose-responses will require study of tissue-specific in vivo endpoints. The in vitro studies strongly suggest that modeling low dose radiation effects will be a complex process, and will likely require separate study of each of these low dose phenomena. Knowledge of instability responses, for example, may not aid in predicting other low dose effects in the same tissue.     

Estimation of the benchmark dose by structural equation models

While epidemiological data typically contain a multivariate response and often also multiple exposure parameters, current methods for safe dose calculations, including the widely used benchmark approach, rely on standard regression techniques. In practice, dose-response modeling and calculation of the exposure limit are often based on the seemingly most sensitive outcome. However, this procedure ignores other available data, is inefficient, and fails to account for multiple testing. Instead, risk assessment could be based on structural equation models, which can accommodate both a multivariate exposure and a multivariate response function. Furthermore, such models will allow for measurement error in the observed variables, which is a requirement for unbiased estimation of the benchmark dose. This methodology is illustrated with the data on neurobehavioral effects in children prenatally exposed to methylmercury, where results based on standard regression models cause an underestimation of the true risk.     

Cancer mortality risk among workers at the Mayak nuclear complex

At present, direct data on risk from protracted or fractionated radiation exposure at low dose rates have been limited largely to studies of populations exposed to low cumulative doses with resulting low statistical power. We evaluated the cancer risks associated with protracted exposure to external whole-body gamma radiation at high cumulative doses (the average dose is 0.8 Gy and the highest doses exceed 10 Gy) in Russian nuclear workers. Cancer deaths in a cohort of about 21,500 nuclear workers who began working at the Mayak complex between 1948 and 1972 were ascertained from death certificates and autopsy reports with follow-up through December 1997. Excess relative risk models were used to estimate solid cancer and leukemia risks associated with external gamma-radiation dose with adjustment for effects of plutonium exposures. Both solid cancer and leukemia death rates increased significantly with increasing gamma-ray dose (P < 0.001). Under a linear dose-response model, the excess relative risk for lung, liver and skeletal cancers as a group (668 deaths) adjusted for plutonium exposure is 0.30 per gray (P < 0.001) and 0.08 per gray (P < 0.001) for all other solid cancers (1062 deaths). The solid cancer dose-response functions appear to be nonlinear, with the excess risk estimates at doses of less than 3 Gy being about twice those predicted by the linear model. Plutonium exposure was associated with increased risks both for lung, liver and skeletal cancers (the sites of primary plutonium deposition) and for other solid cancers as a group. A significant dose response, with no indication of plutonium exposure effects, was found for leukemia. Excess risks for leukemia exhibited a significant dependence on the time since the dose was received. For doses received within 3 to 5 years of death the excess relative risk per gray was estimated to be about 7 (P < 0.001), but this risk was only 0.45 (P = 0.02) for doses received 5 to 45 years prior to death. External gamma-ray exposures significantly increased risks of both solid cancers and leukemia in this large cohort of men and women with occupational radiation exposures. Risks at doses of less than 1 Gy may be slightly lower than those seen for doses arising from acute exposures in the atomic bomb survivors. As dose estimates for the Mayak workers are improved, it should be possible to obtain more precise estimates of solid cancer and leukemia risks from protracted external radiation exposure in this cohort.     

Improving the Development and Use of Biologically Based Dose Response Models (BBDR) in Risk Assessment

Biologically based dose-response (BBDR) models predict health outcomes (response) resulting from the presence of a toxicant at a biological target (dose). The benefits of BBDR models are many, and research programs are increasingly focusing on mechanistic research to support model development; however, progress has been slow. Impediments to progress include the complexity of dose response modeling, the need for a multidisciplinary team and consistent funding support, and difficulty in identifying and extracting the needed data. Of immediate concern is the lack of transparency of published models to the supporting data and literature, difficulty in accessing model code and simulation conditions sufficient to allow independent replication of results, and absence of well-defined quality criteria. Suggestions are presented to improve the development and use of BBDR models in risk assessment and to address the above limitations. Examples from BBDR models for methylmercury neurotoxicity and 5-fluorouracil embryotoxicity are presented to illustrate the suggestions including what kinds of databases are needed to support model development and transparency, quality assurance for modeling, and how the internet can advance database development and collaboration within the biological modeling community.     

Time and dose dependency of bone-sarcomas in patients injected with radium-224

Summary The time course and dose dependency of the incidence of bone-sarcomas among 900 German patients treated with high doses of radium-224 is analysed in terms of a proportional hazards model with a log-normal dependency of time to tumor and a linear-quadratic dose relation. The deduced dose dependency agrees well with a previous analysis in terms of a non-parametric proportional hazards model, and confirms the temporal distribution which has been used in the Radioepidemiological Tables of NIH. However, the linear-quadratic dose-response model gives a risk estimate for low doses which is somewhat less than half that obtained under the assumption of linearity.Dedicated to Prof. W. Jacobi on the occasion of his 60th birthdayWork performed under Euratom contracts BI6-D-083-D, BI6-F-111-D, U.S. Department of Energy contract DE-AC 02-76 EV-00119, the U.S. National Cancer Institute     

Human exposure to endocrine disrupters: carcinogenic risk assessment

Human exposure to endocrine disrupters (EDs) is widespread and is considered to pose a growing threat to human health. Recent advances in molecular and genetic research and better understanding of mechanisms of blastic cell transformation have led to efforts to improve cancer risk assessment for populations exposed to this family of xenobiotics. In risk assessment, low dose extrapolation of cancer incidence data from both experimental animals and epidemiology studies has been largely based on models assuming linear correlation at low doses, despite existence of evidence showing otherwise. Another weakness of ED risk assessment is poor exposure data in ecological studies. Those are frequently rough estimates derived from contaminated items of local food basket surveys. Polyhalogenated hydrocarbons are treated as examples. There is growing sense of urgency to develop a biologically based dose response model of cancer risk, integrating emerging data from molecular biology and epidemiology to provide more realistic data for risk assessors, public, public health managers and environmental issues administrators.     

Likelihood models for clustered binary and continuous outcomes: application to developmental toxicology

In developmental toxicology, methods based on dose response modeling and quantitative risk assessment are being actively pursued. Among live fetuses, the presence of malformations and reduction in fetal weight are of primary interest, but ordinarily, the dose-response relationships are characterized in each of the outcomes separately while appropriately accounting for clustering within litters. Jointly modeling the outcomes, allowing different relationships with dose while incorporating the correlation between the fetuses and the outcomes, may be more appropriate. We propose a likelihood-based model that is an extension of a correlated probit model to incorporate continuous outcomes. Our model maintains a marginal dose-response interpretation for the individual outcomes while taking into account both the correlations between outcomes on an individual fetus and those due to clustering. The joint risk of malformation and low birth weight can then be estimated directly. This approach is particularly well suited to estimating safe dose levels as part of quantitative risk assessment.     

Combining multiple comparisons and modeling techniques in dose-response studies

The analysis of data from dose-response studies has long been divided according to two major strategies: multiple comparison procedures and model-based approaches. Model-based approaches assume a functional relationship between the response and the dose, taken as a quantitative factor, according to a prespecified parametric model. The fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose-response model. Multiple comparison procedures regard the dose as a qualitative factor and make very few, if any, assumptions about the underlying dose-response model. The primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect. One approach is to evaluate the significance of contrasts between different dose levels, while preserving the family-wise error rate. Such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation. We describe a unified strategy to the analysis of data from dose-response studies which combines multiple comparison and modeling techniques. We assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose-response curve, while preserving the family-wise error rate. The selected model is then used to provide inference on adequate doses.     

Time sequence of cancer occurrence. Implications in low level radiation risk assessment

A total of 8,229 C57 Black mice of both sexes were randomly assigned to various groups. In some groups, mice aged 33 +/- 3 days were submitted to either sham, neutron or cobalt external radiation at 32, 45, 63, 88 and 123 mGy or at 18, 25, 36 and 51 cGy dose levels, respectively. In other groups, mice either at birth or weaning, were injected with tritiated thymidine or tritiated water, or were given tritiated water as drinking water for the entire lifespan. The main purpose of the experiment was to investigate the low dose-response relationship of cancer induction, especially leukemogenesis and to evaluate the excess risk, using actuarial age-specific rates. Following neutron or cobalt exposure, the phenotypic occurrence of lymphocytic lymphomas was earlier in appearance and higher in yield during the first decades of lifespan in irradiated groups versus matching controls, whereas such occurrence was markedly lower in yield at a later age. Under parallel experimental conditions, induction of reticulum cell lymphomas, however, was uniformly enhanced throughout the entire lifespan. Induction rates of all tumors (reticular and solid) pooled were significantly increased, and more so following cobalt than neutron irradiation. In mice injected with tritiated thymidine, the overall tumor incidence was increased monotonically throughout the lifespan. In mice exposed to tritiated water, the incidence of lymphocytic lymphomas was markedly increased throughout the lifespan, whereas no such effect was observed for reticulum cell tumors. In the light of tumor data analysis, it appears that selection of a particular type of tumor as a dependent variable for dose-response assessment cannot disregard the primary modulation of the whole tumor spectrum, In C57 Black murine leukemogenesis, the shape and structure of the dose-response regression curve over the entire lifespan dose not fit the linear-quadratic model. It is, however, theorized that our data are consistent with the two-mutation clonal expansion model, assuming creation of initiated cells which are added to the pool of spontaneously occurring initiated cells and implying that the excess risk is initially high at early age and then decreases with increasing age following exposure. It is concluded that murine radiocarcinogenesis investigation may contribute to improving the assessment as well as understanding the underlying mechanisms of low level radiation hazards.     

Improving Risk Assessment: Toxicological Research Needs

A workshop convened to define research needs in toxicology identified several deficiencies in data and methods currently applied in risk assessment. The workshop panel noted that improving the link between chemical exposure and toxicological response requires a better understanding of the biological basis for inter-and intra-human variability and susceptibility. This understanding will not be complete unless all life stages are taken into consideration. Because animal studies serve as a foundation for toxicological assessment, proper accounting for cross-species extrapolation is essential. To achieve this, adjustments for dose-rate effects must be improved, which will aid in extrapolating toxicological responses to low doses and from short-term exposures. Success depends on greater use of validated biologically based dose-response models that include pharmacokinetic and pharmacodynamic data. Research in these areas will help define uncertainty factors and reduce reliance on underlying default assumptions. Throughout the workshop the panel recognized that biomedical science and toxicology in particular is on the verge of a revolution because of advances in genomics and proteomics. Data from these high-output technologies are anticipated to greatly improve risk assessment by enabling scientists to better define and model the elements of the relationship between exposure to biological hazards and health risks in populations with differing susceptibilities.     

Improving Risk Assessment: Research Opportunities in Dose Response Modeling to Improve Risk Assessment

Substantial improvements in dose response modeling for risk assessment may result from recent and continuing advances in biological research, biochemical techniques, biostatistical/mathematical methods and computational power. This report provides a ranked set of recommendations for proposed research to advance the state of the art in dose response modeling. The report is the result of a meeting of invited workgroup participants charged with identifying five areas of research in dose response modeling that could be incorporated in a national agenda to improve risk assessment methods. Leading topics of emphasis are interindividual variability, injury risk assessment modeling, and procedures to incorporate distributional methods and mechanistic considerations into now-standard methods of deriving a reference dose (RfD), reference concentration (RfC), minimum risk level (MRL) or similar dose-response parameter estimates.     

Detrimental and protective bystander effects: a model approach

This work integrates two important cellular responses to low doses, detrimental bystander effects and apoptosis-mediated protective bystander effects, into a multistage model for chromosome aberrations and in vitro neoplastic transformation: the State-Vector Model. The new models were tested on representative data sets that show supralinear or U-shaped dose responses. The original model without the new low-dose features was also tested for consistency with LNT-shaped dose responses. Reductions of in vitro neoplastic transformation frequencies below the spontaneous level have been reported after exposure of cells to low doses of low-LET radiation. In the current study, this protective effect is explained with bystander-induced apoptosis. An important data set that shows a low-dose detrimental bystander effect for chromosome aberrations was successfully fitted by additional terms within the cell initiation stage. It was found that this approach is equivalent to bystander-induced clonal expansion of initiated cells. This study is an important step toward a comprehensive model that contains all essential biological mechanisms that can influence dose-response curves at low doses.