Sherman, Claire D.; Portier, Christopher J. Calculation of the cumulative distribution function of the time to a small observable tumor. (English) Zbl 1323.92109 Bull. Math. Biol. 62, No. 2, 229-240 (2000). Summary: 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. The second author et al. [Math. Biosci. 135, No. 2, 129–146 (1996; Zbl 0859.92013)] 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. Cited in 1 Document MSC: 92C50 Medical applications (general) Keywords:cumulative distribution function; Kolmogorov backward equations; tumor incidence; multistage mathematical models; carcinogenesis Citations:Zbl 0859.92013 PDFBibTeX XMLCite \textit{C. D. Sherman} and \textit{C. J. Portier}, Bull. Math. Biol. 62, No. 2, 229--240 (2000; Zbl 1323.92109) Full Text: DOI