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We’re Reading the Coronavirus Numbers Wrong
Up-to-the-minute reports and statistics can unintentionally distort the facts.
Numbers have a certain mystique: They seem precise, exact, sometimes even beyond doubt. But outside the field of pure mathematics, this reputation rarely is deserved. And when it comes to the coronavirus epidemic, buying into that can be downright dangerous.
Naturally, everyone wants to know how deadly COVID-19, the disease caused by the new coronavirus, is. The technical term for that is the case fatality rate — which is, put simply, the number of people who have died from the disease (D) divided by the total number of people who were infected with it (I), or D/I. As of Tuesday morning, at least 1,873 people were thought to have died from the disease worldwide and 72,869 people to have been infected.
But those figures may not mean what you think.
The number of deaths (D) seems like it should be easy enough to determine: After all, dead is dead. And yet ascribing a cause of death can be tricky.
The coronavirus might be blamed for the deaths of vulnerable people, especially seniors, already suffering from other illnesses, such as diabetes and other chronic conditions. On the other hand, some deaths will be attributed to other illnesses that might more accurately be ascribed to COVID-19.
Even more problematic is figuring out the total number of infected people (I) — call that the mystery of the denominator. Patients who have tested positive and are hospitalized are included in that tally, of course. But what about those who are being treated without formally having been tested? Or those who might be infected and yet display no symptoms?
Another complicating factor is the remaining number of unresolved or indeterminate cases: Medical experts still aren’t sure, for example, how long the infection’s incubation period may be.
And then, in addition to the uncertainty inherent in the basic numbers, there are the distortions unintentionally created by the way those numbers are reported by medical officials and presented by the media.
Last week, the authorities of Hubei, the province in China at the center of the epidemic, revised their definition of what it means to be infected by the new coronavirus: On Thursday, they started including people who displayed symptoms associated with COVID-19 — coughing, a fever, difficulty breathing — even if those people hadn’t been tested or had tested negative for the virus. As a result, the number of new daily cases increased by a factor of nine overnight.
But what did that spike reveal, in fact?
If the daily tally of newly infected people increases, does that mean the disease actually is spreading at that moment? That it is more contagious than we had known?
And if the number of deaths — or the ratio of deaths to infections — jumps from one day to the next, does that mean the disease has just gotten more lethal? Or that it actually is more lethal than we thought it was the day before?
Not necessarily, though it may seem or feel that way. The shifts might be short-term adjustments or simply the effects, or artifacts, of delayed disclosures — a kind of numerical optical illusion.
Yet when news outlets reported last week, after the revision in what counts as an infection, the largest jump in reported cases “in a single day and more than twice the previous record high,” readers could be forgiven for assuming that the situation had just taken a turn for the worse. Even articles that stated the broader circumstances of the increase could be misleading: Some, by announcing in their headlines a “dramatic spike” or a “surge” in the number of cases; others, by discussing the swell while stating that local officials had been sacked for it.
The fact that China suddenly broadened its criteria also raised fears that its earlier numbers might have been incorrect: too low, and perhaps deliberately so. National pride and the fear of economic costs or a popular backlash might have motivated underreporting, the suspicion went.
But the reasons for the shift could also be more mundane. Maybe the medical authorities in China didn’t report more infections previously because they couldn’t — because, say, they were short of reliable test kits (which they were). It’s possible that the numbers were fudged. But maybe they weren’t, or not as much as some people seem to fear. The change in criteria for what counts as an infection may indicate, not so much nefarious evidence of a cover-up now exposed, but the struggles of a local health care system overwhelmed by a sudden and colossal medical crisis.
Last Thursday, the Hubei authorities also reported a leap in the new daily tally of deaths: 242, compared with 94 for Wednesday. That’s a big jump, but not nearly as big as the increase in the number of newly infected people over the same period. Which could be a cause for some measure of relief: The disease’s lethality would seem to have decreased or be lower than was previously thought. Yet that’s not the takeaway likely to have prevailed.
Some of the reporting has amounted to a set of contradictory pronouncements, confusing at best. Journalists could display more critical distance and a modicum of skepticism toward the data they relay, instead of turning the media coverage into a hall of mirrors.
One major problem is the doing of no one in particular. The story about the coronavirus’s spread is evolving quickly, with medical authorities in China and elsewhere disclosing figures daily (or more often), and the media reporting the information immediately to satisfy the fast-paced, staccato rhythms of publishing cycles. But up-to-the-minute, blow-by-blow accounts of hard data can create mistaken impressions about the underlying facts, even if both the data and the accounts are accurate.
Last Thursday, a surge in the number of infections was reported, because of that change in official criteria. On Monday, China announced a drop in the number of new cases for the third consecutive day. Now what should we make of that?
Constant on-the-nose reporting, however much it seems to serve transparency, has limitations, too.
It’s a short-term, and shortsighted, approach that’s difficult to resist, especially when people are afraid and the authorities are taking draconian actions. It’s only natural to compare and contrast whatever hard facts are available. And yet it’s especially dangerous to do that precisely because people are so anxious, and fear can trick the mind.
A view from a loftier perch — a month’s, or even just a week’s, perspective — would, and will, produce far more reliable information.
As of Tuesday, the case fatality rate of COVID-19 appeared to be about 2.5 percent. That’s in keeping with what it was, for example, from the beginning of the outbreak up to Jan. 28. By comparison, the case fatality rate for the seasonal flu in the United States ranges between 0.10 percent and 0.18 percent. For SARS, it’s about 10 percent and for MERS, about 35 percent. For Ebola, it has varied between 25 percent and 90 percent, depending on outbreaks, averaging approximately 50 percent.
And so based on what we know so far, COVID-19 seems to be much less fatal than other coronavirus infections and diseases that turned into major epidemics in recent decades. The operative words here are “based on what we know so far” — meaning, both no more and no less than that, and also that our take on the situation might need to change as more data come in.
Remember, too, that even if only a small percentage of the people infected with COVID-19 die in the end, the death toll in absolute numbers could still be dreadful if the total population of infected turns out to be very large.
However much we would like to know all the relevant facts about the coronavirus, we don’t know them right now, and we should accept the discomfort of that uncertainty. Which is all the more reason to abide by one of the things we do know at this point: You should wash your hands regularly.
John Allen Paulos is a professor of mathematics at Temple University and the author of “A Mathematician Reads the Newspaper” and, most recently, “A Numerate Life.”
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