Question

The most commonly used test for HIV has a sensitivity of 0.997 and a specificity of 0.985. In other words, a person infected with HIV will test positive for the virus 99.7% of the time while a person NOT infected with HIV will test NEGATIVE for the virus 98.5% of the time. Research current rates of infection for the indicated population in order to answer the following questions.

1. If a US randomly selected US resident is tested for HIV and the test shows a positive result, what is the probability that they are infected? In other words, what is the probability that a positive result is accurate?

2. If a US randomly selected US resident is tested for HIV and the test shows a negative result, what is the probability that they are infected?

3. Comment on the results from the previous questions. If you were to test positive for HIV, would it make sense to get retested? What if you were to test negative? 4.

What is the probability that a positive HIV test is accurate for a resident of Pakistan? How likely is a negative test to be accurate?

5. What is the probability of a positive vs. a negative result being accurate in the Democratic Republic of Congo?

6. What is the probability of a positive vs. a negative result being accurate in Lesotho?

7. The science of diagnostic testing is basically the same no matter what you are testing for. As of 2015, approximately 7% of Americans had consumed cannabis in the last month. At the same time, approximately 0.5% of Americans had consumed cocaine in the past month. How much would you trust a positive test result for each drug?

Answer 1

1) 0.997

2)1-0.997=0.003

3)if the result is positive,definitely I should get retested and take treatment ; but if the result is negative,practically it's not possible to get retested infinitely. And statically too probability of not infected but tested positive is more than infected but tested negative.

4) no specific countries data available .so ans= 0.985

5) =0.997-0.985=0.012

6) same as que 5, as not separate data available

7) the science of diagnostic testing is same ,hence the positive result for infected persons will be 99.7% only.

for proper explanation,please allow handwritten answers.