Page 101 - 20dynamics of cancer

86 CHAPTER 5

to have a toolbox of possible explanations that one thoroughly under-
stands. Such understanding prevents the common tendency to latch
onto the first available explanation that seems to fit the data, without
full consideration of reasonable alternatives.
The fifth section presents the equations for a simple model of pro-
gression through a series of stages. I emphasize that the equations are
completely equivalent to a simple diagram that illustrates the flow be-
tween stages of progression. The equations introduce the notation and
structure of a formal model, paving the way for more detailed analysis
in the following chapters.
The sixth section develops technical definitions for incidence and ac-
celeration that follow from the formal specification of the model in the
previous section. Incidence provides the key measure of occurrence for
cancer: the cases of cancer per year, at each age, for a given population
of individuals. Incidence is a rate—cases per year—just as velocity is
a rate. Acceleration is the rate of change in incidence with age: how
fast incidence increases or decreases as individuals become older. The-
ories about the carcinogenic role of particular biochemical mechanisms
must ultimately link those mechanisms to their effects on incidence and
acceleration.

5.1 Background

MULTISTAGE PROGRESSION IS A FRAMEWORK, NOT A HYPOTHESIS
Most mathematical models of cancer progression descend from Ar-
mitage and Doll’s (1954) paper on multistage theory. The phrase “multi-
stage theory” has led to some confusion. A multistage model simply
assumes that cancer does not arise in a single step—an assumption
supported by much evidence. So, “multistage theory” is not really a
particular theory; it is a framework that describes the kind of dynamical
processes used to model progression through multiple stages.
This framework provides tools to develop testable quantitative hy-
potheses that link progression dynamics to the curves of age-specific
cancer incidence. Progression dynamics also provides a notion of cau-
sality: a process causes cancer to the extent that the process alters the
age-specific incidence curve.