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Suppose the five-year
survival in a cohort of patients with Stage 3 colon cancer is
50%. Then, the fractional survival of the cohort, S/S0, is 0.5
at five years, and it is easy to calculate the life expectancy
of the cohort.
m = *ln[0.5]/5 =
0.14 or 14% per year
However, what happens
if your patient is not "average," but has another serious
illness that also threatens to kill her? For example, while patients
with advanced colon cancer usually die of colon cancer, sometimes
they die of the diseases that are prevalent in their age cohort.
That "background"
illnesses can shorten life expectancy is intuitively obvious,
but how do we represent the effect of these illnesses in the model
(the D.E.A.L.E.) that we use to calculate life expectancy?
If two illnesses are
independent of one another (the presence of one illness does not
increase the chance of dying of another illness), the total mortality
rate faced by an individual is given by a simple relationship:
| mtotal
= m1 + m2
+ maverage |
Where m1 and m2 are
the death rates from the two serious diseases and m average is
the death rate for a person in average health of the same age
as the patient.
Using this relationship
and the survival (S/S0), for two diseases
(often available from a research article) and the mortality rate
for an average person (available from standardized tables), you
can calculate the total mortality rate for a person with the two
serious diseases. The person's life expectancy is:
| Life
expectancy = 1/mtotal |
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