Mechanistic modeling of multiple tumorigenesis: an application to data on lung tumors in mice exposed to urethane

Modeling cancer detection: tumor size as a source of information on unobservable stages of carcinogenesis

This paper is concerned with modern approaches to mechanistic modeling of the process of cancer detection. Measurements of tumor size at diagnosis represent a valuable source of information to enrich statistical inference on the processes underlying tumor latency. One possible way of utilizing this information is to model cancer detection as a quantal response variable. In doing so, one relates the chance of detecting a tumor to its current size. We present various theoretical results emerging from this approach and illustrate their usefulness with numerical examples and analyses of epidemiological data. An alternative approach based on a threshold type mechanism of tumor detection is briefly described.

A model of multiple tumorigenesis allowing for cell death: quantitative insight into biological effects of urethane

This paper considers the utility of a stochastic model of carcinogenesis proposed by Yakovlev and Polig [Math. Biosci. 132 (1996) 1-33] in the analysis of experimental data on multiple tumors induced by chemical carcinogens. The model provides a good description of published data on multiple tumors developing in the lungs of mice in response to different schedules of urethane. The distribution of pulmonary tumor counts appears to be negative binomial for each period of time after exposure to urethane. Our results suggest that the rate of administration of urethane has little effect both on the mean number of initiated cells per unit dose and on the rate of formation of lesions responsible for cell death. As our estimates show, more than 80% of initiated cells die in the course of tumor promotion. The model is robust to variations in the rate of urethane excretion given a fixed total dose of the carcinogen. Some prospects for further development of the model to allow for expansion of promoted cell clones are discussed.