You are asked to interpret the results from a diagnostic test for HIV in an asymptomatic man whose test was positive when he volunteered to donate blood. After taking his history, you learn that he is an intravenous-drug user. You know that the overall prevalence of HIV infection in your community one in 500, and that the prevalence in intravenous-drug users is 20 times as high as in the community at large.

a. Estimate the pretest probability that this man is infected with HIV.

b. The man tells you that two people with whom he shared needles subsequently died of AIDS. Which heuristic will be useful in making a subjective adjustment to the pretest probability in part (a)?

c. Use the sensitivity and specificity that you worked out in Problem 2(a) to calculate the posttest probability of the patient having HIV after a positive and negative test. Assume that the pretest probability is 0.10.

d. If you wanted to increase the posttest probability of disease given a positive test result, would you change the TPR or TNR of the test?