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If, for example, n stages remain before death, then the predicted slope
of the log-log plot (acceleration) is n − 1. As individuals age, they tend
to progress through the early stages. If there are n stages remaining
at birth, then later in life the typical individual will have progressed
through some of the early stages, say a of those stages. Then, at that
later age, there are n − a stages remaining and the slope of the log-
log plot (acceleration) is n − a − 1. As time continues, a rises and the
acceleration declines (Frank 2004a, 2004b).

10.3 Reliability Models

For cancer, I have been using various stepwise multistage models.
Those stepwise models were originally developed for cancer in the 1950s
(see Chapter 4) based on the idea of a sequence of changes to cells or
tissues, for example, a sequence of somatic mutations in a cell lineage.
Later empirical research has supported stepwise progression, based on
both genetic and morphological stages in tumorigenesis.
Cancer researchers sometimes argue about what kinds of changes
to cells and tissues determine stages in progression, the order of such
changes, the number of different pathways of progression for a given
type tissue and tumor, and how many rate-limiting changes must be
passed for carcinogenesis. But those arguments take place within the
multistage framework, which provides the only broad theoretical struc-
ture for studies of cancer. The multistage framework developed inter-
nally within the history of cancer research, with relatively little outside
influence. For those reasons, I have presented the multistage theory
with reference only to cancer.
By contrast, studies of heart disease and other causes of mortality face
different biological problems and have a different theoretical tradition.
On the biological side, most diseases do not have widely accepted stages
of progression or widely accepted processes, such as somatic mutation,
that drive transitions between stages. Certainly, some multistage pro-
gression ideas exist for noncancerous diseases (Peto 1977), and some
theories about somatic mutation have been posed (e.g., Andreassi et al.
2000; Vijg and Dolle 2002; Kirkwood 2005; Wallace 2005; Bahar et al.
2006). But those ideas and theories do not form a cohesive framework
in current studies of mortality.