Page 317 - 20dynamics of cancer

302 CHAPTER 14

depends on cumulative exposure and the current exposure rate, instead
of cumulative mitoses and the current mitotic rate.
Although Eq. (14.2) is the right idea, the approximation will in fact
often be highly inaccurate. The actual incidence at each age depends
on the distribution of individuals in particular stages of progression.
When rates of transition between stages change with age, the distribu-
tion of individuals in particular stages becomes particularly distorted
with regard to the approximation in Eq. (14.2), which assumes a regu-
lar distribution pattern. For these reasons, I always advocate a direct
calculation of the exact pattern of incidence, which can easily be accom-
plished for almost any set of assumptions, as explained in the earlier
theory chapters. I took the trouble here to step through the difficulties
encountered by Pike’s analysis, because his approach and the associated
problems occur often in the literature.

CLONAL SUCCESSION VERSUS MULTILINEAGE PROGRESSION
Frequent clonal expansion during progression causes cells to share
a recent common ancestor. By contrast, less frequent clonal expansion
allows different lineages to persist and differentiate over time. Do the
early stages of carcinogenesis proceed by successive rounds of clonal
expansion or by persistence of multiple lineages?
I discussed two relevant studies earlier in this chapter. Kim et al.
(2004) showed a correlation between multilineage persistence and can-
cer risk. In their study, inherited APC mutations caused colon crypts
to maintain more genetic diversity than crypts without such mutations.
Kim et al. (2004) interpreted the greater diversity to mean that different
cells in APC-mutated crypts traced their ancestry back to a more dis-
tant common ancestor than did cells in crypts that lack APC mutations.
Greater multilineage persistence and genetic diversity in APC-mutated
crypts correlate with a higher rate of cancer, but no evidence directly
links diversity and lineage persistence to progression.
Tsao et al. (1999) studied cell lineage history between tissues sampled
from colorectal adenomas and adjacent cancerous outgrowths. They
analyzed cases in which the tissues had lost DNA mismatch repair, a
key initiating event in carcinogenesis. They found that two patients
apparently maintained distinct cell lineages during much of the time