Exact solutions of the clonal expansion model and their application to the incidence of solid tumors of atomic bomb survivors

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Abstract
We derive explicit hazard functions for the clonal expansion model in the "exact formulation" and in the "epidemiological approximation" for the spontaneous rate and for short-time exposure. We investigate which combination of the biological parameters can be determined from the incidence function, and which cannot. We then analyze the incidence data of all solid tumors of atomic bomb survivors (1958-1987). We restrict ourselves to adults at exposure (> 20 years) and to attained age (< 80 years, and we consider the two cities (Hiroshima and Nagasaki) and the two sexes separately. With four parameters, we find good fits in each case, comparable to the quality of fit of epidemiological age-at-exposure and age-attained models used for comparison. The parameters which describe the spontaneous risk agree very well for the two cities, while they are quite different for the two sexes. The apparent flattening of the risk for elderly men can be described with the exact formulation of the clonal expansion model, but may be due to other causes than the mechanisms modeled. The dose-response parameters differ by more than two standard deviations (factor 2 to 3) between the two cities, when considering the same sex. They are bigger of the men of Nagasaki and the women of Hiroshima. One example for model application to tumors of specific organs (men's lung tumor) is considered.

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