Lab test false positive rates may feel counter-intuitive. Let’s take a closer look at the state-of-the-art Covid-19 real time PCR test.
In Interpreting a covid-19 test result Watson & al., The BJM, May 2020 say that the sensitivity of the test is between 71–98%, and specificity around 95%.
The English statistics authority estimates that in August 2020 about 0.5‰ of the population had the virus. In Finland, THL estimates that there have been a bit under 8000 cases, which would be 1.5‰ of the population. Of these, most are already healed, and the current incidence rate is around 0.03‰ i.e. about a decade better that in England.
What do the numbers mean in practice? If we pick a random person and the test shows a positive result, what is the probability that the person is actually healthy? Let T = positive test result, and V = has virus. In the BJM article they use sensitivity of 70% for real-life testing. Let’s be generous and say that 1‰ of the population has the virus. Then, according to Bayes’ theorem, we can calculate that there’s a 99% chance the result is a false positive!
How about the opposite case? Pick a random person, test shows negative. What is the probability that the person has the virus anyway? It’s 0.03%.
The key above is the “random person”. The calculations show that there’s no point in testing everyone. In reality, the tested patients are not picked randomly, but they are, and should be, chosen based on their exposure to the virus and/or relevant symptoms.