Page 105 - 20dynamics of cancer

90 CHAPTER 5

Second, the acceleration of cancer incidence with age declines at later
ages for the common epithelial cancers—breast, prostate, lung, and col-
orectal (Figure 2.3). Several other cancers also show a steady and some-
times rather sharp decline in acceleration at later ages. In some cases,
the patterns of acceleration differ between countries (see Appendix). On
the whole, declines in acceleration later in life appear to be typical for
many cancers.
Third, several cancers show very high early or midlife accelerations,
sometimes with accelerations at early ages rising to a midlife peak (Fig-
ure 2.3). For example, prostate cancer has an exceptionally high midlife
peak (Figure A.2); leukemia (Figure A.6) and in some cases colon cancer
(Figure A.4) show rises in early life.
Fourth, smokers who quit by age 50 have a lower acceleration in lung
cancer risk later in life than do those who never smoked or who continue
to smoke (Figure 2.8).
Fifth, exposure to a carcinogen often causes the median number of
years to tumor formation to decline linearly with dosage when measured
on log-log scales (Figures 2.10, 2.11).
Sixth, given a set of individuals who have suffered breast cancer at
a particular age, the close relatives of those individuals have high and
nearly constant annual risk (zero acceleration) for breast cancer after
the age at which the affected individuals were diagnosed. By contrast,
individuals whose relatives have not suffered breast cancer have lower
risk per year, but their risk accelerates with age (Peto and Mack 2000).
These observations provide a sample of interesting puzzles, most of
which have yet to be explained in a convincing way. Dynamical models
of cancer progression provide the only source of plausible hypotheses
to explain the range of observed patterns.

5.3 Progression Dynamics through Multiple Stages

Models of progression dynamics analyze transitions through stages.
The simplest type of model follows progression through a linear se-
quence. This linear model arose over 50 years ago, when people first
observed clear patterns in the age-specific incidence of cancer.
Figure 5.1 illustrates the type of pattern that was apparent to early ob-
servers: the incidence of colorectal cancer increases in a roughly linear