The day after I discussed Bayes rule in the class I am teaching, Freakonomics posted an interesting post on amniocentesis.
An amniocentesis (or an “amnio”) is a fairly common procedure among pregnant women that involves the extraction of a small sample of amniotic fluid surrounding a fetus. The main benefit of an amnio is that it can diagnose genetic disorders in a fetus, including Down syndrome. But there is also a real cost, as roughly 1 in 200 tests causes a spontaneous miscarriage (estimates of this probability vary).
The article discusses women aged 35 or older, who are are recommended to have amnio, but women younger than 35 are also advised to have amnio if a blood test suggests that their baby is likely to have Down syndrome or neural tube defects. Here’s where Bayes rule kicks in: the probability that the baby has Down syndrome is a mere 3% if the test is positive (about 0.02% if the test is negative). So the babies that are miscarried are unlikely to have Down syndrome. I did a quick decision tree to help me determine to refuse amnio if the test was positive (luckily, I didn’t have to make that tough choice). I know of other OR geeks who also used decision trees to to decide whether to do amnio.
The article writes about a paper that applies utility theory and dynamic programming to determines when (and when not) to have amnio. Pretty nifty stuff.