Question

The Food and Drug Administration does not regulate these tests, but White House coronavirus task force coordinator Dr. Deborah Birx has said that she expects manufacturers to achieve a standard of 90% specificity (and 90% sensitivity, another measure of test performance that's less important in this context). Here's what would happen if you used a test with 90% specificity in a population in which only 1% of the people have coronavirus. Nobody knows for sure, but that could be the situation in many parts of the country. In that instance, more than 90% of the positive results would be false positives, and falsely reassuring. Instead of the estimation given in the above paragraphs, we will calculate the probabilities exactly. Our assumption is that (1) If a person does not have antibody, then 90% chance the test result shows Negative. (2) If a person has antibody, then 90% chance the test result shows Positive. (Equivalently, the test has 90% specificity and 90% sensitivity). Assuming further that 1% of the population have antibody.

Question: (hint: Bayes’ theorem)

(1) What is the percentage of the population that will test Positive for antibody?

(2) Given someone is tested Positive for antibody, what is the probability that person has antibody? (

3) What percentage of the Positive results are false positives?

Answer 1