One of my earliest memories concerns an escape, a short-lived flight from the confines of a sanatorium on an island in the North sea, Norderney, where I had been shipped for one of my perennial recuperation stints from childhood disease. Measles, Mumps, Scarlet fever, Whooping cough – I forget. I ran away onto a street that was being resurfaced, the smell of fresh tar sweetly tickling my nose, towards a meadow filled with buttercups, into which I threw myself and rolled around as any self-respecting four-year-old would do. Is it just me, or are old memories coming up in force these days, as if the sense of end times triggers a perusal of one’s life?

Ok, let’s cut the dramatic flair, and get to the point of the story. I have caught myself daydreaming that if and when testing for anti-bodies is widely available I will get the test and upon testing positive will re-experience that same sense of freedom of the meadow of yore – running out of confinement into a sunny, yellow, brilliant, sweet smelling world. Hah.

Here is the trick – the promise of an anti-body test, however sensitively testing who had the dreaded crud and who not, is one that is misleading and likely creating a dangerous situation. Here is the deal, more or less in the words of my Beloved who has brilliantly taught the underlying principles of Bayes’ Theorem for years. (Hearing it’s mathematics you are shutting off? DON’T! It’ll really be interesting, I promise.)

Let’s assume we have a test that we trust – it finds antibodies 94% of the time in people who did indeed have the disease and misses them only 6% of them time. It is also correct 96% of the time for those people who don’t have antibodies showing that they did not yet catch Covid-19 and gives us only 4% of false alarms – detecting antibodies, when you really didn’t have the disease. So far so good? We have a hit rate of 94%, a miss rate of 6% and a false alarm rate of 4%. To repeat, this is pretty encouraging: If you really do have the antibodies, there’s a 94% chance that the test will (correctly) confirm that you have the antibodies. If you really DON’T have the antibodies, there’s only a 4% chance that the test will (falsely!) say you do have the antibodies. That’s the false alarm number.

Here is the problem, though. Let’s assume that we give the test to the entire population of U.S. citizens, for sake of argument let’s round them to 330,000,000. If 1% of that population actually had the virus, over 3 million people were sick in other words, we would correctly detect the antibodies in 94% of these people, or precisely in 3,102,000 cases. So far so good.

Now let’s look at the remaining 99% of citizens who did not yet catch the virus. We had said earlier that the false alarm rate for these cases was low, around 4%, where a test said it found antibodies when you really didn’t have them because you never had the virus. We are talking about 326,700,000 people in this population of uninfected people of whom 4% would be 13,068,000. Over 13 million people, in other words, would be told they had the virus, when they actually didn’t, because even a small false alarm rate becomes a big number when it is applied to a huge number of people in a particular category (here the not-yet infected.) Again, 3 million people would get a correct assessment of their status – you previously had the crud and don’t have to fear infection- and over 13 million would get the same message incorrectly. IN OTHER WORDS, the test is wrong four-times more often than it’s right!

How would you, as an individual, know in which group you are if the test comes back positive? Yes, you had the cough, some fever, all the known symptoms, but they could just as well have been from the hideous rhino virus going around this spring – but if the test tells you you have antibodies to Covid 19 it is more likely mistaken than not. The real up-shot is, of course, that it gives many, many people who tested positively a sense of security that might be false and expose them to infection if they go back out into the world going about their business as they used to. But, since they’re not safe, we’re on our way toward disaster.

Many people find this confusing, because, after all, we said that the test detects Covid 94% of the time. How could that sort of test be WRONG more often than not? The key is to understand what that 94% actually is. The 94% (officially called the test’s “sensitivity”) is the ability to detect the virus when it’s there. That’s not the same as the test’s accuracy (which is the test’s ability to tell whether you’ve got the virus or not). Accuracy can be (and, in this case, IS) rather low if you give a sensitive test a lot of opportunity to be wrong. That’s because the false alarm rate is a small percentage, but — again – it’s a small percent of a big number, and that’s a lot of errors. That’s what drives down the overall accuracy.

Note that all this would change if and when a larger percentage of the population actual had indeed been ill, say 30 million people instead of 1 million which was our assumed number. But also note, that there are other troubles associated with testing beyond the issues discussed so far. The podcast below and the NYT article from yesterday spell those out.

https://slate.com/podcasts/what-next-tbd/2020/03/where-are-coronavirus-tests

Meadows have to wait, folks, like it or not, until we have a vaccine. (Or at least meadows where you meet other people – you can still enjoy them tout seul….)

Photographs today are from last week’s walk at a local meadow and my current backyard, daisies, dandelions (!) and all.

And here is a spring symphony.… Schumann’s 1st, op. 38