  Cancers are caused by the accumulation of genetic alterations. Since this
accumulation takes time, the incidence of most cancers is thought to increase
exponentially with age. However, careful measurements of the age-specific
incidence shows that the specific incidence for many forms of cancer rises with
age to a maximum, then decreases. This decrease in the age-specific incidence
with age is an anomaly. Understanding this anomaly should lead to a better
understanding of how tumors develop and grow. Here I derive the shape of the
age-specific incidence, showing that it should follow the shape of a Weibull
distribution. Measurements indicate that the age-specific incidence for colon
cancer does indeed follow a Weibull distribution. This analysis leads to the
interpretation that for colon cancer two sub-populations exist in the general
population: a susceptible population and an immune population. Colon tumors
will only occur in the susceptible population. This analysis is consistent with
the developmental origins of disease hypothesis and generalizable to many other
common forms of cancer.
