## Friday, November 7, 2014

### Screening for Down's Syndrome

In our discussion on Bayes theorem in the seminar yesterday, I brought up a personal anecdote. During my wife's first pregnancy, she was offered the choice of taking an integrated test to screen for Down's syndrome in the fetus.

I looked up the numbers for the accuracy and false positive rates and found that they were about 95% and 5% respectively (somewhat of a coincidence that these numbers add up to 100%).

The baseline rate of the syndrome steadily increases with the age of the mother.

For a 25 year old mother, it is 0.0001 (1/1100).
For a 35 year old mother it is 0.004 (1/250).
For a 45 year old mother it is 0.05 (1/20).

You can run these numbers through one of the online calculators I wrote about yesterday.

If the test is positive, then the posterior probabilities are again a function of age:

For a 25 year old mother, it is 1.7%.
For a 35 year old mother it is 7.1%.
For a 45 year old mother it is 50%.

Thus, at that time I concluded that the taking the test would only have been meaningful if my spouse were around 45 years old.

For young mothers, even a positive test result is not of particularly great practical value.