Bayesian statistics and the absurdity of 70% sensitivity for colon cancer

I saw a patient with this lab in their chart:

Who the hell thought a test with a sensitivity of 70% would make a good screening test?

— Joel Topf, MD FACP (@kidney_boy) March 30, 2016

I got some push back:
@kidney_boy sens+spec impt in diagnostics, also I think you’re missing that test is for those who can’t/won’t be screened by other methods

— Shannon P (@kentuckyshan) March 30, 2016

I don’t know anything about Methylated Septin and not much more about colon cancer but a 70% sensitivity for a screening test seems a bit absurd. So I ran the numbers.

Using a colon cancer prevalence of 1,169,000 in the U.S. compared to an adult population of 245,270,000 gives a pre-test probability of 0.47%.

Getting a negative Methylated Septin result lowers the post-test probability to 0.2%.

Getting a positive Methylated Septin result increases the post-test probability to 2.9%.

Think about that, 97% of the people with a positive Methylated Septin* are actually cancer free.

*assuming you are testing an unselected population.