Page 173 - 20dynamics of cancer

158 CHAPTER 8

1.0 0.8 (a) 1 (c)
Fraction surviving 0.6 0.4 Incidence 0.1

Mlh3
0.01
0.2
Mlh1
Mlh3Pms2
4 6 8 10 12 14 16 4 8 16
1.0 0.8 (b) 5 (d)
Fraction surviving 0.6 0.4 Acceleration 4 3

0.2

4 6 8 10 12 14 16 2 4 8 16
Age in months Age in months

Figure 8.8 Age of gastrointestinal tumor (adenoma) onset in mice with differ-
ent mismatch repair genotypes. Panels as in Figure 8.7. Redrawn from Frank
et al. (2005).

Acceleration in Figure 8.7d shows the slope of the incidence curves.
The accelerations are constant over time because I forced the incidence
curves to be linear. With more data, one could estimate nonlinear inci-
dence curves, which would allow changes in acceleration with age.

HYPOTHESES AND TESTS

Multistage theory makes three qualitative predictions about the dy-
namics of cancer. First, the fewer the number of steps in progression
that must be passed, the lower the acceleration of cancer with age. In lab
experiments, the theory predicts that abrogation of tumor suppressor
functions or introduction of oncogenes reduces the acceleration. Sec-
ond, small to moderate increases in the mutation rate cause greater can-
cer incidence at earlier ages but do not affect the acceleration. Third,
large increases in mutation rate can cause such rapid transitions be-
tween stages that certain mutations required for carcinogenesis may no
longer limit the rate of tumor formation. If some transitions no longer