NPR recently reported on a trial of a new genetic test for type 1 diabetes (a.k.a. juvenile onset diabetes, an auto immune disease not related to diet and exercise). I've tried to transfer the article's words into a possible contingency table, but clearly the disease outcomes are not yet known.


disease
free
type 1
diabetes
test negative 1936 4
test positive 57 3

This is clearly a significant test as the test-positives are much more likely than the test-negatives to get diabetes. Nevertheless, the vast majority of the test-positives will not get diabetes. Note that with these small cell counts fisher exact is preferred over a typical chi-squared contingency test. 


type1=matrix(c(1936,57,4,3),nrow=2)
fisher.test(type1)
The piece quotes a test cost of $7. I image the $14,000 is less than the prevented expense of 2-3 test-positive's ICU visits. (However, I note that the patient cost for even simple tests is rarely less than $20, in which case the savings are less clear.) The test-positive hospitalization savings come about because the patients would "regularly" take a $75 blood test which would show precursor antibodies. (Ten biennial tests for the 60 are $45,000.)

Report the p value from fisher, the false positive rate, the false negative rate, the power and the actual (not fisher reported) odds ratio.