In July 2012 the FDA approved the OraQuick home H.I.V. test, a saliva test that

Question

In July 2012 the FDA approved the OraQuick home H.I.V. test, a saliva test that takes only 20-40 minutes to determine if a person has H.I.V. Suppose a heterosexual non-IV-drug-abusing white male does a routine test with this kit. Suppose that 0.02% of such individuals have HIV. The test gives a false negative in 1-in-12 people with HIV. It also gives a false positive in 1-in-4,500 people without HIV.

What is the chance this man will test positive?
Note: This person's HIV status is unknown.

If the man tests positive then what is the chance he has HIV?

If the man were in a high risk group where 5% of men have HIV then what is the chance he has HIV if he tests positive?

Explanation / Answer

1) chance this man will test positive =P(have disease and test positive+does not have disease and test positive)

=0.0002*(1-1/12)+(1-0.0002)*(1/4500)=0.0004055

2)  chance he has HI given test positive =P(have disease and test positive)/P(test positive)

=0.0002*(1-1/12)/0.0004055 =0.4521

3)

probability of test positive =0.05*(1-1/12)+(1-0.05)*(1/4500)=0.046044

chance he has HI given test positive =P(have disease and test positive)/P(test positive)

==0.05*(1-1/12)/0.046044=0.995415

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