A mathematical approach predicting the number of events in different tumors.

Supported by different investigations, multi-step models for tumorigenesis have been proposed for epithelial tumors. The age specific incidence of some cancers shows an exponential rise with increasing patient age. Yet, the onset and the slope of incidence curves varies between tumor types. One simple explanation for this disparity is that the number of mutations required for transformation differs in various tissues. We used a homogeneous Poisson process to estimate the number of events (N) and the intensity or event rate (lambda) that might be needed for cancer development in various tissues (colon, prostate, oralpharynx, larynx). Estimations were performed, including 95% confidence intervals, for the male and female population. The expected number of events needed was higher in adenocarcinomas (colorectal carcinoma: N approximately 10 for females and N approximately 11.0 for males; prostatic cancer: N approximately 23) than in squamous cell carcinomas (oropharynx: N approximately 5-6 for females and N approximately 6 for males; larynx: N approximately 7 for females and N approximately 8 males). Still, alternative models fixing N to values within the 95% confidence intervals determined, showed good coincidence with epidemiological data. Although the herein applied mathematical model neglects several biologic conditions, especially a presumed acceleration of mutation rates after tumor initiation it offers a plausible theory for the given epidemiologic data and matches with molecular biologic findings in the investigated cancers.