Correct Diagnosis?
Suppose a new very rare strain of COVID has an incidence rate of 0.01% (that is, it afflicts 0.01% of the population). A new test is devised to test this:
- Initial testing shows it produce false negatives at a rate of 0.5% (that is, 0.5% of those that have the disease will test negative), and
- produces false positive at a rate is 0.2% (that is, about 0.2% of people who take the test test positive, even though they do not have the disease).
How accurate is this test?
Let A = having the disease
Let B = testing positive
- Suppose a randomly selected person takes the test and tests positive. What is the probability that this person actually has the disease? (Find \(P(A|B)\) using Bayes’ Rule.)
- Suppose a randomly selected person takes the test and tests negative. What is the probability that this person does not have the disease? (Find \(P(A^c|B^c)\) using Bayes’ Rule.)
Based on this, what recommendations would you make to doctors using this test.