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Calculation of the cumulative distribution function of the time to a small observable tumor

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Abstract

Multistage mathematical models of carcinogenesis (when applied to tumor incidence data) have historically assumed that the growth kinetics of cells in the malignant state are disregarded and the formation of a single malignant cell is equated with the emergence of a detectable tumor. The justification of this simplification is, from a mathematical point of view, to make the estimation of tumor incidence rates tractable. However, analytical forms are not mandatory in the estimation of tumor incidence rates. Portier et al. (1996b, Math. Biosci. 135, 129–146) have demonstrated the utility of the Kolmogorov backward equations in numerically calculating tumor incidence. By extending their results, the cumulative distribution function of the time to a small observable tumor may be numerically obtained.

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Authors and Affiliations

  1. Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA, 94132, USA

    Claire D. Sherman

  2. Laboratory of Computational Biology and Risk Assessment, National Institute of Environmental Health Sciences, P.O. Box 12233, Research Triangle Park, NC, 27709, USA

    Christopher J. Portier

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  1. Claire D. Sherman
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  2. Christopher J. Portier
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Correspondence to Claire D. Sherman.

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Sherman, C.D., Portier, C.J. Calculation of the cumulative distribution function of the time to a small observable tumor. Bull. Math. Biol. 62, 229–240 (2000). https://doi.org/10.1006/bulm.1999.0148

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  • DOI: https://doi.org/10.1006/bulm.1999.0148

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