3. For a sample of 100.000 subjects, Table 8.22 cross-classifies whether a subject is HIV+ by whether a diagnostic test for HIV+ status is positive (i.e.. indicates that the subject is HIV+).

a) Construct the conditional distributions for the test result, given the true discase status.

b) For those who truly are HIV+, what percentage are diagnosed as HIV+ by the diag- nostic test? For those who are not HIV+. what percentage get a negative test result? Does the diagnostic test appear to be a good one?

c) Construct the conditional distribution on disease status, for those who have a positive diagnostic test result Of those subjects, what percentage truly are HIV+? Comment. (For discussion of the possibility of a high false positive rate even for a seemingly good diag- nostic test, see Chatterjee et al.. 1995. pp. 37-40). TABLE 8.22 Diagnostic Test Positive Negative HIV+ Yes 475 25 Status No 4975 94.525