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series. By contrast, functionally redundant components act in parallel;
disease arises when all components fail independently.
In the final section, I argue that my extensive development of multi-
stage theory for cancer provides the sort of quantitative framework
needed to apply reliability theory to mortality. For cancer, I have shown
how multistage theory leads to many useful hypotheses: the theory pre-
dicts how age-incidence curves change in response to genetic pertur-
bations (inherited mutations) and environmental perturbations (muta-
gens and mitogens). Reliability theory will develop into a useful tool for
studies of mortality and aging to the extent that one can devise testa-
ble hypotheses about how age-incidence curves change in response to
measurable perturbations.

10.1 Leading Causes of Death

Figure 10.1 illustrates mortality patterns for non-Hispanic white fe-
males in the United States for the years 1999 and 2000. The top row
of panels shows the age-specific death rate per 100,000 individuals on
a log-log scale. The columns plot all causes of death, death by heart
disease, and death by cancer.
The curves for death rate in the top row have different shapes. To
study quantitative characteristics of death rates, it is useful to present
the data in a different way. The second row of panels shows the same
data, but plots the age-specific acceleration of death instead of the age-
specific rate of death. The log-log acceleration (LLA) is simply the slope
of the rate curve in the top panel at each age. Plots of acceleration
emphasize how changes in the rate of mortality vary with age (Horiuchi
and Wilmoth 1997, 1998; Frank 2004a).
The bottom row of panels shows one final plotting transformation
to aid in visual inspection of mortality patterns. The bottom row takes
the plots in the row above, transforms the age axis to a linear scale to
spread the ages more evenly, and applies a mild smoothing algorithm
that retains the same shape but smooths the jagged curves. I use the
transformations in Figure 10.1 to plot mortality patterns for the leading
causes of death in Figure 10.2, using the style of plot in the bottom row
of Figure 10.1.
Figure 10.2 illustrates the mortality patterns for non-Hispanic white
males in the United States for the years 1999 and 2000. Each plot shows