Class 11:  HIV Testing



The standard test for the HIV virus is the EIA (enzyme immunoassay) that tests for the presence of HIV antibodies in the blood.  According the U.S. Preventative Services Task Force’s 2005 report, “A large study of HIV testing in 752 U.S. laboratories reported a sensitivity of 99.7% and specificity of 98.5% for enzyme immunoassay.”   A sensitivity of 99.7% means that for every 1000 people tested who have the virus, we can expect 997 to test positive and 3 to have a false negative result.  The specificity of 98.5% means that for every 1000 people tested who do not have the virus, we can expect 985 to test negative and 15 to have a false positive.   The Center for Disease Control estimates that 1.1 million people in the US are infected with HIV.  The US population is around 307 million.


Assume that a large group of people in the US are tested using the EIA.  If a person tests positive, what is the chance that this person has the HIV virus?  How does your answer change if you are testing a group of people at high risk, such as incarcerated adults?  About 2.9% or incarcerated adults are estimated to be infected with HIV.


If a person tests positive on the EIA, then another EIA test is carried out.  If this is positive, a confirmatory test, called the Western blot test, is carried out.  If this is positive, the person is assumed to have the HIV virus.  In calculating the probability that a person who tests positive on the set of three tests has the disease, is it reasonable to assume that these three tests are independent chance experiments?


Journal Assignment is postponed till next time:

In a column in Parade magazine, Marilyn vos Savant raised the following question:


Suppose we assume that 5%of people are drug-users. A test is 95% accurate, which we'll say means that if a person is a user, the result is positive 95%of the time; and if she or he isn't, it's negative 95%of the time. A randomly chosen person tests positive. Is the individual highly likely to be a drug-user?


Marilyn's answer was:


Given your conditions, once the person has tested positive, you may as well flip a coin to determine whether she or he is a drug-user. The chances are only 50-50. But the assumptions, the makeup of the test group and true accuracy of the tests themselves are additional considerations.


How can Marilyn’s answer be correct?   Please include a calculation in your answer! What does she mean that the make-up of the test group is an additional consideration?


Homework on Blackboard