The public and the press have little understanding of what a positive test for any disease means. Iceland has decided to test its entire population for COVID-19, which as can be seen from the data below is an act of well meaning folly. I’ll make this explanation as simple as I can.
Any medical test has a sensitivity and specificity value; 90% sensitivity is very high for such a test. Let’s assume that the new rapid test for COVID-19 has a 90% sensitivity and specificity and that we have enough kits to test every American. Let’s also assume that there are 300 million Americans in order to keep the arithmetic simple.
Suppose that 1% of this population has the coronavirus – that’s 3 million people. This figure is almost certainly too high, but let’s use it anyway. Our test being 90% sensitive and specific will be positive for 2.7 of the 3 million with the virus. But it will also be positive for 2.97 million Americans who don’t have the virus (10% of 297 million).
What’s wanted from a test is its positive predictive value (PPV). This value is the number of positive tests that truly indicate the presence of what’s being tested for, COVID-19, in this example.
Here’s the arithmetic: we have 2.7 million true positives plus 29.7 million false positives. To get the PPV we must divide 2.7 million by 27 million plus 29.7 million. That’s a little more than 8%. Raise the sensitivity and specificity to 95% and keep the prevalence (the number of people with the disease at the time of testing) at 1% and the PPV is 16%.
The most common error about screening is assuming that a positive test reveals the prevalence of the disease. It’s the other way around. The prevalence must be known before the PPV can be calculated. Below is a table indicating the PPV of a test that is 95% sensitive and specific at different prevalence values. Remember that almost no medical test is that sensitive.
The takeaway point is that the larger the population tested the greater the number of false positive tests that will be observed. Our public health officials have rightly advised that only a selected number of people be tested for COVID-19. They have not explained the problem of false positive tests when a large population the vast majority of whom do not have the virus is tested.