Chapter 4.4, Problem 21E

HIV Risks. The New York State Department of Health estimates a 10% rate of HIV infection among the at-risk population and a 0.3% rate in the general population. Tests for HIV are 95% accurate in detecting both true negatives and true positives. Random selection and testing of 5,000 at-risk people and 20,000 people from the general population results in the following table.

1. a. Verify that incidence rates for the general and at-risk populations are 0.3% and 10%, respectively. Also verify that detection rates for the general and at-risk populations are 95%.
2. b. Consider the at-risk population. Of those with HIV, what percentage test positive? Of those who test positive, what percentage have HIV? Explain why these two percentages are different.
3. c. Suppose a person in the at-risk category tests positive for HIV. As a doctor using this table, how would you describe the patient’s chance of actually having HIV? Compare this figure with the overall incidence rate of HIV infection.
4. d. Consider the general population. Of those with HIV, what percentage test positive? Of those who test positive, what percentage have HIV? Explain why these two percentages are different.
5. e. Suppose a person in the general population tests positive for HIV. As a doctor using this table, how would you describe the patient’s chance of actually having HIV? Compare this figure to the overall incidence rate of HIV infection.