Page 133 - 20dynamics of cancer

118 CHAPTER 7

–2
(a)
–3
Incidence –4

–5
–6

10 (b)
Acceleration 8 6

2 4
1.0 (c)
0.8
Frequency 0.6

0.4
0.2
0
20 40 80
Age

Figure 7.1 Multiple pathways of progression in a tissue influence age-onset
patterns of cancer. This figure shows epidemiological patterns for k = 3 path-
ways in a tissue in which there is a single line of progression, L = 1. On
the y axis, the panels measure (a) log incidence, (b) log-log acceleration (LLA),
and (c) frequency of cancer for each pathway. The x axis plots age on a log-
arithmic scale. The lifetime probability of cancer per individual at age 80 is
m = 0.1. In each panel, the long-dash curve shows the pathway for which
n 1 = 4, u 1 = 0.0103, and the lifetime probability of cancer is 0.01; the short-
dash curve shows the pathway for which n 2 = 8, u 2 = 0.0413, and the lifetime
probability of cancer is 0.02; and the dot-dash curve shows the pathway for
which n 3 = 13, u 1 = 0.1016, and the lifetime probability of cancer is 0.07. The
solid curve shows the aggregate over all pathways.

To keep the analysis simple, I focus on k pathways in one line. The
solution for multiple lines scales up according to the theory outlined in
Section 6.3. Typically, if the total probability of cancer, m, by age T is