Page 167 - 20dynamics of cancer

152 CHAPTER 8

6
8
5 4
Incidence 3 2 X 10 -4 4

1 R 2
0 (a) (b)

10 20 40 80 20 30 40 50
Age Age

Figure 8.4 Age-specific incidence of inherited and sporadic colon cancer. (a)
Inherited colon cancer (FAP) caused by mutation of the APC gene (solid circles)
6
and sporadic cases (open circles) per 10 population, shown on a log 10 scale.
Description of the data in Figure 2.6. (b) Ratio of sporadic colon cancer incidence
(I C ) to inherited FAP incidence (I F ) at each age multiplied by 10 −4 , using the
data in the previous panel. From Frank (2005).

the ratio of sporadic to inherited age-specific incidence, R = I S /I I . This
ratio increases about 3-fold with age, varying between about 2–6 ×10 −4 .

RATIO OF SPORADIC TO INHERITED INCIDENCE
In Section 7.2, I developed theory to predict the ratio of age-specific
incidence between two genotypes under the assumption of simple step-
wise progression through n stages with constant transition rates. One
could certainly use more complex models, but there are not enough data
to justify particular assumptions. So I stick with the simplest model to
see how well it explains the data.
I start with the assumption that sporadic colon cancer requires pro-
gression through n stages. Inherited FAP requires progression through
only n − 1 stages, because at birth those individuals have already ad-
vanced by one stage. From Eq. (7.3), we have the ratio of sporadic to
inherited cases
ut
R ≈ , (8.3)
n − 1
noting that the colon has multiple lines of progression, thus the ratio of
S n−2 /S n−1 in Eq. (7.3) will be close to one.
If transitions occur as somatic mutations, then the transition rate per
year is the mutation rate per cell division, v, multiplied by the number of
cell divisions per year, D, providing the substitution u = vD in Eq. (8.3).