Page 181 - 20dynamics of cancer

166 CHAPTER 9

between mechanism and incidence provide a way to test hypotheses
about carcinogenic effects on the rate of transition between stages, on
the number of stages affected, and on the particular order of affected
transitions.
By altering both carcinogen treatment and animal genotype, one may
test explicit hypotheses about carcinogenic action. For example, if a car-
cinogen is believed to cause a particular genetic change, then a knock-
out of that genotype should be less affected by the carcinogen when
measured by age-incidence curves. Such tests can manipulate different
components of progression and compare the outcomes to quantitative
theories of incidence.

9.1 Carcinogen Dose-Response

Lung cancer incidence increases with roughly the fourth or fifth power
of the number of years (duration) of cigarette smoking but with only
the first or second power of the number of cigarettes smoked per day
(dosage). The stronger response to duration than dosage occurs in
nearly all studies of carcinogens. Peto (1977) concluded: “The fact that
the exponent of dose rate is so much lower than the exponent of time is
one of the most important observations about the induction of carcino-
mas, and everyone should be familiar with it—and slightly puzzled by
it!”
In this section, I first summarize the background concepts and two
studies of duration and dosage. I then consider five different explana-
tions. The most widely accepted explanation is that cancer progresses
through several stages, causing incidence to rise with a high power of
duration, but that a carcinogen usually affects only one or two of those
stages in progression, causing incidence to rise with only the first or
second power of dosage. However, several alternative explanations also
fit the data, so fitting provides little insight. In a later section, I dis-
cuss ways to formulate comparative tests. Such comparative tests may
help to distinguish between alternative hypotheses and to reveal the
processes by which carcinogens influence progression.

BACKGROUND

In the standard theory, the usual approximation of incidence is I(t) ≈
n n−1
ku t , where k is a constant, n is the number of rate-limiting transi-