Imagine an articulate chief lemming bragging that not only had his followers jumped off a cliff, but that they had done so in far greater numbers than any other slice of the rodents. This is the position occupied by the US regarding testing for COVID-19.We’ve done more testing than any other country and bragged a lot about doing so; but no one seems to have survived to give a proper interpretation of the results.
To begin with, the tests currently in use do not test for the entire virus, rather they just test for various fragments of it. Many of the results are thus false, sometimes false positives and sometimes false negatives. This means one has to interpret their results with caution. Our medical authorities, to say nothing of our political ones, don’t seem to be able to do this.
All medical students are taught the basics of screening in their introductory statistics course. The problem is that most of them either didn’t go or slept through the course. The rest immediately forgot what they had learned.
When testing for anything, a medical professional needs to know the positive predicative value (PPV) of the test as well as the negative predictive value. I’ll focus on the former.
In order to know the PPV—i.e., the percent likelihood that a positive test is a true positive—the sensitivity of the test must be known as well as prevalence of the disease, at least to an approximate degree. According to a recent article in the New England Journal of Medicine, the sensitivity of the tests for COVID-19 is about 70 percent. The prevalence in any of the tested populations is not yet known, so we cannot calculate the PPV, although we can calculate what it would be at any prevalence level we want to assume. I’ll get back to this below.
A test for COVID-19 that is 70 percent sensitive will only catch 70 percent of the tested subjects with the disease. Therefore, 30 percent will falsely test negative. Additionally, Bayes’s theorem, the mere mention of which defeats the numeracy of all but the most resolute of physicians, says that a 70 percent sensitive test will be positive in 30 percent of the tested population that doesn’t have the disease. (I am assuming a specificity that is also 70 percent. The specificity of the various tests used has not been given.) Consider testing for COVID-19 in 1 million subjects, none of whom harbors the virus. Three hundred thousand will test positive.
Read more: The False-Positive Panic over COVID-19
