May 18, 2020: Imperative #5, Plus Numbers for Numbers Fans

The University of Washington has developed a highly accurate serological test for antibodies to the virus that causes COVID-19.* Most of us can’t get it, but I know some Seattle people who have been tested, and who tested positive, and I’m delighted! Reports are that the UW test is over 99% accurate. WooHOO.

 

Providence has developed another serological test and is giving it to healthcare workers, to get base data on that cohort, but my doctor (at Providence) says regular, non-healthcare-worker patients (like me) can’t get it yet. Other serological tests are out there now. One is available to all comers, up the street at ZoomCare, and another through a different urgent care place, for $77. 

You may or may not be a numbers person. If you are, don’t wade through today’s post; you know this already and have a better example. See you later! Take care!

 

I am not a professional numbers person, but I’m a numbers fan, whatever that means. So I was determined to understand some of the numbers around current testing. The UW test reportedly has over 99% accuracy. Other tests reportedly have 90% or 95% or 97%, and those differences matter much more than you might think.

 

The other thing that matters is the population you are testing. Articles kept explaining, yet I kept not grasping, how a test with 90% accuracy could deliver, say, 66% false positive results. (We’re only interested in false positives today. False negatives are fascinating in different ways.)

 

Eventually I grasped the problem, though I still have to review what “sensitivity” and “specificity” mean. It’s in this article about antibodytesting (and in many others), here in the section called “Time for the numbers.”

 

If that makes your eyes glaze over though, here’s my attempt at a nutshell version:

 

If almost nobody has had the disease,
and if you test almost everybody,
and if your test is not very, very accurate,
then
the people who get false positive test results OUTNUMBER those who get true positive results.

 

That’s it. That’s the whole deal.

 

You can run the numbers with larger or smaller populations, and with more or less accurate tests. The lower the percentage of people who have had the disease (Oregon is low, no matter how lame our level of testing has been), the worse the results from an inaccurate test.

 

Here’s my example, but you can do it all with a pencil yourself. You don’t even need to use a formula. You can do it by making little dots on the page and circling them.

 

In a perfect statistical world, if 5% of people had the disease and you test 200 random individuals, then 10 people (5% of 200) should test positive and the remaining 190 should test negative.

 

But –

 

If your test is only 90% accurate, 19 of those 190 people will instead test positive. Those will be false positives.

 

SO instead of 10 people out of your original 200 learning that they test positive, 29 (10 true plus 19 false) will get a positive result. And those 19 people - 66%, of the 29 who got “positive” results - will not in fact have antibodies.

 

Do I want to get tested? Sure, in theory. But not here, and not now.

 

* I believe these days, we’re calling the disease COVID-19, with that “D” in “COVID” handily acting as a mnemonic – D = Disease! Meanwhile, the virus is called SARS-CoV-2. Someday, I shall master this, but in the meantime, I still miss that fleeting “N” the one that, in the beginning - lived on the front of the disease name: NCOVID-19, with “N” meaning “Novel.” Ah, well. Sic transit novelty.