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Imagine you are the
emergency department physician at a major hospital in Colorado.
Rescuers bring in a mountain climber who fell into a crevasse
several days earlier.
You examine the patient
and find he suffered a compound fracture of his ankle as a result
of the fall. You note that there is a large open wound with bone
protruding from it. The ankle is swollen, dusky, and discolored
and creptitant to the touch. The patient is agitated and disoriented
and has a high fever.
You conclude that the
patient has gangrene of the foot and generalized sepsis.
You consult with a
trauma surgeon, who proposes three options:
- Amputate the
foot - This will require the patient to use a prosthetic
foot for the rest of his life.
- Amputate the
foot and perform a foot transplant - This is an option because
a young man has died in an auto accident and is a possible donor
of a foot. This alternative has some downside risks: death during
the transplant surgery and rejection of the transplanted foot,
which would require a prosthetic foot. A successful transplant
would require lifelong anti-rejection medication.
- Treat the patient
with antibiotics -This alternative runs the risk of treatment
failure, which could lead to death or to spread of infection
to the upper leg, a complication that would require amputation
of the leg rather than just the foot.
You and your consultant
are expected-outcome decision makers, so your task is to decide
which of the three treatments has the highest expected outcome
decision problem.
The rock climber can
experience only one outcome, yet, since two of the three alternative
actions could lead to more than one outcome, chance plays a role
in determining his fate. For example, he could die during surgery,
reject the transplanted foot, or live happily with a functioning
transplanted foot.
Question
2.2.1
Assuming that the probability
of each outcome is known, what is the best way to represent the
average outcome of an action that could lead to any one of three
outcomes?
 | Subjectively
weight the probabilities based on your personal values and
preferences. |
 | Take
the sum of the numerical values for the outcomes after weighting
each by the probability that it will occur. |
 | Add
all the probabilities together and divide by the number of
outcomes possible. |
 | Ask
the patient what treatment he prefers and use that treatment. |
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