DrVirgo
Forum Hero
Topics: 1096
Posts: 3,515
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10. A screening test is applied to a population of 1000 in
which the prevalence of disease Y is 10%. The sensitivity
of this test is 96%, and the specificity is 92%. The
diagnostic workup for each person found to have a true
positive result in the screening test costs $50. A newer
screening test has the same sensitivity (96%) but an
improved specificity of 96%. However, the new test
costs 50 cents more per test than the older screening
test. If the newer screening test were to be used, how
much money would be saved or lost?
(A) $1300 saved
(B) $1300 lost
(C) $500 saved
(D) $1800 saved
(E) $500 lost
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| DrVirgo
Forum Hero
Topics: 1096
Posts: 3,515
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Please attempt this one...
Let me know how you calculated the right answer.
I will post the correct answer with the entire explanation soon.
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Our greatest glory is not in never falling, but in rising every time we fall.
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| hero
Forum Guru
Topics: 42
Posts: 552
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let see, new one is 0.5$ more expensive, and we want to screen 1000 ppl, what makes 0,5 x 1000 =500$ lost
(i didn't try this as. test yet, saving it as a last assessment )
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| DrVirgo
Forum Hero
Topics: 1096
Posts: 3,515
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Its a bit more complicated than that... I got half way up to the 1800 part only, but then got lost...
Here is the explanation:
The correct answer is A. Regardless of which test is
used, the entire population, or 1000 people, will be
screened.We do not know the cost of the original test,
but we know that the new test costs 50 cents more per
application. Therefore, screening the population of
1000 will cost ($0.50 × 1000), or $500, more with the
new test than the old.
However, the specificity of the new test (96%) is higher
than the specificity of the old test (92%).We know that
the prevalence of disease Y is 10%, so 90% of the population,
or 900 people, are disease-free. The original test
will correctly identify 92%, or 828, of these 900 subjects,
and there will be 72 false-positive results. Each
person whose test result is falsely positive will need the
diagnostic workup that costs $50 per person. The newer
test will correctly identify 96%, or 864, of the 900 subjects
who are disease-free, and there will be 36 falsepositive
results. There are 36 fewer false-positive tests
with the new test than with the old.
Old Test New Test
Positive test 72 36
Negative test 828 864
Actual nondiseased 900 900
The number of true-positive results remains unchanged
because the sensitivity of the new test is the same as that
of the old test (i.e., 96%).
All of the subjects that test positive will require the $50
workup, and there will be 36 fewer of these with the
new test. The savings resulting from not having to do
the workups for 36 people is 36 × $50, or $1800.When
the $500 in additional costs associated with the new test
is subtracted from the $1800 savings, there is a net savings
of $1300 if the new test is used.
___________________
Our greatest glory is not in never falling, but in rising every time we fall.
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