Page 168 - 20dynamics of cancer

GENETICS OF PROGRESSION 153

I use v ≈ 10 −6 , as discussed in the previous section. The colon epithe-
lium turns over every few days, and stem cells that ultimately renew the
tissue probably divide at least once per week, or about D ≈ 50 times per
year. For the number of stages, n, epidemiological and molecular esti-
mates usually fall in the range 4–7 (Armitage and Doll 1954; Fearon and
Vogelstein 1990; Luebeck and Moolgavkar 2002). All of these numbers
are provisional, but they allow us to predict that the ratio of sporadic to
inherited incidence rates should be roughly

ut vDt −5
R ≈ = ≈ 10 t.
n − 1 n − 1
The data for inherited FAP and sporadic cases can be compared on the
range t = 20–40, so R is predicted to increase over the range 2–4 ×
10 −4 . Figure 8.4b shows that the ratio of incidences is of the predicted
magnitude and increases with age, although the increase with age is
slightly greater than predicted.

ACCELERATION IN SPORADIC VERSUS INHERITED CASES
Multistage theory predicts that sporadic cases must progress through
at least one more stage than inherited cases. More stages in progres-
sion leads to a higher acceleration, so the theory predicts that cases of
sporadic colon cancer should accelerate with age more rapidly than the
acceleration of inherited cases.
Figure 8.5 shows the same data as in Figure 8.4, with the incidence
curves forced to be straight lines. This forced linearity allows an ap-
proximate estimate of the log-log slope of R versus t, as shown in Fig-
ure 8.5c. The estimated value of 1.5 for this slope is reasonably close to
the predicted value of 1, the difference in the number of stages between
sporadic and inherited forms.
The theory can be refined in many ways, for example, taking account
of the number of independent cell lineages at risk for stepping through
the various transition stages. But most reasonable assumptions apply
to both the inherited and sporadic rates of transition, and so the ratio
of incidence rates remains roughly the same under such refinements.
At present, we have little quantitative information about the differ-
ent processes that drive progression. Without such details, we get the
most insight from simple theories that lead to easily tested comparative
predictions. For sporadic versus inherited cancers, two predictions of