Mathematics

Kash Shields

24 October, 13:48

For many years the only way to test if a person had tuberculosis (TB) required a laboratory procedure that could take up to several weeks to produce a definite result. There are now DNA-based tests to detect TB that can be done in a couple of hours.

We have the following data on a DNA test for TB

· If a person does not have TB then the DNA test always is negative.

· If a person does have TB, then the DNA test will be positive 94% of the time.

Assume that we will use the test in Africa where the rate of incidence of TB is 450 per 100,000.

Has TB

Does not have TB

Row Totals

Test result: negative

Test result: positive

P

Column Totals

Q

100,000

What is the probability of a false negative test result? A false negative is P (TB given a negative test).

· 27 out of 99,577 = 0.00027

· 99,550 out of 99,577 = 0.99993

· 27 out of 450 = 0.06

· 0 out of 99,550 = 0