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Notebook Medicine

What the tests can tell us

Deputy Chief Patricia Cassidy of the Jersey City Police Department has blood drawn to test for coronavirus antibodies at a testing site in Jersey City, N.J.,on Monday. (ASSOCIATED PRESS)


What the tests can tell us

New antibody testing suggests the coronavirus may be less deadly than feared, but it’s still more dangerous than seasonal flu

Early tests to detect the coronavirus were designed literally to do that: They detect the virus itself, identifying patients who harbor it. Those tests help with decisions about quarantines and treatment, but they have a key weakness. They don’t reveal whether a patient has already encountered the virus and then successfully recovered.

But new antibody tests (or “serological tests”), capable of recognizing a successful immune response to the coronavirus, are now entering the market. Not only can they identify people whose blood plasma might help the sickest patients recover, but antibody tests make possible new studies measuring how many people in a given region have already beaten SARS-CoV-2. What can they tell us about the virus’s death rate?

In early April, a team at Stanford University tested over 3,000 Californians, concluding between 2.5 percent and 4.3 percent of residents in Santa Clara County already had immunity to the coronavirus. The study fueled a debate among statisticians: Were the tests reliable, and were the 1.5 percent of tests that came back positive truly evidence that 2.5 percent to 4.3 percent of Santa Clara residents were immune? And were the study participants a representative sample of their community? The study had recruited volunteers by posting a Facebook ad for free coronavirus tests, raising concerns that people with recent symptoms were more likely to sign up in order to learn whether they’d had the virus.

Andrew Gelman, a professor of statistics at Columbia University, analyzed the study in a detailed (and profanity-sprinkled) blog post. He criticized the study from several angles, but also noted that a 3 percent immunity rate doesn’t sound implausible, and would imply a relatively low death rate of 0.16 percent, or 1 in 600 people exposed to the virus: “That’s good news, relatively speaking: we’d still like to avoid 300 million Americans getting the virus and 500,000 dying, but that’s still better than the doomsday scenario.”

Assuming the Stanford study is accurate, 96 percent of people in Santa Clara County have yet to encounter the virus. Studies in regions with larger outbreaks have found higher immunity rates. One gave a preliminary look at 500 people in the German town of Gangelt, finding current coronavirus infections in 2 percent of study participants and evidence of immunity in 14 percent—for a case fatality rate of about 0.37 percent. A study of New York residents tested 3,000 people, finding 14.9 percent with evidence of immunity. In New York City, the immunity rate was about 21 percent. 

So is this virus just like the flu, as some argue? It feels reassuring to say the case fatality rate is “only” 0.37 percent in the German study, and I’d certainly take that over the 3 percent to 5 percent initially reported in places like Wuhan. It’s less reassuring to look at New York City’s 18,000 deaths (as of May 4), divide them by 21 percent of NYC’s 8.3 million people, and come up with a case fatality rate of about 1 percent.

I rejoice with those who celebrate that the coronavirus does not normally claim the lives of 3 percent to 5 percent of those it infects, as initially feared, and I share the hope of those who eagerly read new reports of promising treatments. But a case fatality rate of 0.37 percent to 1 percent would still be far higher than flu: As America moves cautiously toward reopening, let’s remember the reason it closed.


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  • Nanamiro
    Posted: Mon, 05/04/2020 07:19 pm

    Certainly, let's remember the reason our country "closed": in order to prevent the overwelming of our medical system, which we have already accomplished. We didn't shut down in order to utterly and completely prevent all transmission and death from the the Coronavirus. It has morphed into that, which is an impossible goal even with a vaccine and treatments.

  •  nxlcsdeo's picture
    Posted: Wed, 05/06/2020 04:58 pm

    Yes, I agree, Nanmiro.  The "models" used to recommend draconian shutdowns ended up being significantly flawed, as we learned more about COVID-19. Not willing to let a good crisis go to waste, however, some political opportunists have harnessed the fear engendered by initial imaginations about the virus, and seem to be on a power trip they want to extend for as long as possible.  

  • TT
    Posted: Mon, 05/04/2020 07:43 pm

    Thank you!

  • DakotaLutheran
    Posted: Tue, 05/05/2020 08:32 am

    The mortality rate is the sum of conditional probabilties, where each conditional probability is of the form: the probability of dying of COVID-19 given that certain conditions obtain. (Here I am assumng that each condition is statistically mutually exclusive of all others, meaning that any one person cannot have more than one.) Among those conditions that we have already been well aware of include age and pre-existing conditions. We might also add the varying kinds of treatments, and, we now hear, about the initial viral load. What this tells us is that number of conditions that would influence the death rate is large. This large diversity challenges data collection since not all of the possible conditions may be collected. What is more, there are probably conditions that we might not be aware of. It is because of this vast diversity and complexity that it is often easier to obtain a statistical estimate of the total conditional probability. If the pool of persons from which the sampled data is drawn contain all (or almost all) of the varying relevant conditions, mixed in approximately the same proportions as you would find in the total population, then your esitmate of the total conditional probability will be "reliable." Bear in mind that we don't know exactly what those relevant conditions are, nor do we know whether it is fully representative of the total population. Our statistical hope rests in two elements of our sampling of the population: that those included in the sampling are randomly selected (which means we blindly select each sample) and that the total number of samples is large. How large is large enough depends upon the variance among various samplings, which we don't know before hand. We don't know if we do our random sampling of the population ten times, how much our results will vary and this is because we are  often doing just one study. As data comes in from many different studies, in many varying circumstances, with varying characteristics of those populations, the variance will become more clear, and the estimate of the total conditional probability will become more reliable. That's just how statistics works: for the most part it is blind, which is also its strength: its reliability doesn't depend upon us knowing very much. 

  •  Deb O's picture
    Deb O
    Posted: Tue, 05/05/2020 11:38 am

    Wow, DakotaLutheran ... this response helped me understand statistics a lot more. I wish World would entertain the idea of guest columnists :)

  • JC
    Posted: Tue, 05/05/2020 10:13 am

    Thanks for highlighting these important antibody studies.  Why, though, does the author spend so much time critiquing the Stanford study when its results have been replicated in many other parts of the US (such as LA county and Miami) and the rest of the world?  Also, the data from NYC are outdated, as New York more recently reported finding antibodies in 25% of NYC residents tested (and the antibodies themselves can take a few weeks to develop, so even that undercounts the number of NYC residents that have had the virus).  All of this suggests that the lockdowns were unnecessary, because the virus had spread too much before the lockdowns for them to be effective and because the hospital systems were never going to be overwhelmed (since the doomsday models were using exaggerated fatality rates).  

  • SNelson
    Posted: Tue, 05/05/2020 01:12 pm


  • CH
    Posted: Tue, 05/05/2020 03:02 pm

    Where is the good news from Dr. Fauci? Every day it is same negativity. Maybe he remembers how little sucess he had on finding an HIV vaccine. With or without a vaccine we can't hide from this or any other virus forever. Our Lord is still on His throne.


  • RC
    Posted: Wed, 05/06/2020 10:00 am

    Dear JC, the author, Dr. Horton is not spending any time criticizing anything. He is only mentioning critical reviews of some of the studies done. As I recall, the NYC hospitals came extremely close to being overwhelmed. Did you not see the pictures of the boxed up bodies being buried on an island because they had no place else to put them?  Did you not see the hospital ship and the tents that were set up for the over flow of patients?  Lastly, while I agree that dooms day predictions were wrong, we did not KNOW that one, two or three months ago. The medical community was doing their best, on very short notice, in case the worst case happened, remember that human lives are at stake and they take that very seriously. Hindsight is always 20-20.

  • JC
    Posted: Thu, 05/07/2020 11:27 am

    Dear RC, If one looked more broadly than the legacy media's doomsday predictions, one would have found months ago that prominent academics (including lots of Stanford University's medical faculty and Oxford faculty, among others) cautioning that the Imperial College's model was flawed and exaggerated the potential harm from COVID-19.  That didn't fit the hysterical narrative and thus wasn't reported in the legacy media.  The pictures of the boxed up bodies have been debunked as fake news - that was a pauper's gravesite that was operating as it ordinarily does.  The hospital ship and Javits Center were hardly used at all, at great waste of taxpayer expense.  

    This is a crisis created by the legacy media, but as Solzhenitsyn sagely pointed out way back in 1978, the legacy media are not accountable to anyone and thus never held to account for the destruction they unleash on society.