Page 221 - 20dynamics of cancer

206 CHAPTER 10

After age 80, acceleration declines sharply and linearly for the remain-
der of life. Some of the causes of death also have a lower peak between
30 and 40 years.
The panels in the upper-right column of Figure 10.2 show causes that
account for about one-third of all deaths. These causes follow steep,
linear rises in mortality acceleration up to 40–50 years, and then steep,
nearly linear declines in acceleration for the remainder of life. The
bottom-right column of panels shows two minor causes of mortality
that are intermediate between the left and upper-right columns.
What can we conclude from these mortality curves? The patterns by
themselves do not reveal the underlying processes. However, the pat-
terns do constrain the possible explanations for changes in age-specific
mortality. For example, any plausible explanation must satisfy the con-
straint of generating an early-life rise in acceleration and a late-life de-
cline in acceleration, with the rise and fall being nearly linear in most
cases. A refined explanation would also account for the minor peak in
acceleration before age 40 for certain causes.

10.2 Multistage Hypotheses

The mortality curves show a rise in acceleration to a mid- or late-life
peak, followed by a steep and nearly linear decline at later ages.
In earlier chapters, I provided an extensive analysis of multistage
models. Within the multistage framework, many alternative assump-
tions can often be fit to the same age-incidence pattern. Thus, fits to
the data can only be regarded as a way to generate specific hypotheses.
With that caveat in mind, I describe some multistage assumptions that
fit the mortality curves and thus provide one line for the development
of particular hypotheses (Frank 2004a).
Several alternative models may cause a rise in acceleration through
the first part of life. Perhaps the simplest alternative focuses on the
transition rates between stages of progression. If transition rates in-
crease slowly with age, then acceleration will rise with age (Figures 6.8,
6.9).
With regard to the late-life decline in acceleration, all multistage mod-
els produce a force that pushes acceleration down at later ages. That
downward force comes from the progression of individuals, as they grow
older, through the early stages of disease (Figures 6.1, 6.2).