Yesterday, we reached into our toolkit and pulled out behavioral economics and Bayesian Inference.
Our big conclusion in that post was that if C-19 tests are 90% accurate and 5% of the people in our reference group are walking around infected, then roughly 2/3’s of all people who get positive test results are not infected … they’re so-called false positives.
- See our prior post If I test positive for COVID, am I infected? for an explanation of the method and a walk-thru of the analysis leading to that conclusion.
Now, let’s change one of our assumptions.
In the prior post, we assumed that we were asymptomatic, have been sheltering-in-place (i.e. minimal social contacts outside of our homes) and don’t work in a COVID-prevalent environment … and we used 5% as our base rate (of virus prevalence among our reference group).
Now, let’s assume that the reference group we’re working with is elderly, has a comorbid medical history of respiratory and heart problems and is experiencing COVID-like symptoms (high fever, persistent cough), have had contact with an infected person. That’s essentially the only group that initially qualified for coronavirus testing. Lets, assume that 75% of the people in that reference group are, in fact, infected with the virus.
Here’s the Bayesian results chart would look like:
The question: what is the likelihood that the people who fit this profile are correctly diagnosed as having the virus (or not)?
The Homa Files 