HIV Risks. The New York State Department of Health estimates a 10% rate of HIV for the “at risk” population and a 0.3% rate for the general population. Tests for HIV are 95% accurate in detecting both true negatives and true positives. Random selection of 5000 “at risk” people and 20,000 people from the general population results in the following table.
“At Risk” Population | |||
Test Positive | Test Negative | ||
Infected | 475 | 25 | |
Not Infected | 225 | 4275 | |
General Population | |||
Test Positive | Test Negative | ||
Infected | 57 | 3 | |
Not Infected | 997 | 18,943 | |
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%.
b. Consider a patient in the “at risk” category. Of those with HIV, what percentage test positive? Of those who test positive, what percentage have HIV? Explain why these two percentages are different.
c. Suppose a patient in the “at risk” category tests positive for the disease. As a doctor using this table, how would you describe the patient’s chance of actually having the disease? Compare this figure to the overall rate of the disease in the “at risk” population.
d. Consider a patient in 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.
e. Suppose a patient in the general population tests positive for the disease. As a doctor using this table, how would you describe the patient’s chance of actually having the disease? Compare this figure to the overall incidence rate of the disease.
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