This work consists of an interactive visualization of the positive predictive value (i.e. precision) of a COVID-19 antibody test given the antibody prevalence in a population (i.e. the fraction of the population that possesses COVID-19 antibodies). The positive predictive value of a test gives the probability of having a condition given a positive test result for a test of that condition.
While this tool presents the result in the context of COVID-19 antibody testing, it can apply to population testing for any condition. For example, in the context of testing for the COVID-19 virus, the selected prevalence would be the fraction of a population that is currently infected with the virus.
The calculator updates the positive predictive value based on user selections for the prevalence in the population and the false positive/negative rates for the test. The population prevalence is used as the prior probability for possessing antibodies.
The work complements two blog posts from April 2020 on the topic of, Where You Live Affects What Your COVID-19 Test Means.
The concept for this visualization comes from one created by Yael Yungster and Jeff Mekler in the second blog post above to illustrate the false positive paradox.
Even with very accurate tests, positive predictive power can be low when a condition is rare in a population. In particular, when the false positive rate is higher than the prevalence of the condition, this can give rise to what's sometimes referred to as a false positive paradox, or a base rate fallacy.
This is calculated with Bayes' Theorem: