Faced with a room full of premeds, my undergrad statistics professor enjoyed giving us problems like, "If one person in a thousand has a certain disease and the test for the disease gives a positive result X percent of the time if the person has the disease and Y percent of the time if they don't, how many false positives does it give if 100,000 people are tested?" For rare diseases, even very high test accuracy often resulted in more false positives than true ones.
Those old assignments came to mind when I read that the CDC is now recommending HIV testing for all adults and adolescents. This is supposed to reduce spread of the virus and ensure that those infected get anti-retroviral treatment before they actually get sick, but I was worried about false initial positives. Fortunately, the numbers are more favorable here than they were in Stats 13.
About 1% of the US population is estimated to have undiagnosed HIV infection. New rapid tests have a false positive rate of about 0.2% and a false negative rate of about 0.1%. So, screening 100,000 individuals would give 0.999*0.01*100,000=999 true positives and only 0.002*0.99*100,000=198 false positives, a pretty good ratio.
Conclusion? Although it makes sense to opt out of testing if you're sure you have no chance of having HIV, universal screening appears to be a good public health measure and I hope it's implemented quickly.