Worked Example

Phenylketonuria (PKU) has a prevalence of 1/15,000 births. About 4 million babies are born in the US every year. If our test has a sensitivity of 99.5% and a specificity of 98.5%, how many false positives and false negatives would we expect? We would expect 266 babies to be born with PKU. Newborn screening would be positive in all but one of these babies (there would be one false negative if the sensitivity is 99.5%). 3,999,734 babies would be born without PKU. Our test would be positive in 59,996 of these babies (a specificity of 98.5% would lead to 59,996 false positives). If you make the cutoff value lower, you would increase sensitivity but decrease specificity. The graph below illustrates the effect of changing the cutoff value for "normal". If you move the cutoff to the right or the left, it changes the sensitivity and specificity and so changes the number of false positives and false negatives.

In newborn screening for phenylketonuria (PKU), we accept a false positive rate higher than we would like to avoid missing a case of PKU. Most screening tests are offered in two stages. The first stage of testing is less expensive, less invasive, and less accurate, leading to false positives. The second stage of testing is more expensive, more invasive, and has greater sensitivity and specificity. Follow-up testing will have a high specificity and a low false positive rate and can be used on the patients who were positive in the initial first screening. In newborn screening the sensitivity and specificity of the test can be altered by changing the cutoff. If the cut off is higher, fewer persons with disease will be classified as positive. This will give more false negatives and the sensitivity will decrease. Let’s try some other examples.