A generalized Luria-Delbrück model.

We develop extensions of the Luria-Delbrück model that explicitly consider non-exponential growth of normal cells and a birth-death process with mean exponential or Gompertz growth of mutants. Death of mutant cells can be important in clones arising during cancer progression. The use of a birth-death process for growth of mutant cells, as opposed to a pure birth process as in previous work on the Luria-Delbrück model, leads to a large increase in the extra Poisson variation in the size of the mutant cell populations, which needs to be addressed in statistical analyses. We also discuss connections with previous work on carcinogenesis models.

From mechanisms to risk estimation--bridging the chasm.

We have a considerable amount of work ahead of us to determine the importance of the wealth of new information emerging in the fields of sub-cellular, cellular and tissue biology in order to improve the estimation of radiation risk at low dose and protracted dose-rate. In this paper, we suggest that there is a need to develop models of the specific health effects of interest (e.g., carcinogenesis in specific tissues), which embody as much of the mechanistic (i.e., biological) information as is deemed necessary. Although it is not realistic to expect that every radiation-induced process should or could be included, we can hope that the major factors that shape the time dependence of evolution of damage can be identified and quantified to the point where reasonable estimations of risk can be made. Regarding carcinogenesis in particular, the structure of the model itself plays a role in determining the relative importance of various processes. We use a specific form of a multi-stage carcinogenic model to illustrate this point. We show in a review of the application of this model to lung cancer incidence and mortality in two exposed populations that for both high- and low-LET radiation, there is evidence of an "inverse dose-rate" or protraction effect. This result could be of some considerable importance, because it would imply that risk from protracted exposure even to low-LET radiation might be greater than from acute exposure, an opinion not currently held in the radiation protection community. This model also allows prediction of the evolution of the risk over the lifetimes of the exposed individuals. One inference is that radiation-induced initiation (i.e., the first cellular carcinogenic event(s) occurring in normal tissue after the passage of the radiation) may not be the driving factor in the risk, but more important may be the effects of the radiation on already-initiated cells in the tissue. Although present throughout the length of the exposure, radiation-induced initiation appears to play a dominating role only very late in life, and only for those individuals who began their exposure early in life. These conclusions are very dependent, of course, on the hypotheses embodied in the initiation-promotion-conversion paradigm of carcinogenesis. We suggest that recently identified processes, such as the "bystander effect", might affect initiation, promotion, and malignant conversion in different ways. Finally, the manner in which the quality of radiation affects these processes must be understood in the context of the mixed high- and low-LET radiations that are found in the space environment. Important directions in critical experiment definition are suggested, including a renewed emphasis on well-designed animal experiments over extended periods of time.

A new perspective of carcinogenesis from protracted high-LET radiation arises from the two-stage clonal expansion model.

When applied to the Colorado Plateau miner population, the two-stage clonal expansion (TSCE) model of radiation carcinogenesis predicts that radiation-induced promotion dominates radiation-induced initiation. Thus, according to the model, at least for alpha-particle radiation from inhaled radon daughters, lung cancer induction over long periods of protracted irradiation appears to be dominated by radiation-induced modification of the proliferation kinetics of already-initiated cells rather than by direct radiation-induced initiation (i.e., mutation) of normal cells. We explore the possible consequences of this result for radiation exposures to space travelers on long missions. Still unknown is the LET dependence of this effect. Speculations of the cause of this phenomenon include the suggestion that modification of cell kinetics is caused by a "bystander" effect, i.e., the traversal of normal cells by alpha particles, followed by the signaling of these cells to nearby initiated cells which then modify their proliferation kinetics.

Analysis of a historical cohort of Chinese tin miners with arsenic, radon, cigarette smoke, and pipe smoke exposures using the biologically based two-stage clonal expansion model.

Hazelton, W. D., Luebeck, E. G., Heidenreich, W. F. and Moolgavkar, S. H. Analysis of a Historical Cohort of Chinese Tin Miners with Arsenic, Radon, Cigarette Smoke, and Pipe Smoke Exposures Using the Biologically Based Two-Stage Clonal Expansion Model. Radiat. Res. 156, 78-94 (2001).The two-stage clonal expansion model is used to analyze lung cancer mortality in a cohort of Yunnan tin miners based on individual histories with multiple exposures to arsenic, radon, cigarette smoke, and pipe smoke. Advances in methodology include the use of nested dose-response models for the parameters of the two-stage clonal expansion model, calculation of attributable risks for all exposure combinations, use of both a fixed lag and a gamma distribution to represent the time between generation of the first malignant cell and death from lung cancer, and scaling of biological parameters allowed by parameter identifiability. The cohort consists of 12,011 males working for the Yunnan Tin Corporation, with complete exposure records, who were initially surveyed in 1976 and followed through 1988. Tobacco and arsenic dominate the attributable risk for lung cancer. Of 842 lung cancer deaths, 21.4% are attributable to tobacco alone, 19.7% to a combination of tobacco and arsenic, 15.8% to arsenic alone, 11% to a combination of arsenic and radon, 9.2% to a combination of tobacco and radon, 8.7% to combination of arsenic, tobacco and radon, 5.5% to radon alone, and 8.7% to background. The models indicate that arsenic, radon and tobacco increase cell division, death and malignant conversion of initiated cells, but with significant differences in net cell proliferation rates in response to the different exposures. Smoking a bamboo water pipe or a Chinese long-stem pipe appears to confer less risk than cigarette use, given equivalent tobacco consumption.

Long man-made fibers and lung cancer risk.

We show that available experimental data from long-term oncogenicity experiments in Fisher rats are consistent with the hypothesis that the oncogenic potential of long man-made mineral fibers is determined mainly by their biopersistence. We present analyses of these data within the initiation-promotion-progression paradigm of carcinogenesis. Our method of analysis can take the temporal pattern of the burden of long fibers in the lungs of individual animals into explicit account. For this analysis, the temporal pattern of lung burden for each animal was imputed from the information obtained from sacrificed animals. The data are consistent with the hypothesis that fibers act as initiators in the rat lung. We present an estimate of the dose-dependent initiation parameter that is based on all the available data.

The role of promotion in carcinogenesis from protracted high-LET exposure.

Recent analysis of epidemiological studies using the two-stage clonal expansion (TSCE) model has shown that radiation-induced promotion dominates radiation-induced initiation for protracted exposures to radon. This strong promotion effect (i.e. enhanced proliferation of already-initiated cells) causes a pronounced 'inverse dose-rate effect', but by a mechanism completely different from those usually discussed in this connection. This rather startling result is discussed along with implications to extended space missions that include a significant amount of high-LET radiation. It is suggested that the effect might be caused by a 'Bystander Effect' by which normal cells in the vicinity of initiated cells are hit by alpha particles and send out signals that modify the cell kinetics of the already-initiated clones.

Effects of 2,3,7,8-tetrachlorodibenzo-p-dioxin on initiation and promotion of GST-P-positive foci in rat liver: A quantitative analysis of experimental data using a stochastic model.

We use a stochastic model describing initiation and clonal growth of altered cells to analyze data from an initiation-promotion hepatocarcinogenesis experiment in female Wistar rats. Starting at 7 weeks of age, the animals were treated for 10 days with the initiating agent diethylnitrosamine (DEN, 10 mg/kg body wt per day). After a 10-week resting period, the animals were treated either with corn oil or with 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) via biweekly sc injections of 1.4 microg/kg body wt of TCDD dissolved in corn oil. Groups of four or five animals were euthanized 3, 17, 31, 73, and 115 days after start of TCDD/corn oil treatment. The data analyzed consist of the number and sizes of GST-P-positive focal transections at various time points. By fitting the model to the data, we estimate the rates of initiation, cell division, and cell death during different time periods of the experiment. The model estimates of cell kinetic parameters are consistent with directly made experimental observations of cell division and cell death. The model predicts that DEN-induced initiation of GST-P-positive cells is highly protracted in controls and TCDD-treated animals alike. We also find that TCDD interferes with the normal rate at which cells with (DEN-inflicted) DNA damage are converted into cells expressing the GST-P-positive phenotype, suggesting a TCDD-mediated "acceleration" of the appearance of de novo GST-P-positive initiated cells from damaged precursor cells. Furthermore, the model predicts a significant reduction in the rate of apoptosis within the first 4 to 5 weeks of TCDD treatment, and after 10 weeks of TCDD treatment, but not in between.

Lung cancer risk associated with exposure to man-made fibers.

We show that available experimental data from long-term experiments are consistent with the hypothesis that the oncogenic potential of man-made fibers is determined completely by their biopersistence. We present an analysis of these data within the initiation-promotion-progression paradigm of carcinogenesis. Our method of analysis takes explicit account of the temporal pattern of fiber burden in the rat lung, and suggests that fibers act as initiators in the lung. We estimate a dose-dependent initiation parameter and show how it can be transported to human populations for assessment of the risk of lung cancer following exposure to man-made fibers.

Biologically based analysis of the data for the Colorado uranium miners cohort: age, dose and dose-rate effects.

This study is a comprehensive analysis of the latest follow-up of the Colorado uranium miners cohort using the two-stage clonal expansion model with particular emphasis on effects related to age and exposure. The model provides a framework in which the hazard function for lung cancer mortality incorporates detailed information on exposure to radon and radon progeny from hard rock and uranium mining together with information on cigarette smoking. Even though the effect of smoking on lung cancer risk is explicitly modeled, a significant birth cohort effect is found which shows a linear increase in the baseline lung cancer risk with birth year of the miners in the cohort. The analysis based on the two-stage clonal expansion model suggests that exposure to radon affects both the rate of initiation of intermediate cells in the pathway to cancer and the rate of proliferation of intermediate cells. However, in contrast to the promotional effect of radon, which is highly significant, the effect of radon on the rate of initiation is found to be not significant. The model is also used to study the inverse dose-rate effect. This effect is evident for radon exposures typical for mines but is predicted to be attenuated, and for longer exposures even reversed, for the more protracted and lower radon exposures in homes. The model also predicts the drop in risk with time after exposure ceases. For residential exposures, lung cancer risks are compared with the estimates from the BEIR VI report. While the risk estimates are in agreement with those derived from residential studies, they are about two- to fourfold lower than those reported in the BEIR VI report.

Quantitative assessment of the risk of lung cancer associated with occupational exposure to refractory ceramic fibers.

We present the results of a quantitative assessment of the lung cancer risk associated with occupational exposure to refractory ceramic fibers (RCF). The primary sources of data for our risk assessment were two long-term oncogenicity studies in male Fischer rats conducted to assess the potential pathogenic effects associated with prolonged inhalation of RCF. An interesting feature of the data was the availability of the temporal profile of fiber burden in the lungs of experimental animals. Because of this information, we were able to conduct both exposure-response and dose-response analyses. Our risk assessment was conducted within the framework of a biologically based model for carcinogenesis, the two-stage clonal expansion model, which allows for the explicit incorporation of the concepts of initiation and promotion in the analyses. We found that a model positing that RCF was an initiator had the highest likelihood. We proposed an approach based on biological considerations for the extrapolation of risk to humans. This approach requires estimation of human lung burdens for specific exposure scenarios, which we did by using an extension of a model due to Yu. Our approach acknowledges that the risk associated with exposure to RCF depends on exposure to other lung carcinogens. We present estimates of risk in two populations: (1) a population of nonsmokers and (2) an occupational cohort of steelworkers not exposed to coke oven emissions, a mixed population that includes both smokers and nonsmokers.

A method for parametric estimation of the number and size distribution of cell clusters from observations in a section plane.

The problem of finding the number and size distribution of cell clusters that grow in an organ or tissue from observations of the number and sizes of transections of such cell clusters in a planar section is considered. This problem is closely related to the well-known corpuscle or Wicksell problem in stereology, which deals with transections of spherical objects. However, for most biological applications, it is unrealistic to assume that cell clusters have spherical shapes since they may grow in various ways. We therefore propose a method that allows for more general spatial configurations of the clusters. Under the assumption that a parametric growth model is available for the number and sizes of the cell clusters, expressions are obtained for the probability distributions of the number and sizes of transections of the clusters in a section plane for each point in time. These expressions contain coefficients that are independent of the parametric growth model and time but depend on which model is chosen for the configuration of the cell clusters in space. These results enable us to perform estimation of the parameters of the growth model by maximum likelihood directly on the data instead of having to deal with the inverse problem of estimation of three-dimensional quantities based on two-dimensional data. For realistic choices of the configuration model, it will not be possible to obtain the exact values of the coefficients, but they can easily be approximated by means of computer simulations of the spatial configuration. Monte Carlo simulations were performed to approximate the coefficients for two particular spatial configuration models. For these two configuration models, the proposed method is applied to data on preneoplastic minifoci in rat liver under the assumption of a two-event model of carcinogenesis as the parametric growth model.

Estimation of unit risk for coke oven emissions.

In 1984, based on epidemiological data on cohorts of coke oven workers, USEPA estimated a unit risk for lung cancer associated with continuous exposure from birth to 1 microgram/m3 of coke oven emissions, of 6.2 x 10(-4). This risk assessment was based on information on the cohorts available through 1966. Follow-up of these cohorts has now been extended to 1982 and, moreover, individual job histories, which were not available in 1984, have been constructed. In this study, lung cancer mortality in these cohorts of coke oven workers with extended follow-up was analyzed using standard techniques of survival analysis and a new approach based on the two stage clonal expansion model of carcinogenesis. The latter approach allows the explicit consideration of detailed patterns of exposure of each individual in the cohort. The analyses used the extended follow-up data through 1982 and the detailed job histories now available. Based on these analyses, the best estimate of unit risk is 1.5 x 10(-4) with 95% confidence interval = 1.2 x 10(-4)-1.8 x 10(-4).

Analysis of the incidence of solid cancer among atomic bomb survivors using a two-stage model of carcinogenesis.

A two-stage stochastic model for carcinogenesis was used to analyze the incidence of cancer of the lung, stomach and colon in the cohort of atomic bomb survivors. We fitted the model assuming that acute exposure to radiation results in the creation of initiated cells that are added to the pool of spontaneously initiated cells. In the cancers analyzed, with the exception of lung cancer in females, we found no evidence that radiation-induced initiation was dependent upon age at exposure. In contrast, we found that spontaneous initiation was dependent upon age at exposure in the cancers analyzed except stomach cancer among males. Because exposure to radiation in this cohort occurred at the same time for all members of the cohort, age at exposure is exactly correlated with birth cohort, and the dependence of spontaneous initiation on age at exposure is a reflection of the cohort effects seen in these cancers in Japan. Even without a dependence of radiation-induced initiation on age at exposure, the two-stage model can explain the temporal behavior of the excess relative risk with age at exposure and time since exposure. In particular, the model predicts that excess relative risk is highest among those exposed as children. Moreover, since radiation-induced initiation is not higher among those exposed as children, the excess relative risk in this group is not due to an inherently higher sensitivity to radiation. Our biologically based approach provides another perspective on the temporal behavior of risk after acute exposure to ionizing radiation.

Air pollution and hospital admissions for respiratory causes in Minneapolis-St. Paul and Birmingham.

We investigated the association between air pollution and hospital admissions for chronic obstructive pulmonary disease and pneumonia among the elderly in Minneapolis-St. Paul, MN, and Birmingham, AL, over the period January 1, 1986, to December 31, 1991. Pollutants included in our analyses were PM10 (particulate matter less than 10 microns in aerodynamic diameter), SO2, NO2, O3, and CO in Minneapolis-St. Paul, and PM10, O3, and CO in Birmingham. After adjusting for temperature, day of week, season, and temporal trends, we found little evidence of association between air pollution and hospital admissions for respiratory causes in Birmingham. In contrast, we found that air pollution was associated with hospital admissions for respiratory causes in Minneapolis-St. Paul. Among the individual pollutants, O3 was most strongly associated with admissions (estimated increase in hospital admissions associated with a 15-parts-per-billion increase in O3 on the previous day = 5.15%; 95% confidence interval = 2.36-7.94%), and this association was robust in the sense that it was little affected by the simultaneous consideration of other pollutants. PM10, SO2, and NO2 were also associated with hospital admissions, although none could be singled out as being more important than the others.

Some properties of the hazard function of the two-mutation clonal expansion model.

We discuss the hazard function of the two-mutation clonal expansion model with time-dependent parameters, with particular emphasis on identifiability of the parameters. We explicitly construct identifiable parameter combinations, and illustrate the properties of the hazard function under perturbations of the underlying biological parameters.

A critical review of the evidence on particulate air pollution and mortality.

We review epidemiologic studies of particulate air pollution and mortality in U.S. cities with respect to important methodologic issues. Many of these studies suffer from serious deficiencies in their control of the confounding effects of other pollutants. As a consequence, the small risks reported to be associated with the particulate component of air pollution could easily be attributed to residual confounding by co-pollutants. Most studies, moreover, have not considered modification of air pollution effects by seasonal factors, making the interpretation of the estimated risks difficult. We use a new analysis of mortality in Philadelphia that considers four pollutants simultaneously as well as seasonal effects to illustrate the methodologic issues raised in this paper. Air pollution, which is a complex mixture, appears to be associated with mortality even at the generally low levels of pollution in U.S. cities, but currently neither the statistical tools nor the biological understanding of mechanisms exists to tease out the contribution made by each component of this mixture. We conclude that it is not possible with the present evidence to show a convincing correlation between particulate air pollution and mortality.

A biologically based model for the analysis of premalignant foci of arbitrary shape.

In many animal carcinogenesis experiments, quantitative data on putative premalignant foci are now routinely collected. Moolgavkar et al. [Carcinogenesis 11:1271 (1990)] considered the analysis of such data from a rat hepatocarcinogenesis experiment within the framework of a two-stage model for carcinogenesis using the assumption that the premalignant clones were spherical. This assumption seems questionable in many organs, including the liver. In this paper, it is relaxed and arbitrary shapes are allowed for the clones. The proposed method is illustrated by reanalysis of the data considered in the earlier paper. The new analysis yields parameter estimates that are more plausible biologically than those of the original analysis.