Page 202 - 20dynamics of cancer

CARCINOGENS 187

1500 (a) 0 (b) 3
1 4 5
1000 2

500

Incidence per 100,000 1500 1000 500 (c) (d)

1500 (e) (f)

1000

500

40 50 60 70 80 40 50 60 70 80
Age

Figure 9.10 Theoretical incidence curves in response to carcinogen application
followed by cessation. The carcinogen affects only a single transition in a model
with n = 6 steps. The legend shows the curve type for each of the i = 0,..., 5
transitions, in which the carcinogen affects only the ith transition. (a and b)
Carcinogen applied from age 0 to age 60. (c and d) Carcinogen applied from age
25 to age 80. (e and f) Carcinogen applied from age 25 to age 60. I calculated
the curves by numerical evaluation of the complete progression dynamics as
described in earlier chapters. I used the following assumptions: the number of
8
lineages per individual, L = 10 ; the transition rate for steps not affected by the
carcinogen, u = 7.24 × 10 −4 ; and the transition rate for the single step affected
by the carcinogen during those ages of exposure, u(1 + d), where d = 70.

Brown 1980). The analyses I just presented improve the accuracy of
such models over previous studies, but the main points hold from ear-
lier work. After that early work, two observations affected subsequent
analyses of smoking cessation. First, none of the curves in Figure 9.10