Biology Reference
In-Depth Information
FIGURE 11.3
Simulation of
10,000 deaths from an exponential
hazard model where the hazard is
0.34. The histogram shows the
“binned” ages from the simula-
tion, while the dashed line shows
the probability density function
for age-at-death when the hazard
is equal to 0.34.
Simulated Deaths
0
5
10
15
20
Age (years)
The five parameters in the Siler model consist of one parameter for the baseline hazard, two
parameters (the magnitude and rate of decline) for juvenile mortality, and two parameters
(the magnitude and rate of increase) for senescent mortality.
Figure 11.4
shows the hazard
for each of the three mortality components and for total mortality (the dashed line) for
Coale and Demeny's (1983)
Model West 1 life table for females plotted on a logarithmic
scale. On a logarithmic scale each of the components of mortality will be a straight line,
with the immature component decreasing with age, the senescent component increasing
with age, and the baseline hazard staying constant with age. For a quick read of
Figure 11.4
,
note where the immature and senescent component lines cross at about six years of age. At
this point both components have small values so that the total hazard is only slightly above
the baseline hazard. At young ages the total hazard is “driven” by the immature component
of mortality, while at advanced ages the total mortality is “driven” by the senescent compo-
nent of mortality.
Our first task in the estimation of age structure for target sample populations is to simu-
late individual ages-at-death based on the hazard model. Note that we are NOT yet esti-
mating individual ages-at-death in the skeletal sample. Instead, we are creating
(numerically generating) a test case against which we will ultimately compare the observed
data
. “R” has a few hazard models, such as the exponential and the Weibull (another model
not discussed here) that can be directly simulated (using “rexp” and “rweibull,” respec-
tively), and that use the inversion method to simulate values. This inversion method can
