A growth rate distribution model for the age dependence of human cancer incidence: a proposed role for promotion in cancer of the lung and breast.

A biological model is proposed to account for the steep rise of human cancer incidence with age. The model casts in mathematical terms the assumptions that each clone destined to give rise to a detectable tumor displays a characteristic net growth rate and that the assembly of such clones displays a distribution of growth rates. Incidence is introduced as the rate of appearance of clones whose size permits detection. While the cancer formation process may involve a series of stages, we assume that the overall kinetics of tumor detection reflect one stage of development whose duration spans the major portion of the latent period between initial cell alteration and final detection. We further assume that the net growth rates of tumor-forming clones increase in the presence of promotors and resume their original growth rates when the promoting substance is removed. Assuming that cigarette smoke has promoting activity, we show how the model could account for the abrupt impact of cessation of smoking on subsequent lung cancer incidence. If we assume that clones destined to be detected as breast cancers experience promotional activity during the period of a woman's fertility, the model predicts that as a consequence of the slowing down of the clones a discontinuous decline in incidence would follow menopause. Since women experience menopause over a range of ages, we show how aggregating the contributions from these menopausal ages results in an overall age dependence of incidence with no discontinuities and with the observed change in the incidence rate for breast cancer near the age range of menopause.