Question: When testing subjects for HIV in surveillance studies WHO protocol states that subjects whose test result is negative on the first test should be classified as HIV negative. Subjects whose test results is positive on a first test should be retested twice and classified as HIV positive if one or both of these retests are positive. If both of the retests are negative then the subject is classified as HIV negative.

Let the sensitivity of a single test be a and the specificity be b. Write down, in terms of a and b, the sensitivity and specificity of the tests carried out under the WHO protocol. Use these expressions to compare the effects of using the WHO protocol as opposed to using a single test. Discuss some of the advantages and disadvantages of the WHO protocol versus the single test. Give assumptions that you have made in carrying out calculations.