Page 130 - 20dynamics of cancer

7 Theory II

This chapter continues to develop the quantitative theory of cancer pro-
gression and incidence.
The first section analyzes multiple pathways of progression in a par-
ticular tissue, in which more than one sequence of events leads to cancer.
With multiple pathways, a fast sequence with relatively few steps would
dominate incidence early in life and keep acceleration low, whereas a se-
quence with more steps would dominate incidence later in life and raise
the acceleration. Such combinations of sequences can cause the aggre-
gate pattern of incidence to have rising acceleration through midlife,
followed by a late-life decline in acceleration.
The second section evaluates how inherited genetic variation affects
incidence. Inherited mutations cause individuals to be born with one or
more steps in progression already passed. If, in a study, different inher-
ited genotypes cannot be distinguished, then all measurements on can-
cer incidence combine the incidences of the different genotypes. Rare
inherited mutations have little effect on the aggregate incidence pat-
tern. Common inherited mutations cause aggregate incidence to shift
between two processes. Mutants dominate early in life: aggregate inci-
dence rises early with a relatively low acceleration, because the mutants
have relatively few steps in progression. Normal genotypes dominate
later life: aggregate incidence accelerates more sharply with later ages,
because the wild type has more steps in progression.
If different genotypes can be distinguished, then one can test directly
the role of particular genes by comparison of mutant and normal pat-
terns of incidence and acceleration. The change with age in the ratio
of wild-type to mutant age-specific incidence measures the difference
in acceleration between the normal and mutant genotype. Under simple
models of progression dynamics, the observed difference in acceleration
provides an estimate for the difference in the number of rate-limiting
stages in progression.
The third section continues study of heterogeneity in predisposition,
focusing on continuous variation caused by genetic or environmental
factors. Continuous variation may arise from a combination of many