A virus has been spread around a population. The prevalence of this virus is 84%. A diagnostic test, with a specificity of 94% and sensitivity of 15%, has been introduced. If a patient is drawn randomly from the population, what is the probability that: a) a person has the virus, given that they tested positive? b) a person has the virus, given that they tested negative?

Oscar Burton 2022-10-13 Answered
A virus has been spread around a population. The prevalence of this virus is 84%. A diagnostic test, with a specificity of 94% and sensitivity of 15%, has been introduced. If a patient is drawn randomly from the population, what is the probability that:
a) a person has the virus, given that they tested positive?
b) a person has the virus, given that they tested negative?
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Answers (1)

Liam Everett
Answered 2022-10-14 Author has 16 answers
First of all Let's define what Sensitivity and Specificity of a test are:
- Sensitivity is defined as
P [ T + | D ]
- Specificity is defined as
P [ T | D ¯ ]
Where T + , T indicate positive and negative test result while D is "disease"
Second let's take 10,000 persons and see what is happening with the given probabilities
D i s e a s e N o t   D i s e a s e T o t a l T + 1260 96 1356 T 7140 1504 8644 T o t a l 8400 1600 10000
What you are requested to calculate is
(a) P [ D | T + ] = 1260 1356 92.92 %
and
(b) P [ D | T ] = 7140 8644 82.60 %
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