In a study performed a few years ago , the following problem was proposed to 18 expert consultants for AIDS patients:
Helen has tested positive for AIDS. How likely do you think she is really an AIDS patient? What would you advise her?
The input data are:
1. The probability of having AIDS, when one belongs to a population without special risk, is 1 in 10,000.
2. The sensitivity of the AIDS test is 99.9%. In other words, the probability of a false negative is 0.1%.
3. The specificity of the AIDS test is 99.99%. In other words, the probability of a false positive is 0.01%.
The result of the study was as follows:
· The 18 experts agreed that the probability that Helen is an AIDS patient is greater than 90%. Most thought that the probability is greater than 99%. Some even claimed that is greater than 99.9%.
· All experts said that they would advise Helen to inform her family, make everybody test for AIDS, and start taking medication.