Page 161 - 20dynamics of cancer

146 CHAPTER 8

final number of cells by around 60 months of age, causing cell division
to slow and reducing the risk per cell with age. Change in overall risk
with age depends on the opposing effects of the rise in cell number and
the decline in the rate of cell division.
Hethcote and Knudson (1978) developed a mathematical theory based
on cellular processes of retinal development, and fit their model to an
extended set of data on inherited and sporadic retinoblastoma. The
basic pattern in the data remains the same as in Figure 8.1, but the later
model fits parameters for the somatic mutation rate and for aspects of
cell population size and cell division rate.
At first glance, the realistic model based on cell populations and cell
division may seem attractive. However, many factors affect the inci-
dence of human cancers, including environment, cell-cell interactions,
tissue structure, and somatic mutations during different phases of tu-
mor development. No model can account for all of those factors, and
so incidence data can never provide accurate estimates for isolated pro-
cesses such as somatic mutation rate or cell division rate.
Knudson’s main insight was simply that age-specific incidence of in-
herited and sporadic retinoblastoma should differ in a characteristic way
if cancer arises by two hits to the same cell. He obtained the data and
showed that very simple differences in incidence do occur. The next step
is to understand why the observed differences follow the particular pat-
terns that they do. Detailed mathematical theory based on cell division
and mutation rate provides insight about the factors involved, but with
regard to data analysis, that theory depends too much on the difficult
task of estimating parameters of mutation and cell division from highly
variable incidence data.

RATIO OF SPORADIC TO INHERITED INCIDENCE
I advocate theory more closely matched to Knudson’s original insight
and to what one can realistically infer given the nature of the data (Frank
2005). According to Knudson’s theory, bilateral tumors arise from single
hits to somatic cells with an inherited mutation. The rate at which a
hit occurs in the developing retina at a particular age depends on many
factors, including the number of target cells and the rate of cell division.
But we cannot get good estimates for those factors, so let us use the
observations for bilateral cases at different ages to estimate the rate