Page 131 - 20dynamics of cancer

116 CHAPTER 7

genetic variants each of small effect and from diverse environmental
factors. I develop the case in which variation occurs in the rate of pro-
gression, caused for example by inherited differences in DNA repair ef-
ficacy or by different environmental exposures to mutagens.
Populations with high levels of variability have very different patterns
of progression when compared to relatively homogeneous groups. In
general, increasing heterogeneity causes a strong decline in the accel-
eration of cancer. To understand the distribution of cancer, it may be
more important to measure heterogeneity than to measure the average
value of processes that determine rates of progression.
The fourth section relates my models of progression and incidence
to the classic Gompertz and Weibull models frequently used to summa-
rize age-specific mortality. The Gompertz and Weibull models simply
describe linear increases with age in the logarithm of incidence. Those
models make no assumptions about underlying process. Instead, they
provide useful tools to reduce data to a small number of estimated pa-
rameters, such as the intercept and slope of age-specific incidence.
Data reductions according to the Gompertz and Weibull models can
be useful descriptive procedures. However, I prefer to begin with an ex-
plicit model of progression dynamics and derive the predicted shape of
the incidence curve. Explicit dynamical models allow one to test com-
parative hypotheses about the processes that influence progression. I
show that the simplest explicit models of progression dynamics yield
incidence curves that often closely match the Weibull pattern.
The final section reviews applications of the Weibull model to dose-
response curves in laboratory studies of chemical carcinogenesis. Most
studies fit well to a model in which incidence rises with a low power
of the dosage of the carcinogen and a higher power of the duration of
carcinogen exposure. Quantitative evaluation of chemical carcinogens
provides a way to test hypotheses about the processes that drive pro-
gression.

7.1 Multiple Pathways of Progression

PR ´ ECIS

Cancer in a particular tissue may progress by different pathways. Ide-
ally, one would be able to measure progression and incidence separately
for each pathway. In practice, observed incidence arises from combined