Page 205 - 20dynamics of cancer

190 CHAPTER 9

1.84. Thus, the model provides a good match to the observed exponent
on the dose-response relation. The earlier section, The Mathematics of
Curves, and Figure 9.3 explain why a model with n = 6 steps can give an
approximately quadratic dose-response curve.
I repeated the same fitting procedure for the data in Figure 9.9a. In
those data, the maximum observed age is 75; otherwise, I used the same
background assumptions as in the previous case. The shift in maximum
observed age altered the two fitted parameters: u = 7.72 × 10 −4 and
d = 1.225. The model provides a close fit to the data (Figure 9.9b). The
log-log slope of the dose-response curve is 1.84, as in the previous case.
In summary, a model with all stages affected fits the data reason-
ably well. The data do not provide any easy way to distinguish between
this model, with all stages affected, and the earlier models in which the
carcinogens affect only one or two stages. Perhaps the most striking
difference arises in the carcinogenic increase in transition rate that one
must assume: when the carcinogen affects all stages, the increase, d,is
about 1.2, or 120 percent. This small increase in transition would be
consistent with a moderate and continuous increase in cell division: the
mitogenic effect perhaps caused by irritation. By contrast, when the car-
cinogen affects only one stage, the required increase in transition rate, d,
may be around 70, and for two stages, d is probably around 8–10. Those
large increases in transition seem too high for a purely mitogenic effect,
and would therefore point to a significant role of direct mutagenesis in
increasing progression.
Fitting models cannot decide between mitogenic and mutagenic hy-
potheses. In the next section, I discuss how to use the quantitative mod-
els as tools to formulate testable hypotheses.

9.3 Mechanistic Hypotheses and Comparative Tests

Two observations set the puzzle. First, cancer incidence rises more
rapidly with duration of exposure than with dosage. In terms of lung
cancer, incidence rises more rapidly with number of years of smoking
than with number of cigarettes smoked per year. Second, lung cancer
incidence remains approximately constant after cessation of smoking
but rises in continuing smokers.