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The two-stage model can be used now to gain insights into the nature of induced carcinogenesis. The examples discussed illustrate the usefulness of two-stage models in characterizing the critical events. They also reveal the types and numbers of assumptions that might be made when data are incomplete or lacking. The models could be used as well to examine a range of assumptions.

The committee encourages diverse applications of the two-stage model to gain insight into its usefulness, particularly for risk assessment. However, the committee also recommends that, whenever the model is applied in formal risk assessment or hypothesis-testing, the reproducibility and scientific validity of the results be ensured by the application of optimal statistical methods (e.g., maximum-likelihood methods) to estimate values of parameters and to test goodness-of-fit. Critical assumptions (those with a major quantitative impact on risk estimates) should be clearly stated. And statistical confidence-interval methods, sensitivity analyses, and related quantitative methods should be applied as appropriate to determine the extent to which the resulting data are consistent with other mathematical representations and ranges of risk.

For the time being, the committee recommends that two-stage models be used primarily to promote research understanding; for health risk assessments, two-stage models can be used in conjunction with other models to add perspective to the evaluation process.

Prospects

Until recently, information about the stages of carcinogenesis has been largely limited to the descriptive and operational terms of ''early" and "late" effects in epidemiologic studies and "initiation" and "promotion" in animal studies. The current growth of concepts and information about molecular carcinogenesis in patients and in experimental systems, however, promises new opportunities for conceptual understanding and model development. As more mechanistic information becomes available, the results of some human and animal studies can be expected to converge and make extrapolations across species more precise. Moreover, the patterns of genetic alterations in preneoplastic and neoplastic cells will probably help to distinguish tumors induced by exposure to specific environmental agents from those in the background (of endogenous or



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THE TWO-STAGE MODEL OF CARCINOGENESIS 214 original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. The two-stage model can be used now to gain insights into the nature of induced carcinogenesis. The examples discussed illustrate the usefulness of two- stage models in characterizing the critical events. They also reveal the types and numbers of assumptions that might be made when data are incomplete or lacking. The models could be used as well to examine a range of assumptions. The committee encourages diverse applications of the two-stage model to gain insight into its usefulness, particularly for risk assessment. However, the committee also recommends that, whenever the model is applied in formal risk assessment or hypothesis-testing, the reproducibility and scientific validity of the results be ensured by the application of optimal statistical methods (e.g., maximum-likelihood methods) to estimate values of parameters and to test goodness-of-fit. Critical assumptions (those with a major quantitative impact on risk estimates) should be clearly stated. And statistical confidence-interval methods, sensitivity analyses, and related quantitative methods should be applied as appropriate to determine the extent to which the resulting data are consistent with other mathematical representations and ranges of risk. For the time being, the committee recommends that two-stage models be used primarily to promote research understanding; for health risk assessments, two-stage models can be used in conjunction with other models to add perspective to the evaluation process. Prospects Until recently, information about the stages of carcinogenesis has been largely limited to the descriptive and operational terms of ''early" and "late" effects in epidemiologic studies and "initiation" and "promotion" in animal studies. The current growth of concepts and information about molecular carcinogenesis in patients and in experimental systems, however, promises new opportunities for conceptual understanding and model development. As more mechanistic information becomes available, the results of some human and animal studies can be expected to converge and make extrapolations across species more precise. Moreover, the patterns of genetic alterations in preneoplastic and neoplastic cells will probably help to distinguish tumors induced by exposure to specific environmental agents from those in the background (of endogenous or