What the tests can tell us

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.