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**Unformatted text preview: **ptimal place for the
doctor to put his response
threshold (β)?
threshold
SDT tells the decision maker where
SDT
to locate the response threshold
for a given objective.
for Suppose the doctor wants to maximize
the expected value of his decision.
the
Decision
“Healthy” “Sick” State of the
World Healthy v(CR)
Sick v(M) v(FA)
v(H) He can assign a value to each of the four
He
possible outcomes.
possible β is the ratio of the height of the distributions
of sick people and healthy people at any
value of g, the # of goodies in the blood.
value
β = p(g|S)/p(g|H)
The optimal place to set β is where it =
The
p(H)/p(S) * [v(CR) + v(FA)]/[v(H) + v(M)] Suppose p(H) = .8 and p(S) = .2
Suppose
Decision
“Healthy” “Sick” State of the
World Healthy 200 50 Sick 200 800 β =p(H)/p(S) * [v(CR) + v(FA)]/[v(H) +
v(M)]
v(M)]
= .8/.2 *(200 + -50)/(800 + -200)
= .8*.2 * 150/600 = 4/1 * 1/4
=1 0.45 “Healthy” 0.4 “Sick” 0.3
0.25
0.2 Healthy Sick 0.15
0.1
0.05 # Goodies in the Blood 14
5 13
0 12
5 12
0 11
5 10
0 85 70 0
55 Probability of Disease 0.35 The optimal location for the response
threshold depends on the costs and
benefits of decisions and the base rate
for the disease.
for Suppose the doctor wants to maximize
the probability of a correct decision.
the
Decision
“Healthy” “Sick” State of the
World Healthy v(CR)
Sick v(M) v(FA)
v(H) Suppose p(H) = .8 and p(S) = .2
Suppose
Decision
“Healthy...

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