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Easier to work with
is the declining exponential function, which is the basis of the
D.E.A.L.E. (Declining Exponential Approximation of Life Expectancy).
The basic assumption of the D.E.A.L.E. is that the death rate
among the survivors in a cohort is constant over time. The declining
exponential function is expressed as follows:
D.E.A.L.E.
(Declining Exponential Approximation of Life Expectancy)
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S(t) =
S0e-mt
Where:
- S(t)
= the number of survivors at time t.
- S0
= the number in the cohort at the start
- t
= time after starting to observe the cohort
- m
= the mortality rate of the cohort
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Recalling that our
goal is to learn how to adjust life expectancy for the presence
of serious co-morbid illness, how do we use the D.E.A.L.E. to
calculate life expectancy? By following these steps:
If m, the mortality rate, is constant over time, 1/m is the
life expectancy of a person in the cohort.
LE = 1/m
Calculating m, the mortality rate, is a matter of simple algebra.
S/S0 = e-mt
Now take the natural logarithm of both sides.
Ln[S/S0] = -mt
Which, given the mortality rate, m,
m = (-1/t) x 1u[S/S0]
Now you can calculate
the life expectancy in a patient with serious illness.
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