Page 100 - 20dynamics of cancer

5 Progression Dynamics

Progression depends on various rate processes, such as the rate of so-
matic mutation and the time for a solid tumor to build a blood supply.
To link rate processes to the observed age-onset curves of cancer inci-
dence, one must understand how the processes combine to determine
the speed of progression. This chapter introduces the quantitative the-
ory that links carcinogenic process and incidence.
The first section provides background on mathematical theories of
progression. The general approach begins with the assumption that
cancer develops through a series of stages. This assumption of multi-
stage progression sets the framework in which to build particular mod-
els of progression dynamics. Within this framework, I argue in favor of
simple theories that make comparative predictions. If one understands
how a particular process affects progression, then one should be able to
predict how altering that process changes progression dynamics.
The second section lists some of the observations on cancer incidence
that a theory should seek to explain. These observations set the target
for mathematical theory and emphasize the need to link progression
dynamics to incidence.
The third section introduces the classical model of multistage pro-
gression. This model predicts an approximately linear relation between
incidence and age when plotted on log-log scales. The observed patterns
match this prediction for several cancers. However, the fit of observa-
tions to theory is not by itself particularly informative. To make further
progress, I emphasize the need for comparative theories. I briefly men-
tion one comparative theory that follows from the classical multistage
model: the ratio of incidence rates between two groups depends on the
difference in the number of rate-limiting steps in progression. I develop
that theory in later chapters.
The fourth section discusses why one should bother with abstract the-
ories that often run ahead of empirical understanding. The main reason
is that we are not likely to have much luck in understanding real sys-
tems if we cannot understand with simple logic how various processes
could in principle combine to influence progression. In addition, it helps