that previous representation of hereditary cancers was consistent with his concept of the two-stage model. Knudson suggested that childhood cancers such as retinoblastoma may represent genetically altered embryonic cells with unconditional cell proliferation. Cancer of the mid-years (osteosarcoma, small cell cancer of the lung, breast cancer) may represent genetic hits—embryonal or not—but with conditional control of cellular proliferation. This control could, in the case of breast cancer for example, be hormonal. Then, it might be that late-age cancers arise from normally dividing tissue in which genetic injury occurs and cell proliferation is enhanced.
TWO-STAGE MODEL OF CLONAL EXPANSION
The next speaker, S.H. Moolgavkar, described the two-stage model of clonal expansion. He noted that from the data presented by Knudson, it is fairly well established that there are two rate-limiting events for retinoblastoma, loss of two antio-ncogenes. For other tumors, particularly adult cancers, the process described by Knudson is more complex, but Moolgavkar stated those data are consistent with their being two rate-limiting and necessary events on the pathway to malignancy. Further, observations of the appearance of tumors in populations of people or animals, providing cell division kinetics are taken into account, are consistent with two necessary steps.
For risk assessment, we need models that relate exposures to the agents of interest to the concentration of the active metabolite in tissue of interest. Secondly, we need models that relate the microdosimetry (interaction of metabolites with macromolecules, for example) with macrodosimetry (tumor formation). Because risk assessment involves extrapolation outside the range of data, the model needs to be at least approximately correct for accurate extrapolation.
Models may have biological or mathematical misspecifications. In describing the Armitage-Doll model and its limitations, Moolgavkar concluded that this model as currently used ignores the fact that cell division and differentiation are likely to be important in carcinogenesis. Also, the waiting time from stage to stage may differ from exponential distributions (mathematical misspecifications likely). Moreover, the
approximations may be useful for epidemiologic studies but do not hold when the probability of tumor is high as in animal studies.
The Moolgavkar two-mutation model postulates two rate-limiting steps called initiation and conversion, represented by irreversible hereditary transitions from normal cells to intermediate cells to cancer cells. In addition to the conversion rates, each cell population has birth and death processes which affect the clonal expansion rates. The ratio of the death rate to the birth rate is the probability that a fraction of initiated cells does not give rise to foci. Moolgavkar postulates that when more than two events are described, as for skin carcinogenesis in mice or for colon tumors in people, only two events may be necessary for the occurrence of the malignant cell and that the other events simply provide a growth advantage (increasing the probability of transformation by increasing the number of target cells for the second event or increasing progression and metastasis after transformation has occurred). The model has been used for human breast and lung cancers and for retinoblastoma.
In presenting examples of applications of the model (radon and lung cancer in rats; N-nitrosomorpholine and liver foci in rats), Moolgavkar emphasized that with this model the shape of the incidence curve is determined by tissue growth and differentiation in contrast with the Armitage-Doll model where the age-specific incidence curve is determined by the number of stages required for malignant transformation. Both examples provided estimates of initiating and converting (promoting) potencies that can be expressed as the proportionate increase per unit dose over background.
The data needs for application of the model include labeling indices for putative intermediate cells at several time points (serial sacrifice studies). Also needed are better models for the cell-cycles. The model assumes, for example, that cells divide and die with exponential waiting times and that all cells in the intermediate foci are in the active dividing stage.
The planned formal discussion ensued. J. Wilson noted that Drs. Knudson and Moolgavkar had brought together two competing theories of carcinogenesis—that mutations lead to cancer and cancer is an adaptive response. He suggested that the inability of current assays to identify initiated cells and to approximate the increased cell number with sufficient sensitivity would be a continual problem. R.J. Sielken reminded us that the components of exposure assessments are probability