Mathematical methods and models for radiation carcinogenesis studies

Research on radiation carcinogenesis requires a twofold approach.
Studies of primary molecular lesions and subsequent cytogenetic
changes are essential, but they cannot at present provide numerical
estimates of the risk of small doses of ionizing radiations. Such
estimates require extrapolations from dose, time, and age
dependences of tumor rates observed in animal studies and
epidemiological investigations, and they necessitate the use of
statistical methods that correct for competing risks. A brief
survey is given of the historical roots of such methods, of the
basic concepts and quantities which are required, and of the
maximum likelihood estimates which can be derived for right
censored and double censored data. Non-parametric and parametric
models for the analysis of tumor rates and their time and dose
dependences are explained.